Eureka Math

Engage NY Eureka Math Kindergarten Module 5 Lesson 17 Answer Key

Eureka Math Kindergarten Module 5 Lesson 17 Problem Set Answer Key

Question 1.
Touch and count the dots from left to right starting at the arrow. Count to the puppy, and then keep counting to his bones and twin brother!

Answer:
I touched and counted the dots from left to right starting at the arrow.First i counted till puppy then i kept counting till his bones and later till his twin brother.

Question 2.
Count again and color the last dot of each row green. When you have finished, go back and see if you can remember your green numbers!
Answer:

Explanation:
I colored the last dots of each row green.When i finished i went back and saw i can remember my green numbers they are 10, 20, 30.

Question 3.
What number did you say when you touched the first puppy?
a. The first bone?
b. The second bone?
c. His twin brother?
Answer:
The number when i touched the first puppy is 15.
The first bone is at the number 21.
The second bone is at the number 28.
His twin brother is at the number 40.

Question 4.
Count each number by 1s. Write the number below when there is a box.

Answer:

Explanation:
I counted each number by 1s and wrote the numbers 18, 19, 20, and 22 below in the box.

Question 5.
Touch and count the rocks from the cow to the grass!

Answer:

Explanation:
I touched and counted the rocks by 1s from the cow to the grass the numbers are from 26 to 32.

Question 6.
Count up by 1s. Help the kitty play with her yarn!

Answer:

Explanation:
I helped the kitty play with her yarn by counting up by 1s from 31 to 40.

Question 7.
Count down by 1s.

Answer:

Explanation:
I counted down by 1s and wrote the numbers 9 , 20 and 30 in the empty boxes given above.

Eureka Math Kindergarten Module 5 Lesson 17 Exit Ticket Answer Key

Question 1.
Touch and count carefully. Cross out the mistake, and write the correct number.
Example:

Answer:

Explanation:
I touched and counted carefully, crossed out the mistake number 29, and wrote the correct number 26.

Answer:

Explanation:
I touched and counted carefully, crossed out the mistake number 43, and wrote the correct number 34.

Answer:

Explanation:
I touched and counted carefully, crossed out the mistake number 29, and wrote the correct number 30.

Answer:

Explanation:
I touched and counted carefully, crossed out the mistake number 40, and wrote the correct number 40.

Eureka Math Kindergarten Module 5 Lesson 17 Homework Answer Key

Question 1.
Draw more to show the number.
Example:

Answer:

Explanation:
I drew more dots to match with the given numbers 23, 27 and 34.

Answer:

Explanation:
I drew more stars and water drops to match with the given numbers 38 and 40.

Engage NY Eureka Math Kindergarten Module 5 Lesson 14 Answer Key

Eureka Math Kindergarten Module 5 Lesson 14 Problem Set Answer Key

Question 1.
Whisper count how many objects there are. Write the number.

Answer:

Explanation:
There are 14 objects in the above picture.So, i wrote the number 14.

Answer:

Explanation:
There are 12 objects in the above picture.So, i wrote the number 12.

Answer:

Explanation:
There are 15 objects in the above picture.So, i wrote the number 15.

Answer:

Explanation:
There are 18 objects in the above picture.So, i wrote the number 18.

Question 2.
Whisper count and draw in more shapes to match the number.

Answer:

Explanation:
I counted and drew more of the same shapes given above to match with the number 13.

Answer:

Explanation:
I counted and drew more of the same shapes given above to match with the number 20.

Question 3.
Early finishers: Write your own teen number in the box. Draw a picture to match your number.

Answer:

Explanation:
I wrote a teen number 13 in the box above and drew a picture to match your number 13.

Eureka Math Kindergarten Module 5 Lesson 14 Exit Ticket Answer Key

Question 1.
Count the stars. Write the number in the box.

Answer:

Explanation:
There are 12 stars in the above picture.So, i wrote the number 12.

Answer:

Explanation:
I counted and drew more of the same shapes given above to match with the number 15.

Eureka Math Kindergarten Module 5 Lesson 14 Homework Answer Key

Question 1.
Count the objects in each group. Write the number in the boxes below the pictures.

Answer:

Explanation:
There are 12 objects in the above picture.So, i wrote the number 12.

Answer:

Explanation:
There are 10 objects in the above picture.So, i wrote the number 10.

Question 2.
Count and draw in more shapes to match the number.

Answer:

Explanation:
I counted and drew more of the same shapes given above to match with the number 19.

Question 3.
Count the dots. Draw each dot in the 10-frame. Write the number in the box below the 10-frames.

Answer:

Explanation:
I counted the number of  dots.There are 18 dots.so, I drew 18 dots in the 10-frame and wrote the number 18 in the box below the 10-frames.

Question 4.
Write a teen number in the box below. Draw a picture to match your number.

Answer:

Explanation:
I wrote a teen number 14 in the box above and drew a picture to match your number 14.

Eureka Math Kindergarten Module 5 Lesson 14 Fluency Template Answer Key

Question 1.
Count the objects in each group and write the number.

Answer:

Explanation:
There are 15 objects in the above picture.So, i wrote the number 15.

Answer:

Explanation:
There are 12 objects in the above picture.So, i wrote the number 12.

Answer:

Explanation:
There are 14 objects in the above picture.So, i wrote the number 14.

Answer:

Explanation:
There are 15 objects in the above picture.So, i wrote the number 15.

Engage NY Eureka Math Kindergarten Module 5 Lesson 16 Answer Key

Eureka Math Kindergarten Module 5 Lesson 16 Problem Set Answer Key

Question 1.
Count up or down by 1s. Help the animals and the girl get what they want!

Answer:

Explanation:
I helped the animal to get what it want by counting up by 1 from 20 to 29.

 

Answer:

Explanation:
I helped the animal to get what it want by counting up by 1 from 40 to 48.

Answer:

Explanation:
I helped the girl to get what she want by counting up by 1 from 92 to 99.

Question 2.

Answer:

Explanation:
I filled the above picture by counting up and down by 1 from 63 to 67 and from 66 to 63.

Eureka Math Kindergarten Module 5 Lesson 16 Exit Ticket Answer Key

Question 1.
Help the cow get to the barn by counting by 1s.

Answer:

Explanation:
I helped the cow to get the barn by counting up by 1 from 50 to 28.

Question 2.
Help the boy get to his present. Count up by 1s. When you get to the top, count down by 1s.

Answer:

Explanation:
I helped the boy to get the present by counting up by 1 from 31 to 34 and then by counting down by 1 from 34 to 31.

Eureka Math Kindergarten Module 5 Lesson 16 Homework Answer Key

Question 1.
Help the rabbit get his carrot. Count by 1s.

Answer:

Explanation:
I helped the rabbit to get its carrot by counting up by 1 from 71 to 78.

Answer:

Explanation:
I helped the rabbit to get its carrot by counting up by 1 from 10 to 19.

Answer:

Explanation:
I filled the table by counting up and down by 1 from 84 to 89 and 89 to 84, and in the same way from 30 to 35 and 35 to 30.

Question 2.
Help the boy mail his letter. Count up by 1s. When you get to the top, count down by 1s.

Answer:

Explanation:
I helped the boy to mail his letter by counting up by 1 from 96 to 99 and by counting down by 1 from 99 to 96.

Engage NY Eureka Math 5th Grade Module 3 Lesson 12 Answer Key

Eureka Math Grade 5 Module 3 Lesson 12 Sprint Answer Key

A
Subtract Fractions with Unlike Units

Question 1.
\(\frac{2}{4}\) – \(\frac{1}{4}\) =
Answer:
\(\frac{2}{4}\) – \(\frac{1}{4}\) = \(\frac{1}{4}\)

Question 2.
\(\frac{1}{2}\) – \(\frac{1}{4}\) =
Answer:
\(\frac{1}{2}\) – \(\frac{1}{4}\) = \(\frac{1}{4}\)
Explanation :
\(\frac{1}{2}\) – \(\frac{1}{4}\) = \(\frac{2}{4}\) – \(\frac{1}{4}\) = \(\frac{1}{4}\)

Question 3.
\(\frac{2}{6}\) – \(\frac{1}{6}\) =
Answer:
\(\frac{2}{6}\) – \(\frac{1}{6}\) = \(\frac{1}{6}\)

Question 4.
\(\frac{1}{3}\) – \(\frac{1}{6}\) =
Answer:
\(\frac{1}{3}\) – \(\frac{1}{6}\) = \(\frac{1}{6}\)
Explanation :
\(\frac{1}{3}\) – \(\frac{1}{6}\) =\(\frac{2}{6}\) – \(\frac{1}{6}\) = \(\frac{1}{6}\)

Question 5.
\(\frac{2}{8}\) – \(\frac{1}{8}\) =
Answer:
\(\frac{2}{8}\) – \(\frac{1}{8}\) = \(\frac{1}{8}\)

Question 6.
\(\frac{1}{4}\) – \(\frac{1}{8}\) =
Answer:
\(\frac{1}{4}\) – \(\frac{1}{8}\) =\(\frac{1}{8}\)
Explanation :
\(\frac{1}{4}\) – \(\frac{1}{8}\) = \(\frac{2}{8}\) – \(\frac{1}{8}\) = \(\frac{1}{8}\)

Question 7.
\(\frac{6}{8}\) – \(\frac{1}{8}\) =
Answer:
\(\frac{6}{8}\) – \(\frac{1}{8}\) = \(\frac{5}{8}\)

Question 8.
\(\frac{3}{4}\) – \(\frac{1}{8}\) =
Answer:
\(\frac{3}{4}\) – \(\frac{1}{8}\) = \(\frac{5}{8}\)
Explanation :
\(\frac{3}{4}\) – \(\frac{1}{8}\) = \(\frac{6}{8}\) – \(\frac{1}{8}\) = \(\frac{5}{8}\)

Question 9.
\(\frac{3}{4}\) – \(\frac{3}{8}\) =
Answer:
\(\frac{3}{4}\) – \(\frac{3}{8}\) = \(\frac{3}{8}\)
Explanation :
\(\frac{3}{4}\) – \(\frac{3}{8}\) = \(\frac{6}{8}\) – \(\frac{3}{8}\) = \(\frac{3}{8}\)

Question 10.
\(\frac{5}{10}\) – \(\frac{2}{10}\) =
Answer:
\(\frac{5}{10}\) – \(\frac{2}{10}\) = \(\frac{3}{10}\)

Question 11.
\(\frac{1}{2}\) – \(\frac{2}{10}\) =
Answer:
\(\frac{1}{2}\) – \(\frac{2}{10}\) = \(\frac{3}{10}\)
Explanation :
\(\frac{1}{2}\) – \(\frac{2}{10}\) = \(\frac{5}{10}\) – \(\frac{2}{10}\) = \(\frac{3}{10}\)

Question 12.
\(\frac{1}{2}\) – \(\frac{2}{10}\) =
Answer:
\(\frac{1}{2}\) – \(\frac{2}{10}\) = \(\frac{3}{10}\)
Explanation :
\(\frac{1}{2}\) – \(\frac{2}{10}\) = \(\frac{5}{10}\) – \(\frac{2}{10}\) = \(\frac{3}{10}\)

Question 13.
\(\frac{4}{10}\) – \(\frac{1}{10}\) =
Answer:
\(\frac{4}{10}\) – \(\frac{1}{10}\) = \(\frac{3}{10}\)

Question 14.
\(\frac{2}{5}\) – \(\frac{1}{10}\) =
Answer:
\(\frac{2}{5}\) – \(\frac{1}{10}\) = \(\frac{3}{10}\)
Explanation :
\(\frac{2}{5}\) – \(\frac{1}{10}\) = \(\frac{4}{10}\) – \(\frac{1}{10}\) = \(\frac{3}{10}\)

Question 15.
\(\frac{2}{5}\) – \(\frac{3}{10}\) =
Answer:
\(\frac{2}{5}\) – \(\frac{3}{10}\) = \(\frac{1}{10}\)
Explanation :
\(\frac{2}{5}\) – \(\frac{3}{10}\) = \(\frac{4}{10}\) – \(\frac{3}{10}\) = \(\frac{1}{10}\)

Question 16.
\(\frac{6}{10}\) – \(\frac{3}{10}\) =
Answer:
\(\frac{6}{10}\) – \(\frac{3}{10}\) =\(\frac{3}{10}\)

Question 17.
\(\frac{3}{5}\) – \(\frac{3}{10}\) =
Answer:
\(\frac{3}{5}\) – \(\frac{3}{10}\) = \(\frac{3}{10}\)
Explanation :
\(\frac{3}{5}\) – \(\frac{3}{10}\) = \(\frac{6}{10}\) – \(\frac{3}{10}\) = \(\frac{3}{10}\)

Question 18.
\(\frac{3}{5}\) – \(\frac{5}{10}\) =
Answer:
\(\frac{3}{5}\) – \(\frac{5}{10}\) = \(\frac{1}{10}\)
Explanation :
\(\frac{3}{5}\) – \(\frac{5}{10}\) = \(\frac{6}{10}\) – \(\frac{5}{10}\) = \(\frac{1}{10}\)

Question 19.
\(\frac{8}{10}\) – \(\frac{1}{10}\) =
Answer:
\(\frac{8}{10}\) – \(\frac{1}{10}\) =  \(\frac{7}{10}\)

Question 20.
\(\frac{4}{5}\) – \(\frac{1}{10}\) =
Answer:
\(\frac{4}{5}\) – \(\frac{1}{10}\) = \(\frac{7}{10}\)
Explanation :
\(\frac{4}{5}\) – \(\frac{1}{10}\) = \(\frac{8}{10}\) – \(\frac{1}{10}\) =  \(\frac{7}{10}\)

Question 21.
\(\frac{4}{5}\) – \(\frac{5}{10}\) =
Answer:
\(\frac{4}{5}\) – \(\frac{5}{10}\) = \(\frac{3}{10}\)
Explanation :
\(\frac{4}{5}\) – \(\frac{5}{10}\) = \(\frac{8}{10}\) – \(\frac{5}{10}\) =  \(\frac{4}{10}\)

Question 22.
\(\frac{4}{5}\) – \(\frac{5}{10}\) =
Answer:
\(\frac{4}{5}\) – \(\frac{5}{10}\) = \(\frac{3}{10}\)
Explanation :
\(\frac{4}{5}\) – \(\frac{5}{10}\) = \(\frac{8}{10}\) – \(\frac{5}{10}\) =  \(\frac{4}{10}\)

Question 23.
\(\frac{4}{5}\) – \(\frac{7}{10}\) =
Answer:
\(\frac{4}{5}\) – \(\frac{7}{10}\) = \(\frac{1}{10}\)
Explanation :
\(\frac{4}{5}\) – \(\frac{7}{10}\) = \(\frac{8}{10}\) – \(\frac{7}{10}\) =  \(\frac{1}{10}\)

Question 24.
\(\frac{2}{12}\) – \(\frac{1}{12}\) =
Answer:
\(\frac{2}{12}\) – \(\frac{1}{12}\) = \(\frac{1}{12}\)

Question 25.
\(\frac{1}{6}\) – \(\frac{1}{12}\) =
Answer:
\(\frac{1}{6}\) – \(\frac{1}{12}\) =\(\frac{1}{12}\)
Explanation :
\(\frac{1}{6}\) – \(\frac{1}{12}\) = \(\frac{2}{12}\) – \(\frac{1}{12}\) = \(\frac{1}{12}\)

Question 26.
\(\frac{6}{12}\) – \(\frac{1}{12}\) =
Answer:
\(\frac{6}{12}\) – \(\frac{1}{12}\) = \(\frac{5}{12}\)

Question 27.
\(\frac{1}{2}\) – \(\frac{1}{12}\) =
Answer:
\(\frac{1}{2}\) – \(\frac{1}{12}\) =  \(\frac{5}{12}\)
Explanation :
\(\frac{1}{2}\) – \(\frac{1}{12}\) = \(\frac{6}{12}\) – \(\frac{1}{12}\) = \(\frac{5}{12}\)

Question 28.
\(\frac{1}{2}\) – \(\frac{5}{12}\) =
Answer:
\(\frac{1}{2}\) – \(\frac{5}{12}\) =  \(\frac{1}{12}\)
Explanation :
\(\frac{1}{2}\) – \(\frac{5}{12}\) = \(\frac{6}{12}\) – \(\frac{5}{12}\) = \(\frac{1}{12}\)

Question 29.
\(\frac{10}{12}\) – \(\frac{5}{12}\) =
Answer:
\(\frac{10}{12}\) – \(\frac{5}{12}\) = \(\frac{5}{12}\)

Question 30.
\(\frac{5}{6}\) – \(\frac{5}{12}\) =
Answer:
\(\frac{5}{6}\) – \(\frac{5}{12}\) = \(\frac{5}{12}\)
Explanation :
\(\frac{5}{6}\) – \(\frac{5}{12}\) = \(\frac{10}{12}\) – \(\frac{5}{12}\) = \(\frac{5}{12}\)

Question 31.
\(\frac{1}{3}\) – \(\frac{3}{12}\) =
Answer:
\(\frac{1}{3}\) – \(\frac{3}{12}\) = \(\frac{1}{12}\)
Explanation :
\(\frac{1}{3}\) – \(\frac{3}{12}\) = \(\frac{4}{12}\) – \(\frac{3}{12}\) = \(\frac{1}{12}\)

Question 32.
\(\frac{2}{3}\) – \(\frac{1}{12}\) =
Answer:
\(\frac{2}{3}\) – \(\frac{1}{12}\) = \(\frac{7}{12}\)
Explanation :
\(\frac{2}{3}\) – \(\frac{1}{12}\) = \(\frac{8}{12}\) – \(\frac{1}{12}\) = \(\frac{7}{12}\)

Question 33.
\(\frac{2}{3}\) – \(\frac{3}{12}\) =
Answer:
\(\frac{2}{3}\) – \(\frac{3}{12}\) = \(\frac{5}{12}\)
Explanation :
\(\frac{2}{3}\) – \(\frac{3}{12}\) = \(\frac{8}{12}\) – \(\frac{3}{12}\) = \(\frac{5}{12}\)

Question 34.
\(\frac{2}{3}\) – \(\frac{7}{12}\) =
Answer:
\(\frac{2}{3}\) – \(\frac{7}{12}\) = \(\frac{1}{12}\)
Explanation :
\(\frac{2}{3}\) – \(\frac{7}{12}\) = \(\frac{8}{12}\) – \(\frac{7}{12}\) = \(\frac{1}{12}\)

Question 35.
\(\frac{1}{4}\) – \(\frac{2}{12}\) =
Answer:
\(\frac{1}{4}\) – \(\frac{2}{12}\) =  \(\frac{1}{12}\)
Explanation :
\(\frac{1}{4}\) – \(\frac{2}{12}\) = \(\frac{3}{12}\) – \(\frac{2}{12}\) = \(\frac{1}{12}\)

Question 36.
\(\frac{1}{5}\) – \(\frac{1}{15}\) =
Answer:
\(\frac{1}{5}\) – \(\frac{1}{15}\) = \(\frac{2}{15}\)
Explanation :
\(\frac{1}{5}\) – \(\frac{1}{15}\) = \(\frac{3}{15}\) – \(\frac{1}{15}\) = \(\frac{2}{15}\)

Question 37.
\(\frac{1}{3}\) – \(\frac{1}{15}\) =
Answer:
\(\frac{1}{3}\) – \(\frac{1}{15}\) =  \(\frac{4}{15}\)
Explanation :
\(\frac{1}{3}\) – \(\frac{1}{15}\) = \(\frac{5}{15}\) – \(\frac{1}{15}\) = \(\frac{4}{15}\)

Question 38.
\(\frac{2}{3}\) – \(\frac{3}{15}\) =
Answer:
\(\frac{2}{3}\) – \(\frac{3}{15}\) =  \(\frac{7}{15}\)
Explanation :
\(\frac{2}{3}\) – \(\frac{3}{15}\) = \(\frac{10}{15}\) – \(\frac{3}{15}\) = \(\frac{7}{15}\)

Question 39.
\(\frac{2}{5}\) – \(\frac{4}{15}\) =
Answer:
\(\frac{2}{5}\) – \(\frac{4}{15}\) = \(\frac{2}{15}\)
Explanation :
\(\frac{2}{5}\) – \(\frac{4}{15}\) = \(\frac{6}{15}\) – \(\frac{4}{15}\) = \(\frac{2}{15}\)

Question 40.
\(\frac{3}{4}\) – \(\frac{2}{12}\) =
Answer:
\(\frac{3}{4}\) – \(\frac{2}{12}\) =  \(\frac{7}{12}\)
Explanation :
\(\frac{3}{4}\) – \(\frac{2}{12}\) = \(\frac{9}{12}\) – \(\frac{2}{12}\) = \(\frac{7}{12}\)

Question 41.
\(\frac{3}{4}\) – \(\frac{5}{16}\) =
Answer:
\(\frac{3}{4}\) – \(\frac{5}{16}\) = \(\frac{7}{16}\)
Explanation :
\(\frac{3}{4}\) – \(\frac{5}{16}\) = \(\frac{12}{16}\) – \(\frac{5}{16}\) = \(\frac{7}{16}\)

Question 42.
\(\frac{4}{5}\) – \(\frac{5}{15}\) =
Answer:
\(\frac{4}{5}\) – \(\frac{5}{15}\) = \(\frac{7}{15}\)
Explanation :
\(\frac{4}{5}\) – \(\frac{5}{15}\) = \(\frac{12}{15}\) – \(\frac{5}{15}\) = \(\frac{7}{15}\)

Question 43.
\(\frac{3}{4}\) – \(\frac{4}{12}\) =
Answer:
\(\frac{3}{4}\) – \(\frac{4}{12}\) =  \(\frac{5}{12}\)
Explanation :
\(\frac{3}{4}\) – \(\frac{4}{12}\) = \(\frac{9}{12}\) – \(\frac{4}{12}\) = \(\frac{5}{12}\)

Question 44.
\(\frac{3}{4}\) – \(\frac{7}{16}\) =
Answer:
\(\frac{3}{4}\) – \(\frac{7}{16}\) = \(\frac{5}{16}\)
Explanation :
\(\frac{3}{4}\) – \(\frac{5}{16}\) = \(\frac{12}{16}\) – \(\frac{7}{16}\) = \(\frac{5}{16}\)

B
Subtract Fractions with Unlike Units

Question 1.
\(\frac{2}{10}\) – \(\frac{1}{10}\) =
Answer:
\(\frac{2}{10}\) – \(\frac{1}{10}\) = \(\frac{1}{10}\)

Question 2.
\(\frac{1}{5}\) – \(\frac{1}{10}\) =
Answer:
\(\frac{1}{5}\) – \(\frac{1}{10}\) = \(\frac{1}{10}\)
Explanation :
\(\frac{1}{5}\) – \(\frac{1}{10}\) = \(\frac{2}{10}\) – \(\frac{1}{10}\) = \(\frac{1}{10}\)

Question 3.
\(\frac{2}{4}\) – \(\frac{1}{4}\) =
Answer:
\(\frac{2}{4}\) – \(\frac{1}{4}\) = \(\frac{1}{4}\)

Question 4.
\(\frac{1}{2}\) – \(\frac{1}{4}\) =
Answer:
\(\frac{1}{2}\) – \(\frac{1}{4}\) = \(\frac{1}{4}\)
Explanation :
\(\frac{1}{2}\) – \(\frac{1}{4}\) = \(\frac{2}{4}\) – \(\frac{1}{4}\) = \(\frac{1}{4}\)

Question 5.
\(\frac{5}{10}\) – \(\frac{2}{10}\) =
Answer:
\(\frac{5}{10}\) – \(\frac{2}{10}\) = \(\frac{3}{10}\)

Question 6.
\(\frac{1}{2}\) – \(\frac{2}{10}\) =
Answer:
\(\frac{1}{2}\) – \(\frac{2}{10}\) = \(\frac{3}{10}\)
Explanation :
\(\frac{1}{2}\) – \(\frac{2}{10}\) = \(\frac{5}{10}\) – \(\frac{2}{10}\) = \(\frac{3}{10}\)

Question 7.
\(\frac{1}{2}\) – \(\frac{4}{10}\) =
Answer:
\(\frac{1}{2}\) – \(\frac{4}{10}\) = \(\frac{1}{10}\)
Explanation :
\(\frac{1}{2}\) – \(\frac{4}{10}\) = \(\frac{5}{10}\) – \(\frac{4}{10}\) = \(\frac{1}{10}\)

Question 8.
\(\frac{4}{10}\) – \(\frac{1}{10}\) =
Answer:
\(\frac{4}{10}\) – \(\frac{1}{10}\) = \(\frac{3}{10}\)

Question 9.
\(\frac{2}{5}\) – \(\frac{1}{10}\) =
Answer:
\(\frac{2}{5}\) – \(\frac{1}{10}\) = \(\frac{3}{10}\)
Explanation :
\(\frac{2}{5}\) – \(\frac{1}{10}\) = \(\frac{4}{10}\) – \(\frac{1}{10}\) = \(\frac{3}{10}\)

Question 10.
\(\frac{2}{5}\) – \(\frac{3}{10}\) =
Answer:
\(\frac{2}{5}\) – \(\frac{3}{10}\) = \(\frac{1}{10}\)
Explanation :
\(\frac{2}{5}\) – \(\frac{3}{10}\) = \(\frac{4}{10}\) – \(\frac{3}{10}\) = \(\frac{1}{10}\)

Question 11.
\(\frac{6}{10}\) – \(\frac{3}{10}\) =
Answer:
\(\frac{6}{10}\) – \(\frac{3}{10}\) =\(\frac{3}{10}\)

Question 12.
\(\frac{3}{5}\) – \(\frac{3}{10}\) =
Answer:
\(\frac{3}{5}\) – \(\frac{3}{10}\) = \(\frac{3}{10}\)
Explanation :
\(\frac{3}{5}\) – \(\frac{3}{10}\) = \(\frac{6}{10}\) – \(\frac{3}{10}\) = \(\frac{3}{10}\)

Question 13.
\(\frac{3}{5}\) – \(\frac{5}{10}\) =
Answer:
\(\frac{3}{5}\) – \(\frac{5}{10}\) = \(\frac{1}{10}\)
Explanation :
\(\frac{3}{5}\) – \(\frac{5}{10}\) = \(\frac{6}{10}\) – \(\frac{5}{10}\) = \(\frac{1}{10}\)

Question 14.
\(\frac{8}{10}\) – \(\frac{1}{10}\) =
Answer:
\(\frac{8}{10}\) – \(\frac{1}{10}\) =  \(\frac{7}{10}\)

Question 15.
\(\frac{4}{5}\) – \(\frac{1}{10}\) =
Answer:
\(\frac{4}{5}\) – \(\frac{1}{10}\) = \(\frac{7}{10}\)
Explanation :
\(\frac{4}{5}\) – \(\frac{1}{10}\) = \(\frac{8}{10}\) – \(\frac{1}{10}\) =  \(\frac{7}{10}\)

Question 16.
\(\frac{4}{5}\) – \(\frac{5}{10}\) =
Answer:
\(\frac{4}{5}\) – \(\frac{5}{10}\) = \(\frac{3}{10}\)
Explanation :
\(\frac{4}{5}\) – \(\frac{5}{10}\) = \(\frac{8}{10}\) – \(\frac{5}{10}\) =  \(\frac{4}{10}\)

Question 17.
\(\frac{4}{5}\) – \(\frac{5}{10}\) =
Answer:
\(\frac{4}{5}\) – \(\frac{5}{10}\) = \(\frac{3}{10}\)
Explanation :
\(\frac{4}{5}\) – \(\frac{5}{10}\) = \(\frac{8}{10}\) – \(\frac{5}{10}\) =  \(\frac{4}{10}\)

Question 18.
\(\frac{4}{5}\) – \(\frac{7}{10}\) =
Answer:
\(\frac{4}{5}\) – \(\frac{7}{10}\) = \(\frac{1}{10}\)
Explanation :
\(\frac{4}{5}\) – \(\frac{7}{10}\) = \(\frac{8}{10}\) – \(\frac{7}{10}\) =  \(\frac{1}{10}\)

Question 19.
\(\frac{2}{8}\) – \(\frac{1}{8}\) =
Answer:
\(\frac{2}{8}\) – \(\frac{1}{8}\) = \(\frac{1}{8}\)

Question 20.
\(\frac{1}{4}\) – \(\frac{1}{8}\) =
Answer:
\(\frac{1}{4}\) – \(\frac{1}{8}\) =\(\frac{1}{8}\)
Explanation :
\(\frac{1}{4}\) – \(\frac{1}{8}\) = \(\frac{2}{8}\) – \(\frac{1}{8}\) = \(\frac{1}{8}\)

Question 21.
\(\frac{6}{8}\) – \(\frac{1}{8}\) =
Answer:
\(\frac{6}{8}\) – \(\frac{1}{8}\) = \(\frac{5}{8}\)

Question 22.
\(\frac{3}{4}\) – \(\frac{1}{8}\) =
Answer:
\(\frac{3}{4}\) – \(\frac{1}{8}\) = \(\frac{5}{8}\)
Explanation :
\(\frac{3}{4}\) – \(\frac{1}{8}\) = \(\frac{6}{8}\) – \(\frac{1}{8}\) = \(\frac{5}{8}\)

Question 23.
\(\frac{3}{4}\) – \(\frac{3}{8}\) =
Answer:
\(\frac{3}{4}\) – \(\frac{3}{8}\) = \(\frac{3}{8}\)
Explanation :
\(\frac{3}{4}\) – \(\frac{3}{8}\) = \(\frac{6}{8}\) – \(\frac{3}{8}\) = \(\frac{3}{8}\)

Question 24.
\(\frac{5}{15}\) – \(\frac{1}{15}\) =
Answer:
\(\frac{5}{15}\) – \(\frac{1}{15}\) = \(\frac{4}{15}\)

Question 25.
\(\frac{1}{3}\) – \(\frac{1}{15}\) =
Answer:
\(\frac{1}{3}\) – \(\frac{1}{15}\) =  \(\frac{4}{15}\)
Explanation :
\(\frac{1}{3}\) – \(\frac{1}{15}\) = \(\frac{5}{15}\) – \(\frac{1}{15}\) = \(\frac{4}{15}\)

Question 26.
\(\frac{3}{15}\) – \(\frac{1}{15}\) =
Answer:
\(\frac{3}{15}\) – \(\frac{1}{15}\) = \(\frac{2}{15}\)

Question 27.
\(\frac{1}{5}\) – \(\frac{1}{15}\) =
Answer:
\(\frac{1}{5}\) – \(\frac{1}{15}\) = \(\frac{2}{15}\)
Explanation :
\(\frac{1}{5}\) – \(\frac{1}{15}\) = \(\frac{3}{15}\) – \(\frac{1}{15}\) = \(\frac{2}{15}\)

Question 28.
\(\frac{1}{5}\) – \(\frac{2}{15}\) =
Answer:
\(\frac{1}{5}\) – \(\frac{2}{15}\) = \(\frac{1}{15}\)
Explanation :
\(\frac{1}{5}\) – \(\frac{2}{15}\) = \(\frac{3}{15}\) – \(\frac{2}{15}\) = \(\frac{1}{15}\)

Question 29.
\(\frac{12}{15}\) – \(\frac{4}{15}\) =
Answer:
\(\frac{12}{15}\) – \(\frac{4}{15}\) = \(\frac{8}{15}\)

Question 30.
\(\frac{4}{5}\) – \(\frac{4}{15}\) =
Answer:
\(\frac{4}{5}\) – \(\frac{2}{15}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{4}{5}\) – \(\frac{2}{15}\) = \(\frac{12}{15}\) – \(\frac{2}{15}\) = \(\frac{10}{15}\)= \(\frac{2}{3}\)

Question 31.
\(\frac{1}{4}\) – \(\frac{2}{12}\) =
Answer:
\(\frac{1}{4}\) – \(\frac{2}{12}\) =  \(\frac{1}{12}\)
Explanation :
\(\frac{1}{4}\) – \(\frac{2}{12}\) = \(\frac{3}{12}\) – \(\frac{2}{12}\) = \(\frac{1}{12}\)

Question 32.
\(\frac{3}{4}\) – \(\frac{2}{12}\) =
Answer:
\(\frac{3}{4}\) – \(\frac{2}{12}\) =  \(\frac{7}{12}\)
Explanation :
\(\frac{3}{4}\) – \(\frac{2}{12}\) = \(\frac{9}{12}\) – \(\frac{2}{12}\) = \(\frac{7}{12}\)

Question 33.
\(\frac{3}{4}\) – \(\frac{4}{12}\) =
Answer:
\(\frac{3}{4}\) – \(\frac{4}{12}\) =  \(\frac{5}{12}\)
Explanation :
\(\frac{3}{4}\) – \(\frac{4}{12}\) = \(\frac{9}{12}\) – \(\frac{4}{12}\) = \(\frac{5}{12}\)

Question 34.
\(\frac{3}{4}\) – \(\frac{8}{12}\) =
Answer:
\(\frac{3}{4}\) – \(\frac{8}{12}\) =  \(\frac{1}{12}\)
Explanation :
\(\frac{3}{4}\) – \(\frac{8}{12}\) = \(\frac{9}{12}\) – \(\frac{8}{12}\) = \(\frac{1}{12}\)

Question 35.
\(\frac{1}{3}\) – \(\frac{3}{12}\) =
Answer:
\(\frac{1}{3}\) – \(\frac{3}{12}\) = \(\frac{1}{12}\)
Explanation :
\(\frac{1}{3}\) – \(\frac{3}{12}\) = \(\frac{4}{12}\) – \(\frac{3}{12}\) = \(\frac{1}{12}\)

Question 36.
\(\frac{1}{6}\) – \(\frac{1}{12}\) =
Answer:
\(\frac{1}{6}\) – \(\frac{1}{12}\) =\(\frac{1}{12}\)
Explanation :
\(\frac{1}{6}\) – \(\frac{1}{12}\) = \(\frac{2}{12}\) – \(\frac{1}{12}\) = \(\frac{1}{12}\)

Question 37.
\(\frac{1}{3}\) – \(\frac{3}{15}\) =
Answer:
\(\frac{1}{3}\) – \(\frac{3}{15}\) =  \(\frac{2}{15}\)
Explanation :
\(\frac{1}{3}\) – \(\frac{3}{15}\) = \(\frac{5}{15}\) – \(\frac{3}{15}\) = \(\frac{2}{15}\)

Question 38.
\(\frac{2}{3}\) – \(\frac{2}{15}\) =
Answer:
\(\frac{2}{3}\) – \(\frac{2}{15}\) =  \(\frac{8}{15}\)
Explanation :
\(\frac{2}{3}\) – \(\frac{2}{15}\) = \(\frac{10}{15}\) – \(\frac{2}{15}\) = \(\frac{8}{15}\)

Question 39.
\(\frac{2}{5}\) – \(\frac{2}{15}\) =
Answer:
\(\frac{2}{5}\) – \(\frac{2}{15}\) = \(\frac{4}{15}\)
Explanation :
\(\frac{2}{5}\) – \(\frac{2}{15}\) = \(\frac{6}{15}\) – \(\frac{2}{15}\) = \(\frac{4}{15}\)

Question 40.
\(\frac{3}{4}\) – \(\frac{4}{12}\) =
Answer:
\(\frac{3}{4}\) – \(\frac{4}{12}\) =  \(\frac{5}{12}\)
Explanation :
\(\frac{3}{4}\) – \(\frac{4}{12}\) = \(\frac{9}{12}\) – \(\frac{4}{12}\) = \(\frac{5}{12}\)

Question 41.
\(\frac{3}{4}\) – \(\frac{7}{16}\) =
Answer:
\(\frac{3}{4}\) – \(\frac{7}{16}\) = \(\frac{5}{16}\)
Explanation :
\(\frac{3}{4}\) – \(\frac{5}{16}\) = \(\frac{12}{16}\) – \(\frac{7}{16}\) = \(\frac{5}{16}\)

Question 42.
\(\frac{4}{5}\) – \(\frac{4}{15}\) =
Answer:
\(\frac{4}{5}\) – \(\frac{4}{15}\) = \(\frac{8}{15}\)
Explanation :
\(\frac{4}{5}\) – \(\frac{4}{15}\) = \(\frac{12}{15}\) – \(\frac{4}{15}\) = \(\frac{8}{15}\)

Question 43.
\(\frac{3}{4}\) – \(\frac{2}{12}\) =
Answer:
\(\frac{3}{4}\) – \(\frac{2}{12}\) =  \(\frac{7}{12}\)
Explanation :
\(\frac{3}{4}\) – \(\frac{2}{12}\) = \(\frac{9}{12}\) – \(\frac{2}{12}\) = \(\frac{7}{12}\)

Question 44.
\(\frac{3}{4}\) – \(\frac{5}{16}\) =
Answer:
\(\frac{3}{4}\) – \(\frac{5}{16}\) = \(\frac{7}{16}\)
Explanation :
\(\frac{3}{4}\) – \(\frac{5}{16}\) = \(\frac{12}{16}\) – \(\frac{5}{16}\) = \(\frac{7}{16}\)

Eureka Math Grade 5 Module 3 Lesson 12 Problem Set Answer Key

Question 1.
Subtract.
a. 3\(\frac{1}{5}\) – 2\(\frac{1}{4}\) =
b. 4\(\frac{2}{5}\) – 3\(\frac{3}{4}\) =
c. 7\(\frac{1}{5}\) – 4\(\frac{1}{5}\) =
d. 7\(\frac{2}{5}\) – 5\(\frac{2}{3}\) =
e. 4\(\frac{2}{7}\) – 3\(\frac{1}{3}\) =
f. 9\(\frac{2}{3}\) – 2\(\frac{6}{7}\) =
g. 17\(\frac{2}{3}\) – 5\(\frac{5}{6}\) =
h. 18\(\frac{1}{3}\) – 3\(\frac{3}{8}\) =
Answer:
a. 3\(\frac{1}{5}\) – 2\(\frac{1}{4}\) = \(\frac{19}{20}\)
Explanation :
3\(\frac{1}{5}\) – 2\(\frac{1}{4}\) = \(\frac{16}{5}\) – \(\frac{9}{4}\)
lcm of 5 and 4 is 20 .
\(\frac{64}{20}\) – \(\frac{45}{20}\) = \(\frac{19}{20}\)

b. 4\(\frac{2}{5}\) – 3\(\frac{3}{4}\) = \(\frac{13}{20}\)
Explanation :
4\(\frac{2}{5}\) – 3\(\frac{3}{4}\) = \(\frac{22}{5}\) – \(\frac{15}{4}\)
lcm of 5 and 4 is 20 .
\(\frac{88}{20}\) – \(\frac{75}{20}\) = \(\frac{13}{20}\)

c. 7\(\frac{1}{5}\) – 4\(\frac{1}{5}\) =
Explanation :
7\(\frac{1}{5}\) – 4\(\frac{1}{5}\) = \(\frac{36}{5}\) – \(\frac{21}{5}\) = \(\frac{15}{5}\) = 3 .

d. 7\(\frac{2}{5}\) – 5\(\frac{2}{3}\) = 1\(\frac{11}{15}\) .
Explanation :
7\(\frac{2}{5}\) – 5\(\frac{2}{3}\) = \(\frac{37}{5}\) – \(\frac{17}{3}\)
lcm of 5 and 3 is 15 .
\(\frac{111}{15}\) – \(\frac{85}{15}\) = \(\frac{26}{15}\) = 1\(\frac{11}{15}\) .

e. 4\(\frac{2}{7}\) – 3\(\frac{1}{3}\) = \(\frac{20}{21}\)
Explanation :
4\(\frac{2}{7}\) – 3\(\frac{1}{3}\) = \(\frac{30}{7}\) – \(\frac{10}{3}\)
lcm of 7 and 3 is 21.
\(\frac{90}{21}\) – \(\frac{70}{21}\) = \(\frac{20}{21}\)

f. 9\(\frac{2}{3}\) – 2\(\frac{6}{7}\) = 6\(\frac{17}{21}\)
Explanation :
9\(\frac{2}{3}\) – 2\(\frac{6}{7}\) = \(\frac{29}{3}\) – \(\frac{20}{7}\)
lcm of 3 and 7 is 21.
\(\frac{203}{21}\) – \(\frac{60}{21}\) = \(\frac{143}{21}\) = 6\(\frac{17}{21}\)

g. 17\(\frac{2}{3}\) – 5\(\frac{5}{6}\) = 11\(\frac{5}{6}\)
Explanation :
17\(\frac{2}{3}\) – 5\(\frac{5}{6}\) = \(\frac{53}{3}\) – \(\frac{35}{6}\)
lcm of 3 and 6 is 6 .
\(\frac{106}{6}\) – \(\frac{35}{6}\) = \(\frac{71}{6}\) = 11\(\frac{5}{6}\)

h. 18\(\frac{1}{3}\) – 3\(\frac{3}{8}\) = 14\(\frac{23}{24}\)
Explanation :
18\(\frac{1}{3}\) – 3\(\frac{3}{8}\) = \(\frac{55}{3}\) – \(\frac{27}{8}\)
lcm of 3 and 8 is 24 .
\(\frac{440}{24}\) – \(\frac{81}{24}\) = \(\frac{359}{24}\) = 14\(\frac{23}{24}\)

Question 2.
Toby wrote the following:
7\(\frac{1}{4}\) – 3\(\frac{3}{4}\) = 4\(\frac{2}{4}\) = 4\(\frac{1}{2}\)
Is Toby’s calculation correct? Draw a number line to support your answer.
Answer:
Tody’s calculation is wrong .
7\(\frac{1}{4}\) – 3\(\frac{3}{4}\) = 3\(\frac{1}{2}\) .
Explanation :
7\(\frac{1}{4}\) – 3\(\frac{3}{4}\) = \(\frac{29}{4}\) – \(\frac{15}{4}\) = \(\frac{14}{4}\) = \(\frac{7}{2}\) = 3\(\frac{1}{2}\) .

Question 3.
Mr. Neville Iceguy mixed up 12\(\frac{3}{5}\) gallons of chili for a party. If 7\(\frac{3}{4}\)gallons of chili was mild, and the rest was extra spicy, how much extra spicy chili did Mr. Iceguy make?
Answer:
Fraction of chili mixed up for a party = 12\(\frac{3}{5}\) gallons = \(\frac{63}{5}\) gallons
Fraction of chilli is mild = 7\(\frac{3}{4}\)gallons = \(\frac{31}{4}\)gallons
Fraction of chilli is extra spicy = x
\(\frac{63}{5}\) =  \(\frac{31}{4}\) + x
x = \(\frac{63}{5}\) – \(\frac{31}{4}\)
lcm of 5 and 4 is 20 .
x = \(\frac{252}{20}\) – \(\frac{155}{20}\) = \(\frac{97}{20}\) = 4\(\frac{17}{20}\)
Therefore, Fraction of chilli is extra spicy = x = 4\(\frac{17}{20}\) gallons .

Question 4.
Jazmyne decided to spend 6\(\frac{1}{2}\) hours studying over the weekend. She spent 1\(\frac{1}{4}\) hours studying on Friday evening and 2\(\frac{2}{3}\) hours on Saturday. How much longer does she need to spend studying on Sunday in order to reach her goal?
Answer:
Total Fraction of time should spend on Studying = 6\(\frac{1}{2}\) hours = \(\frac{13}{2}\) hours
Fraction of Time spent on Friday for studying = 1\(\frac{1}{4}\) hours = \(\frac{5}{4}\) hours
Fraction of Time spent on Saturday for studying = 2\(\frac{2}{3}\) hours = \(\frac{8}{3}\) hours
Fraction of Time should spend on Sunday for studying = x
\(\frac{13}{2}\) = \(\frac{5}{4}\) + \(\frac{8}{3}\) + x
lcm of 2 , 4 , and 3 is 12 .
x = \(\frac{13}{2}\) – \(\frac{5}{4}\) – \(\frac{8}{3}\)
x = \(\frac{78}{12}\) – \(\frac{15}{12}\) – \(\frac{32}{12}\)
x = \(\frac{78}{12}\) – \(\frac{47}{12}\)
x = \(\frac{31}{12}\)
x = 2\(\frac{7}{12}\)
Therefore, Fraction of Time should spend on Sunday for studying = x = 2\(\frac{7}{12}\) hours .

Eureka Math Grade 5 Module 3 Lesson 12 Exit Ticket Answer Key

Subtract.
Question 1.
5\(\frac{1}{2}\) – 1\(\frac{1}{3}\) =
Answer:
5\(\frac{1}{2}\) – 1\(\frac{1}{3}\) = 4\(\frac{1}{6}\) .
Explanation :
5\(\frac{1}{2}\) – 1\(\frac{1}{3}\) = \(\frac{11}{2}\) – \(\frac{4}{3}\)
lcm of 2 and 3 is 6
\(\frac{33}{6}\) – \(\frac{8}{6}\) = \(\frac{25}{6}\) = 4\(\frac{1}{6}\) .

Question 2.
8\(\frac{3}{4}\) – 5\(\frac{5}{6}\) =
Answer:
8\(\frac{3}{4}\) – 5\(\frac{5}{6}\) = 2\(\frac{11}{12}\)
Explanation :
8\(\frac{3}{4}\) – 5\(\frac{5}{6}\) = \(\frac{35}{4}\) – \(\frac{35}{6}\)
lcm of 4 and 6 is 12 .
\(\frac{105}{12}\) – \(\frac{70}{12}\) = \(\frac{35}{12}\) = 2\(\frac{11}{12}\)

Eureka Math Grade 5 Module 3 Lesson 12 Homework Answer Key

Question 1.
Subtract.
a. 3\(\frac{1}{4}\) – 2\(\frac{1}{3}\) =
b. 3\(\frac{2}{3}\) – 2\(\frac{3}{4}\) =
c. 6\(\frac{1}{5}\) – 4\(\frac{1}{4}\) =
d. 6\(\frac{3}{5}\) – 4\(\frac{3}{4}\) =
e. 5\(\frac{2}{7}\) – 4\(\frac{1}{3}\) =
f. 8\(\frac{2}{3}\) – 3\(\frac{5}{7}\) =
g. 18\(\frac{3}{4}\) – 5\(\frac{7}{8}\) =
h. 17\(\frac{1}{5}\) – 2\(\frac{5}{8}\) =
Answer:
a. 3\(\frac{1}{4}\) – 2\(\frac{1}{3}\) = \(\frac{11}{12}\)
Explanation :
3\(\frac{1}{4}\) – 2\(\frac{1}{3}\) = \(\frac{13}{4}\) – \(\frac{7}{3}\)
lcm of 4 and 3 is 12
\(\frac{39}{12}\) – \(\frac{28}{12}\) = \(\frac{11}{12}\)

b. 3\(\frac{2}{3}\) – 2\(\frac{3}{4}\) = \(\frac{11}{12}\)
Explanation :
3\(\frac{2}{3}\) – 2\(\frac{3}{4}\) = \(\frac{11}{3}\) – \(\frac{11}{4}\)
lcm of 3 and 4 is 12
\(\frac{44}{12}\) – \(\frac{33}{12}\) = \(\frac{11}{12}\)

c. 6\(\frac{1}{5}\) – 4\(\frac{1}{4}\) = 3\(\frac{13}{20}\)
Explanation :
6\(\frac{1}{5}\) – 4\(\frac{1}{4}\) = \(\frac{31}{5}\) – \(\frac{17}{4}\)
lcm of 4 and 5 is 20 .
\(\frac{124}{20}\) – \(\frac{51}{20}\) = \(\frac{73}{20}\) = 3\(\frac{13}{20}\) .

d. 6\(\frac{3}{5}\) – 4\(\frac{3}{4}\) = 1\(\frac{17}{20}\)
Explanation :
6\(\frac{3}{5}\) – 4\(\frac{3}{4}\) = \(\frac{33}{5}\) – \(\frac{19}{4}\)
lcm of 4 and 5 is 20 .
\(\frac{132}{20}\) – \(\frac{95}{20}\) = \(\frac{37}{20}\) = 1\(\frac{17}{20}\)

e. 5\(\frac{2}{7}\) – 4\(\frac{1}{3}\) = \(\frac{20}{21}\)
Explanation :
5\(\frac{2}{7}\) – 4\(\frac{1}{3}\) = \(\frac{37}{7}\) – \(\frac{13}{3}\)
lcm of 3 and 7 is 21.
\(\frac{111}{21}\) – \(\frac{91}{21}\) = \(\frac{20}{21}\)

f. 8\(\frac{2}{3}\) – 3\(\frac{5}{7}\) = 4\(\frac{20}{21}\)
Explanation :
8\(\frac{2}{3}\) – 3\(\frac{5}{7}\) = \(\frac{26}{3}\) – \(\frac{26}{7}\)
lcm of 3 and 7 is 21.
\(\frac{182}{21}\) – \(\frac{78}{21}\) = \(\frac{104}{21}\) = 4\(\frac{20}{21}\)

g. 18\(\frac{3}{4}\) – 5\(\frac{7}{8}\) = 11\(\frac{9}{8}\)
Explanation :
18\(\frac{3}{4}\) – 5\(\frac{7}{8}\) = \(\frac{75}{4}\) – \(\frac{47}{8}\)
lcm of 4 and 8 is 8 .
\(\frac{130}{8}\) – \(\frac{47}{8}\) = \(\frac{97}{8}\) = 11\(\frac{9}{8}\)

h. 17\(\frac{1}{5}\) – 2\(\frac{5}{8}\) = 14\(\frac{23}{40}\)
Explanation :
17\(\frac{1}{5}\) – 2\(\frac{5}{8}\) = \(\frac{86}{5}\) – \(\frac{21}{8}\)
lcm of 5 and 8 is 40 .
\(\frac{688}{40}\) – \(\frac{105}{40}\) = \(\frac{583}{40}\) = 14\(\frac{23}{40}\)

Question 2.
Tony wrote the following:
7\(\frac{1}{4}\) – 3\(\frac{3}{4}\) = 4\(\frac{1}{4}\) – \(\frac{3}{4}\)
Is Tony’s statement correct? Draw a number line to support your answer.
Answer:
Yes Tony’s statement is correct .
7\(\frac{1}{4}\) – 3\(\frac{3}{4}\) = 4\(\frac{1}{4}\) – \(\frac{3}{4}\) = 3\(\frac{1}{2}\) .
Explanation :
7\(\frac{1}{4}\) – 3\(\frac{3}{4}\) = \(\frac{29}{4}\) – \(\frac{15}{4}\) = \(\frac{14}{4}\) = \(\frac{7}{2}\) = 3\(\frac{1}{2}\) .
4\(\frac{1}{4}\) – \(\frac{3}{4}\) = \(\frac{17}{4}\) – \(\frac{3}{4}\) = \(\frac{14}{4}\) = \(\frac{7}{2}\) = 3\(\frac{1}{2}\) .
Therefore , 7\(\frac{1}{4}\) – 3\(\frac{3}{4}\) = 4\(\frac{1}{4}\) – \(\frac{3}{4}\) = 3\(\frac{1}{2}\) .

Question 3.
Ms. Sanger blended 8\(\frac{3}{4}\) gallons of iced tea with some lemonade for a picnic. If there were 13\(\frac{2}{5}\) gallons of the beverage, how many gallons of lemonade did she use?
Answer:
Fraction of gallons of iced tea with some lemonade for a picnic = 8\(\frac{3}{4}\) = \(\frac{35}{4}\) gallons .
Fraction of gallons of the beverage = 13\(\frac{2}{5}\) = \(\frac{67}{5}\) .
Fraction of gallons of the lemonade = x
\(\frac{67}{5}\) = \(\frac{35}{4}\) – x
x =  \(\frac{67}{5}\) – \(\frac{35}{4}\)
lcm of 4 and 5 is 20 .
x = \(\frac{268}{20}\) – \(\frac{175}{20}\)
x = \(\frac{93}{20}\) = 4\(\frac{13}{20}\)
Therefore, Fraction of gallons of the lemonade = x = 4\(\frac{13}{20}\) gallons .

Question 4.
A carpenter has 10\(\frac{1}{2}\) feet of wooden plank. He cuts off 4\(\frac{1}{4}\) feet to replace the slat of a deck and 3\(\frac{2}{3}\) feet to repair a bannister. He uses the rest of the plank to fix a stair. How many feet of wood does the carpenter use to fix the stair?
Answer:
Total Fraction of wooden plank = 10\(\frac{1}{2}\) feet = \(\frac{21}{2}\) feet
Fraction of wooden plank cut off = 4\(\frac{1}{4}\) feet = \(\frac{17}{4}\) feet
Fraction of wooden plank used to repair a bannister = 3\(\frac{2}{3}\) feet = \(\frac{11}{3}\) feet
Fraction of wooden plank used for stair = x feet
10\(\frac{1}{2}\) = \(\frac{17}{4}\) + \(\frac{11}{3}\) + x
\(\frac{21}{2}\) = \(\frac{17}{4}\) + \(\frac{11}{3}\) + x
lcm of 2 , 4 and 3 is 12 .
\(\frac{126}{12}\) = \(\frac{51}{4}\) + \(\frac{44}{3}\) + x
x = \(\frac{126}{12}\) – \(\frac{95}{4}\)
x = \(\frac{31}{4}\) = 7\(\frac{3}{4}\) .
Therefore, Fraction of wooden plank used for stair = 7\(\frac{3}{4}\) feet .

Engage NY Eureka Math 5th Grade Module 3 Lesson 11 Answer Key

Eureka Math Grade 5 Module 3 Lesson 11 Problem Set Answer Key

Question 1.
Generate equivalent fractions to get like units. Then, subtract.
a. \(\frac{1}{2}\) – \(\frac{1}{3}\) =
b. \(\frac{7}{10}\) – \(\frac{1}{3}\) =
c. \(\frac{7}{8}\) – \(\frac{3}{4}\) =
d. 1\(\frac{2}{5}\) – \(\frac{3}{8}\) =
e. 1\(\frac{3}{10}\) – \(\frac{1}{6}\) =
f. 2\(\frac{1}{3}\) – 1\(\frac{1}{5}\) =
g. 5\(\frac{6}{7}\) – 2\(\frac{2}{3}\) =
h. Draw a number line to show that your answer to (g) is reasonable.
Answer:
a. \(\frac{1}{2}\) – \(\frac{1}{3}\) = \(\frac{1}{6}\)
Explanation :
\(\frac{1}{2}\) – \(\frac{1}{3}\)
lcm of 2 and 3 is 6
\(\frac{3}{6}\) – \(\frac{2}{6}\) = \(\frac{1}{6}\)

b. \(\frac{7}{10}\) – \(\frac{1}{3}\) = \(\frac{11}{30}\)
Explanation :
\(\frac{7}{10}\) – \(\frac{1}{3}\)
lcm of 10 and 3 is 30 .
\(\frac{21}{30}\) – \(\frac{10}{30}\) = \(\frac{11}{30}\)

c. \(\frac{7}{8}\) – \(\frac{3}{4}\) = \(\frac{1}{8 }\)
Explanation :
\(\frac{7}{8}\) – \(\frac{3}{4}\)
lcm of 8 and 4 is 8 .
\(\frac{7}{8}\) – \(\frac{6}{8 }\) = \(\frac{1}{8 }\)

d. 1\(\frac{2}{5}\) – \(\frac{3}{8}\) = 1\(\frac{31}{40}\)
Explanation :
1\(\frac{2}{5}\) – \(\frac{3}{8}\) = \(\frac{7}{5}\) – \(\frac{3}{8}\)
lcm of 5 and 8 is 40 .
\(\frac{56}{40}\) – \(\frac{15}{40}\) = \(\frac{71}{40}\) = 1\(\frac{31}{40}\)

e. 1\(\frac{3}{10}\) – \(\frac{1}{6}\) = 1\(\frac{4}{30}\)
Explanation :
1\(\frac{3}{10}\) – \(\frac{1}{6}\) = \(\frac{13}{10}\) – \(\frac{1}{6}\)
lcm of 6 and 10 is 30.
\(\frac{39}{30}\) – \(\frac{5}{30}\) = \(\frac{34}{30}\) = 1\(\frac{4}{30}\)

f. 2\(\frac{1}{3}\) – 1\(\frac{1}{5}\) =1\(\frac{2}{15}\)
Explanation :
2\(\frac{1}{3}\) – 1\(\frac{1}{5}\) = \(\frac{7}{3}\) – \(\frac{6}{5}\)
lcm of 3 and 5 is 15 .
\(\frac{35}{15}\) – \(\frac{18}{15}\) = \(\frac{17}{15}\) = 1\(\frac{2}{15}\)

g. 5\(\frac{6}{7}\) – 2\(\frac{2}{3}\) = 3\(\frac{4}{21}\) .
Explanation :
5\(\frac{6}{7}\) – 2\(\frac{2}{3}\) = \(\frac{41}{7}\) – \(\frac{8}{3}\)
lcm of 7 and 3 is 21 .
\(\frac{123}{21}\) – \(\frac{56}{21}\) = \(\frac{67}{21}\) = 3\(\frac{4}{21}\) .

Question 2.
George says that, to subtract fractions with different denominators, you always have to multiply the denominators to find the common unit; for example:
\(\frac{3}{8}-\frac{1}{6}=\frac{18}{48}-\frac{8}{48}\)
Show George how he could have chosen a denominator smaller than 48, and solve the problem.
Answer:
\(\frac{3}{8}\) – \(\frac{1}{6}\) = \(\frac{3}{8}\) – \(\frac{1}{6}\)
lcm of 8 and 6 is 24 .
[late3x]\frac{9}{24}[/latex] – \(\frac{4}{24}\) = \(\frac{5}{24}\)
Multiplies of 8 and 6 are .
8 : 16, 24, 32, 40, 48 .
6 : 12, 18, 24, 30, 36, 48.
common multiple smaller than 48 is 24 .

Question 3.
Meiling has 1\(\frac{1}{4}\) liter of orange juice. She drinks \(\frac{1}{3}\) liter. How much orange juice does she have left? (Extension: If her brother then drinks twice as much as Meiling, how much is left?)
Answer:
Fraction of Quantity of Juice with Meiling = 1\(\frac{1}{4}\) = \(\frac{5}{4}\)
Fraction of Quantity of Juice drank by Meiling = \(\frac{1}{3}\)
Fraction of Quantity of Juice left = \(\frac{5}{4}\) – \(\frac{1}{3}\) = \(\frac{15}{12}\) – \(\frac{4}{12}\) = \(\frac{11}{12}\) .
Therefore , Fraction of Quantity of Juice left = \(\frac{11}{12}\) .

Question 4.
Harlan used 3\(\frac{1}{2}\) kg of sand to make a large hourglass. To make a smaller hourglass, he only used 1\(\frac{3}{7}\) kg of sand. How much more sand did it take to make the large hourglass than the smaller one?
Answer:
Fraction of Quantity of sand used for large hourglass = 3\(\frac{1}{2}\) kg = \(\frac{7}{2}\) kg
Fraction of Quantity of sand used for small hourglass = \(\frac{10}{7}\) kg
Fraction of Quantity of sand to make the large hourglass than the smaller one = \(\frac{7}{2}\) – \(\frac{10}{7}\) = \(\frac{49}{14}\) – \(\frac{20}{14}\) = \(\frac{29}{14}\) = 2\(\frac{1}{14}\) .
Therefore, Fraction of Quantity of sand to make the large hourglass than the smaller one = 2\(\frac{1}{14}\) .

Eureka Math Grade 5 Module 3 Lesson 11 Exit Ticket Answer Key

Generate equivalent fractions to get like units. Then, subtract.
a. \(\frac{3}{4}\) – \(\frac{3}{10}\) =
b. 3\(\frac{1}{2}\) – 1\(\frac{1}{3}\) =
Answer:
a. \(\frac{3}{4}\) – \(\frac{3}{10}\) = \(\frac{9}{20}\)
Explanation :
\(\frac{3}{4}\) – \(\frac{3}{10}\)
lcm of 4 and 10 are 20 .
\(\frac{15}{20}\) – \(\frac{6}{20}\) = \(\frac{9}{20}\)

b. 3\(\frac{1}{2}\) – 1\(\frac{1}{3}\) = 2\(\frac{1}{6}\)
Explanation :
3\(\frac{1}{2}\) – 1\(\frac{1}{3}\) = \(\frac{7}{2}\) – \(\frac{4}{3}\)
lcm of 2 and 3 is 6
\(\frac{21}{6}\) – \(\frac{8}{6}\) = \(\frac{13}{6}\) = 2\(\frac{1}{6}\)

Eureka Math Grade 5 Module 3 Lesson 11 Homework Answer Key

Question 1.
Generate equivalent fractions to get like units. Then, subtract.
a. \(\frac{1}{2}\) – \(\frac{1}{5}\) =
b. \(\frac{7}{8}\) – \(\frac{1}{3}\) =
c. \(\frac{7}{10}\) – \(\frac{3}{5}\) =
d. 1\(\frac{5}{6}\) – \(\frac{2}{3}\) =
e. 2\(\frac{1}{4}\) – 1\(\frac{1}{5}\) =
f. 5\(\frac{6}{7}\) – 3\(\frac{2}{3}\) =
g. 15\(\frac{7}{8}\) – 5\(\frac{3}{4}\) =
h. 15\(\frac{5}{8}\) – 3\(\frac{1}{3}\) =
Answer:
a. \(\frac{1}{2}\) – \(\frac{1}{5}\) = \(\frac{3}{10}\)
Explanation :
\(\frac{1}{2}\) – \(\frac{1}{5}\)
lcm of 2 and 5 is 10 .
\(\frac{5}{10}\) – \(\frac{2}{10}\) = \(\frac{3}{10}\)

b. \(\frac{7}{8}\) – \(\frac{1}{3}\) = \(\frac{13}{24}\)
Explanation :
\(\frac{7}{8}\) – \(\frac{1}{3}\)
lcm of 8 and 3 is 24 .
\(\frac{21}{24}\) – \(\frac{8}{24}\) = \(\frac{13}{24}\)

c. \(\frac{7}{10}\) – \(\frac{3}{5}\) = \(\frac{1}{10}\)
Explanation :
\(\frac{7}{10}\) – \(\frac{3}{5}\)
lcm of 10 and 5 is 10 .
\(\frac{7}{10}\) – \(\frac{6}{10}\) =  \(\frac{1}{10}\)

d. 1\(\frac{5}{6}\) – \(\frac{2}{3}\) = \(\frac{1}{2}\)
Explanation :
1\(\frac{5}{6}\) – \(\frac{2}{3}\) = \(\frac{11}{6}\) – \(\frac{2}{3}\)
lcm of 6 and 3 is 6
\(\frac{11}{6}\) – \(\frac{4}{6}\) = \(\frac{3}{6}\) = \(\frac{1}{2}\)

e. 2\(\frac{1}{4}\) – 1\(\frac{1}{5}\) = 1\(\frac{1}{20}\)
Explanation :
2\(\frac{1}{4}\) – 1\(\frac{1}{5}\) = \(\frac{9}{4}\) – \(\frac{6}{5}\)
lcm of 4 and 5 is 20 .
\(\frac{45}{20}\) – \(\frac{24}{20}\) = \(\frac{21}{20}\) = 1\(\frac{1}{20}\)

f. 5\(\frac{6}{7}\) – 3\(\frac{2}{3}\) = 2 \(\frac{4}{21}\)
Explanation :
5\(\frac{6}{7}\) – 3\(\frac{2}{3}\) = \(\frac{41}{7}\) – \(\frac{11}{3}\)
lcm of 7 and 3 is 21
\(\frac{123}{21}\) – \(\frac{77}{21}\) = \(\frac{46}{21}\) = 2 \(\frac{4}{21}\)

g. 15\(\frac{7}{8}\) – 5\(\frac{3}{4}\) = 10\(\frac{1}{8}\)
Explanation :
15\(\frac{7}{8}\) – 5\(\frac{3}{4}\) = \(\frac{127}{8}\) – \(\frac{23}{4}\)
lcm of 8 and 4 is 8 .
\(\frac{127}{8}\) – \(\frac{46}{8}\) = \(\frac{81}{8}\) = 10\(\frac{1}{8}\) .

h. 15\(\frac{5}{8}\) – 3\(\frac{1}{3}\) = 12 \(\frac{7}{24}\)
Explanation :
15\(\frac{5}{8}\) – 3\(\frac{1}{3}\) = \(\frac{125}{8}\) – \(\frac{10}{3}\)
lcm of 3 and 8 is 24 .
\(\frac{375}{24}\) – \(\frac{80}{24}\) = \(\frac{295}{24}\) =12 \(\frac{7}{24}\)

Question 2.
Sandy ate \(\frac{1}{6}\) of a candy bar. John ate \(\frac{3}{4}\) of it. How much more of the candy bar did John eat than Sandy?
Answer:
Fraction of candy ate by sandy = \(\frac{1}{6}\)
Fraction of candy ate by John = \(\frac{3}{4}\)
Fraction of the candy bar ate more by John eat than Sandy = \(\frac{3}{4}\) – \(\frac{1}{6}\) = \(\frac{9}{12}\) – \(\frac{2}{12}\) = \(\frac{7}{12}\)
Therefore, Fraction of the candy bar ate more by John eat than Sandy = \(\frac{7}{12}\) .

Question 3.
4\(\frac{1}{2}\) yards of cloth are needed to make a woman’s dress. 2\(\frac{2}{7}\) yards of cloth are needed to make a girl’s dress. How much more cloth is needed to make a woman’s dress than a girl’s dress?
Answer:
Fraction of cloth needed to make women’s dress = 4\(\frac{1}{2}\) yards = \(\frac{9}{2}\) yards
Fraction of cloth needed to make girl’s dress = 2\(\frac{2}{7}\) yards = \(\frac{16}{7}\) yards
Fraction of more cloth needed to make a woman’s dress than a girl’s dress = \(\frac{9}{2}\) – \(\frac{16}{7}\)
= \(\frac{63}{14}\) – \(\frac{32}{14}\) = \(\frac{31}{14}\) = 2\(\frac{3}{14}\) yards .
Therefore, Fraction of more cloth needed to make a woman’s dress than a girl’s dress = 2\(\frac{3}{14}\) yards

Question 4.
Bill reads \(\frac{1}{5}\) of a book on Monday. He reads \(\frac{2}{3}\) of the book on Tuesday. If he finishes reading the book on Wednesday, what fraction of the book did he read on Wednesday?
Answer:
Fraction of book read on Monday =\(\frac{1}{5}\)
Fraction of book read on Tuesday = \(\frac{2}{3}\)
Fraction of book read on both days = \(\frac{1}{5}\) + \(\frac{2}{3}\) = \(\frac{3}{15}\) + \(\frac{10}{15}\) = \(\frac{13}{15}\) .
Therefore, Fraction of book read on both days = \(\frac{13}{15}\)

Question 5.
Tank A has a capacity of 9.5 gallons. 6\(\frac{1}{3}\) gallons of the tank’s water are poured out. How many gallons of water are left in the tank?
Answer:
Fraction of Capacity of Tank A = 9.5 gallons
Fraction of Capacity of water poured out = 6\(\frac{1}{3}\) gallons = \(\frac{19}{3}\) gallons .
Fraction of Capacity of water left = 9.5 – \(\frac{19}{3}\) = \(\frac{95}{10}\) – \(\frac{19}{3}\) = \(\frac{285}{30}\) – \(\frac{190}{30}\) = \(\frac{95}{30}\) = \(\frac{19}{6}\) = 3\(\frac{1}{6}\)
Therefore, Fraction of Capacity of water left = 3\(\frac{1}{6}\) .

Engage NY Eureka Math 5th Grade Module 3 Lesson 10 Answer Key

Eureka Math Grade 5 Module 3 Lesson 10 Sprint Answer Key

A
Add and Subtract Whole Numbers and Ones with Fraction Units

Question 1.
3 + 1 =
Answer:
3 + 1 = 4
Explanation :
Adding 1 to 3 we get 4 a s sum .

Question 2.
3 + \(\frac{1}{2}\) =
Answer:
3 + \(\frac{1}{2}\) = 3\(\frac{1}{2}\)
Explanation :
3 + \(\frac{1}{2}\) = \(\frac{6}{2}\) + \(\frac{1}{2}\) = \(\frac{7}{2}\) = 3\(\frac{1}{2}\)

Question 3.
3\(\frac{1}{2}\) + 1 =
Answer:
3\(\frac{1}{2}\) + 1 = 4\(\frac{1}{2}\)
Explanation :
3\(\frac{1}{2}\) + 1 = \(\frac{7}{2}\) + \(\frac{2}{2}\) = \(\frac{9}{2}\) =4\(\frac{1}{2}\)

Question 4.
3 – 1 =
Answer:
3 – 1 = 2
Explanation :
subtracting 1 from 3 we get 2 .

Question 5.
3\(\frac{1}{2}\) – 1 =
Answer:
3\(\frac{1}{2}\) – 1 = 2\(\frac{1}{2}\)
Explanation :
3\(\frac{1}{2}\) – 1 = \(\frac{7}{2}\) – \(\frac{2}{2}\) = \(\frac{5}{2}\) =2\(\frac{1}{2}\)

Question 6.
4 – 2 =
Answer:
4 – 2 = 2
Explanation :
Subtracting 2 from 4 we get difference as 2.

Question 7.
4\(\frac{1}{2}\) – 2 =
Answer:
4\(\frac{1}{2}\) – 2 = 2\(\frac{1}{2}\)
Explanation :
4\(\frac{1}{2}\) – 2 = \(\frac{9}{2}\) – \(\frac{4}{2}\) = \(\frac{5}{2}\) =2\(\frac{1}{2}\)

Question 8.
5 – 2 =
Answer:
5 – 2 = 3
Explanation :
Subtracting 2 from 5 we get difference as 3.

Question 9.
5\(\frac{1}{3}\) – 2 =
Answer:
5\(\frac{1}{3}\) – 2 = 3\(\frac{1}{3}\)
Explanation :
5\(\frac{1}{3}\) – 2 = \(\frac{16}{3}\) – \(\frac{6}{3}\) = \(\frac{10}{3}\) =3\(\frac{1}{3}\)

Question 10.
5\(\frac{2}{3}\) – 2 =
Answer:
5\(\frac{2}{3}\) – 2 = 3\(\frac{2}{3}\)
Explanation :
5\(\frac{2}{3}\) – 2 = \(\frac{17}{3}\) – \(\frac{6}{3}\) = \(\frac{11}{3}\) =3\(\frac{2}{3}\)

Question 11.
5\(\frac{2}{3}\) + 2 =
Answer:
5\(\frac{2}{3}\) + 2 = 7\(\frac{2}{3}\)
Explanation :
5\(\frac{2}{3}\) + 2 = \(\frac{17}{3}\) + \(\frac{6}{3}\) = \(\frac{23}{3}\) = 7\(\frac{2}{3}\)

Question 12.
6 + 2 =
Answer:
6 + 2 = 8
Explanation :
Adding 2 to 6 we get sum as 8 .

Question 13.
6 + \(\frac{3}{4}\) =
Answer:
6 + \(\frac{3}{4}\) = 6\(\frac{3}{4}\)
Explanation :
6 + \(\frac{3}{4}\) = \(\frac{24}{4}\) + \(\frac{3}{4}\) = \(\frac{27}{4}\) = 6\(\frac{3}{4}\)

Question 14.
6\(\frac{3}{4}\) + 2 =
Answer:
6\(\frac{3}{4}\) + 2 = 8\(\frac{3}{4}\)
Explanation :
6\(\frac{3}{4}\) + 2 = \(\frac{27}{4}\) + \(\frac{8}{4}\) = \(\frac{35}{4}\) = 8\(\frac{3}{4}\)

Question 15.
6\(\frac{3}{4}\) – 2 =
Answer:
6\(\frac{3}{4}\) – 2 = 4\(\frac{3}{4}\)
Explanation :
6\(\frac{3}{4}\) – 2 = \(\frac{27}{4}\) – \(\frac{8}{4}\) = \(\frac{19}{4}\) = 4\(\frac{3}{4}\)

Question 16.
6\(\frac{3}{4}\) – 3 =
Answer:
6\(\frac{3}{4}\) – 3 = 3\(\frac{3}{4}\)
Explanation :
6\(\frac{3}{4}\) – 3 = \(\frac{27}{4}\) – \(\frac{12}{4}\) = \(\frac{15}{4}\) = 3\(\frac{3}{4}\)

Question 17.
6\(\frac{3}{4}\) – 4 =
Answer:
6\(\frac{3}{4}\) – 4 = 2\(\frac{3}{4}\)
Explanation :
6\(\frac{3}{4}\) – 4 = \(\frac{27}{4}\) – \(\frac{16}{4}\) = \(\frac{11}{4}\) = 2\(\frac{3}{4}\)

Question 18.
6\(\frac{3}{4}\) – 6 =
Answer:
6\(\frac{3}{4}\) – 6 = \(\frac{3}{4}\)
Explanation :
6\(\frac{3}{4}\) – 6 = \(\frac{27}{4}\) – \(\frac{24}{4}\) = \(\frac{3}{4}\)

Question 19.
6\(\frac{3}{4}\) – \(\frac{3}{4}\) =
Answer:
6\(\frac{3}{4}\) – \(\frac{3}{4}\) = 6
Explanation :
6\(\frac{3}{4}\) – \(\frac{3}{4}\) = \(\frac{27}{4}\) – \(\frac{3{4}\) = \(\frac{24}{4}\) = 6

Question 20.
2\(\frac{5}{6}\) + 3 =
Answer:
2\(\frac{5}{6}\) + 3 = 5\(\frac{5}{6}\)
Explanation :
2\(\frac{5}{6}\) + 3 = \(\frac{17}{6}\) + \(\frac{18}{6}\) = \(\frac{35}{6}\) = 5\(\frac{5}{6}\)

Question 21.
2\(\frac{1}{6}\) + 3 =
Answer:
2\(\frac{1}{6}\) + 3 = 5\(\frac{1}{6}\)
Explanation :
2\(\frac{1}{6}\) + 3 = \(\frac{13}{6}\) + \(\frac{18}{6}\) = \(\frac{31}{6}\) = 5\(\frac{1}{6}\)

Question 22.
2\(\frac{5}{6}\) + 7 =
Answer:
2\(\frac{5}{6}\) + 7 = 9\(\frac{5}{6}\)
Explanation :
2\(\frac{5}{6}\) + 7 = \(\frac{17}{6}\) + \(\frac{42}{6}\) = \(\frac{59}{6}\) = 9\(\frac{5}{6}\)

Question 23.
3\(\frac{5}{6}\) + 7 =
Answer:
3\(\frac{5}{6}\) + 7 = 10\(\frac{5}{6}\)
Explanation :
3\(\frac{5}{6}\) + 7 = \(\frac{23}{6}\) + \(\frac{42}{6}\) = \(\frac{65}{6}\) = 10\(\frac{5}{6}\)

Question 24.
7\(\frac{5}{6}\) + 3 =
Answer:
7\(\frac{5}{6}\) + 3 = 10\(\frac{5}{6}\)
Explanation :
7\(\frac{5}{6}\) + 3 = \(\frac{47}{6}\) + \(\frac{18}{6}\) = \(\frac{65}{6}\) = 10\(\frac{5}{6}\)

Question 25.
10\(\frac{5}{6}\) – 3 =
Answer:
10\(\frac{5}{6}\) – 3 = 7\(\frac{5}{6}\)
Explanation :
10\(\frac{5}{6}\) – 3 = \(\frac{65}{6}\) – \(\frac{18}{6}\) = \(\frac{47}{6}\) = 7\(\frac{5}{6}\)

Question 26.
10\(\frac{5}{6}\) – 7 =
Answer:
10\(\frac{5}{6}\) – 7 = 3\(\frac{5}{6}\)
Explanation :
10\(\frac{5}{6}\) – 7 = \(\frac{65}{6}\) – \(\frac{42}{6}\) = \(\frac{23}{6}\) = 3\(\frac{5}{6}\)

Question 27.
3 + \(\frac{4}{5}\) + 2 =
Answer:
3 + \(\frac{4}{5}\) + 2 = 5\(\frac{4}{5}\)
Explanation :
3 + \(\frac{4}{5}\) + 2 = 5 + \(\frac{4}{5}\) = \(\frac{25}{5}\) + \(\frac{4}{5}\) = \(\frac{29}{5}\) = 5\(\frac{4}{5}\)

Question 28.
5 + \(\frac{7}{8}\) + 4 =
Answer:
5 + \(\frac{7}{8}\) + 4 = 9 \(\frac{7}{8}\)
Explanation :
5 + \(\frac{7}{8}\) + 4 = 9 + \(\frac{7}{8}\) = \(\frac{72}{8}\) + \(\frac{7}{8}\) = \(\frac{79}{8}\) = 9\(\frac{7}{8}\)

Question 29.
7 + \(\frac{4}{5}\) – 2 =
Answer:
7 + \(\frac{4}{5}\) – 2 = 5\(\frac{4}{5}\)
Explanation :
7 + \(\frac{4}{5}\) – 2 = 5 + \(\frac{4}{5}\) = \(\frac{29}{5}\) + \(\frac{4}{5}\) = \(\frac{33}{5}\) = 5\(\frac{4}{5}\)

Question 30.
9 + \(\frac{5}{12}\) – 5 =
Answer:
9 + \(\frac{5}{12}\) – 5 = 4\(\frac{5}{12}\)
Explanation :
9 + \(\frac{5}{12}\) – 5 = 4 + \(\frac{5}{12}\) = \(\frac{48}{12}\) + \(\frac{5}{12}\) + \(\frac{53}{12}\) = 4\(\frac{5}{12}\) .

Question 31.
7 + \(\frac{1}{5}\) + \(\frac{1}{5}\) + 2
Answer:
7 + \(\frac{1}{5}\) + \(\frac{1}{5}\) + 2 = 9\(\frac{2}{5}\)
Explanation :
7 + \(\frac{1}{5}\) + \(\frac{1}{5}\) + 2 = 9 + \(\frac{2}{5}\) = \(\frac{45}{5}\) + \(\frac{2}{5}\) = \(\frac{47}{5}\) = 9\(\frac{2}{5}\)

Question 32.
7 + \(\frac{2}{5}\) + 2 =
Answer:
7 + \(\frac{2}{5}\) + 2 =  9\(\frac{2}{5}\) 
Explanation :
7 + \(\frac{2}{5}\) + 2 = 9 + \(\frac{2}{5}\) = \(\frac{45}{5}\) + \(\frac{2}{5}\) = \(\frac{47}{5}\) = 9\(\frac{2}{5}\)

Question 33.
7 + \(\frac{2}{5}\) + 2 + \(\frac{2}{5}\) =
Answer:
7 + \(\frac{2}{5}\) + 2 + \(\frac{2}{5}\) = 9\(\frac{4}{5}\)
Explanation :
7 + \(\frac{2}{5}\) + 2 + \(\frac{2}{5}\) = 9 + \(\frac{4}{5}\) = \(\frac{45}{5}\)  + \(\frac{4}{5}\) = \(\frac{49}{5}\) = 9\(\frac{4}{5}\)

Question 34.
7\(\frac{2}{5}\) + 2\(\frac{2}{5}\) =
Answer:
7\(\frac{2}{5}\) + 2\(\frac{2}{5}\) = 9\(\frac{4}{5}\)
Explanation :
7\(\frac{2}{5}\) + 2\(\frac{2}{5}\) = \(\frac{37}{5}\)  + \(\frac{12}{5}\) = \(\frac{49}{5}\) = 9\(\frac{4}{5}\)

Question 35.
6 + \(\frac{1}{3}\) + 1 + \(\frac{1}{3}\) =
Answer:
6 + \(\frac{1}{3}\) + 1 + \(\frac{1}{3}\) = 7 \(\frac{2}{3}\)
Explanation :
6 + \(\frac{1}{3}\) + 1 + \(\frac{1}{3}\) = 7 + \(\frac{2}{3}\) = \(\frac{22}{3}\) + \(\frac{2}{3}\) = \(\frac{24}{3}\)

Question 36.
6\(\frac{1}{3}\) + 1\(\frac{1}{3}\) =
Answer:
6\(\frac{1}{3}\) + 1\(\frac{1}{3}\) = 7\(\frac{2}{3}\)
Explanation :
6\(\frac{1}{3}\) + 1\(\frac{1}{3}\) = \(\frac{19}{3}\) + \(\frac{4}{3}\) = \(\frac{23}{3}\) = 7\(\frac{2}{3}\)

Question 37.
6 + \(\frac{2}{3}\) – 1 =
Answer:
6 + \(\frac{2}{3}\) – 1 = 5\(\frac{2}{3}\)
Explanation :
6 + \(\frac{2}{3}\) – 1 = 5 + \(\frac{2}{3}\) = \(\frac{15}{3}\) + \(\frac{2}{3}\) = \(\frac{17}{3}\) = 5\(\frac{2}{3}\)

Question 38.
6\(\frac{2}{3}\) – 1\(\frac{1}{3}\) =
Answer:
6\(\frac{2}{3}\) – 1\(\frac{1}{3}\) = 5\(\frac{1}{3}\)
Explanation :
6\(\frac{2}{3}\) – 1\(\frac{1}{3}\) = \(\frac{20}{3}\) – \(\frac{4}{3}\) = \(\frac{16}{3}\) = 5\(\frac{1}{3}\)

Question 39.
6\(\frac{2}{3}\) – 1\(\frac{2}{3}\) =
Answer:
6\(\frac{2}{3}\) – 1\(\frac{2}{3}\) = 5
Explanation :
6\(\frac{2}{3}\) – 1\(\frac{2}{3}\) = \(\frac{20}{3}\) – \(\frac{5}{3}\) = 5

Question 40.
3 + \(\frac{4}{7}\) + 1 + \(\frac{2}{7}\) =
Answer:
3 + \(\frac{4}{7}\) + 1 + \(\frac{2}{7}\) = 4 \(\frac{6}{7}\)
Explanation :
3 + \(\frac{4}{7}\) + 1 + \(\frac{2}{7}\) = 4 + \(\frac{6}{7}\) = \(\frac{28}{7}\) + \(\frac{6}{7}\) = \(\frac{34}{7}\) = 4\(\frac{6}{7}\)

Question 41.
3\(\frac{4}{7}\) + 1\(\frac{2}{7}\) =
Answer:
3\(\frac{4}{7}\) + 1\(\frac{2}{7}\) = 4\(\frac{6}{7}\)
Explanation :
3\(\frac{4}{7}\) + 1\(\frac{2}{7}\) = \(\frac{25}{7}\) + \(\frac{9}{7}\) = \(\frac{34}{7}\) = 4\(\frac{6}{7}\)

Question 42.
7\(\frac{4}{5}\) – 2\(\frac{3}{5}\) =
Answer:
7\(\frac{4}{5}\) – 2\(\frac{3}{5}\) = 5\(\frac{1}{5}\)
Explanation :
7\(\frac{4}{5}\) – 2\(\frac{3}{5}\) = \(\frac{39}{5}\) – \(\frac{13}{5}\) = \(\frac{26}{5}\) = 5\(\frac{1}{5}\)

Question 43.
7\(\frac{4}{5}\) – 2\(\frac{2}{5}\) =
Answer:
7\(\frac{4}{5}\) – 2\(\frac{2}{5}\) = 5\(\frac{2}{5}\)
Explanation :
7\(\frac{4}{5}\) – 2\(\frac{2}{5}\) = \(\frac{39}{5}\) – \(\frac{12}{5}\) = \(\frac{27}{5}\) = 5\(\frac{2}{5}\)

Question 44.
13\(\frac{7}{9}\) – 7\(\frac{5}{9}\) =
Answer:
13\(\frac{7}{9}\) – 7\(\frac{5}{9}\) = 6\(\frac{2}{9}\)
Explanation :
13\(\frac{7}{9}\) – 7\(\frac{5}{9}\) = \(\frac{124}{9}\) – \(\frac{68}{9}\) = \(\frac{56}{9}\)= 6\(\frac{2}{9}\)

B
Add and Subtract Whole Numbers and Ones with Fraction Units

Question 1.
2 + 1 =
Answer:
2 + 1 = 3
Explanation :
adding 1 to 2 we get sum as 3 .

Question 2.
2 + \(\frac{1}{2}\) =
Answer:
2 + \(\frac{1}{2}\) = 2\(\frac{1}{2}\)
Explanation :
2 + \(\frac{1}{2}\) = \(\frac{4}{2}\) + \(\frac{1}{2}\) = \(\frac{5}{2}\) =2\(\frac{1}{2}\)

Question 3.
2\(\frac{1}{2}\) + 1 =
Answer:
2\(\frac{1}{2}\) + 1 = 3\(\frac{1}{2}\)
Explanation :
2\(\frac{1}{2}\) + 1 = \(\frac{5}{2}\)  + \(\frac{2}{2}\) = \(\frac{7}{2}\) = 3\(\frac{1}{2}\)

Question 4.
2 – 1 =
Answer:
2 – 1 = 1
Explanation :
Subtracting 1 from 2 we get 1as difference .

Question 5.
2\(\frac{1}{2}\) – 1 =
Answer:
2\(\frac{1}{2}\) – 1 = 1\(\frac{1}{2}\)
Explanation :
2\(\frac{1}{2}\) – 1 = \(\frac{5}{2}\)  – \(\frac{2}{2}\) = \(\frac{3}{2}\) = 1\(\frac{1}{2}\)

Question 6.
5 – 2 =
Answer:
5 – 2 = 3
Explanation :
subtract 2 from 5 we get 3 as difference .

Question 7.
5\(\frac{1}{2}\) – 2 =
Answer:
5\(\frac{1}{2}\) – 2 = 3\(\frac{1}{2}\)
Explanation :
5\(\frac{1}{2}\) – 2 = \(\frac{11}{2}\)  – \(\frac{4}{2}\)  = \(\frac{7}{2}\) = 3\(\frac{1}{2}\)

Question 8.
6 – 2 =
Answer:
6 – 2 = 4
Explanation :
subtract 2 from 6 we get 4 as difference .

Question 9.
6\(\frac{1}{3}\) – 2 =
Answer:
6\(\frac{1}{3}\) – 2 = 4\(\frac{1}{3}\)
Explanation :
6\(\frac{1}{3}\) – 2 = \(\frac{19}{3}\) – \(\frac{6}{3}\)= \(\frac{13}{3}\)= 4\(\frac{1}{3}\)

Question 10.
6\(\frac{2}{3}\) – 2 =
Answer:
6\(\frac{2}{3}\) – 2 = 4\(\frac{2}{3}\)
Explanation :
6\(\frac{2}{3}\) – 2 = \(\frac{20}{3}\) – \(\frac{6}{3}\)= \(\frac{14}{3}\)= 4\(\frac{2}{3}\)

Question 11.
6\(\frac{2}{3}\) + 2 =
Answer:
6\(\frac{2}{3}\) + 2 = 8\(\frac{2}{3}\)
Explanation :
6\(\frac{2}{3}\) + 2 = \(\frac{20}{3}\) + \(\frac{6}{3}\)= \(\frac{26}{3}\)= 8\(\frac{2}{3}\)

Question 12.
7 + 2 =
Answer:
7 + 2 = 9
Explanation:
Adding 2 to 7 we get sum as 9

Question 13.
7 + \(\frac{3}{4}\) =
Answer:
7 + \(\frac{3}{4}\) = 7\(\frac{3}{4}\)
Explanation :
7 + \(\frac{3}{4}\) = \(\frac{28}{4}\) + \(\frac{3}{4}\) = \(\frac{31}{4}\)= 7\(\frac{3}{4}\)

Question 14.
7\(\frac{3}{4}\) + 2 =
Answer:
7\(\frac{3}{4}\) + 2= 9\(\frac{3}{4}\)
Explanation :
7\(\frac{3}{4}\) + 2 = \(\frac{31}{4}\) + \(\frac{8}{4}\) = \(\frac{39}{4}\)= 9\(\frac{3}{4}\)

Question 15.
7\(\frac{3}{4}\) – 2 =
Answer:
7\(\frac{3}{4}\) – 2= 5\(\frac{3}{4}\)
Explanation :
7\(\frac{3}{4}\) – 2 = \(\frac{31}{4}\) – \(\frac{8}{4}\) = \(\frac{23}{4}\)= 5\(\frac{3}{4}\)

Question 16.
7\(\frac{3}{4}\) – 3 =
Answer:
7\(\frac{3}{4}\) – 3= 4\(\frac{3}{4}\)
Explanation :
7\(\frac{3}{4}\) – 3 = \(\frac{31}{4}\) – \(\frac{12}{4}\) = \(\frac{19}{4}\)= 4\(\frac{3}{4}\)

Question 17.
7\(\frac{3}{4}\) – 4 =
Answer:
7\(\frac{3}{4}\) – 4= 3\(\frac{3}{4}\)
Explanation :
7\(\frac{3}{4}\) – 4 = \(\frac{31}{4}\) – \(\frac{16}{4}\) = \(\frac{15}{4}\)= 3\(\frac{3}{4}\)

Question 18.
7\(\frac{3}{4}\) – 7 =
Answer:
7\(\frac{3}{4}\) – 7= \(\frac{3}{4}\)
Explanation :
7\(\frac{3}{4}\) – 7 = \(\frac{31}{4}\) – \(\frac{28}{4}\) = \(\frac{3}{4}\)

Question 19.
7\(\frac{3}{4}\) – \(\frac{3}{4}\) =
Answer:
7\(\frac{3}{4}\) – \(\frac{3}{4}\) = 7
Explanation :
7\(\frac{3}{4}\) – \(\frac{3}{4}\) = \(\frac{31}{4}\) – \(\frac{3}{4}\) = \(\frac{28}{4}\) = 7

Question 20.
3\(\frac{5}{6}\) + 2 =
Answer:
3\(\frac{5}{6}\) + 2 = 5\(\frac{5}{6}\)
Explanation :
3\(\frac{5}{6}\) + 2 = \(\frac{23}{6}\) + \(\frac{12}{6}\) = \(\frac{35}{6}\) = 5\(\frac{5}{6}\)

Question 21.
3\(\frac{1}{6}\) + 2 =
Answer:
3\(\frac{5}{6}\) + 2 = 5\(\frac{5}{6}\)
Explanation :
3\(\frac{5}{6}\) + 2 = \(\frac{23}{6}\) + \(\frac{12}{6}\) = \(\frac{35}{6}\) = 5\(\frac{5}{6}\)

Question 22.
3\(\frac{5}{6}\) + 6 =
Answer:
3\(\frac{5}{6}\) + 6 = 9\(\frac{5}{6}\)
Explanation :
3\(\frac{5}{6}\) + 6 = \(\frac{23}{6}\) + \(\frac{36}{6}\) = \(\frac{59}{6}\) = 9\(\frac{5}{6}\)

Question 23.
4\(\frac{5}{6}\) + 6 =
Answer:
4\(\frac{5}{6}\) + 6 = 10\(\frac{5}{6}\)
Explanation :
4\(\frac{5}{6}\) + 6 = \(\frac{29}{6}\) + \(\frac{36}{6}\) = \(\frac{65}{6}\) = 10\(\frac{5}{6}\)

Question 24.
6\(\frac{5}{6}\) + 4 =
Answer:
6\(\frac{5}{6}\) + 4 = 10\(\frac{5}{6}\)
Explanation :
6\(\frac{5}{6}\) + 4 = \(\frac{41}{6}\) + \(\frac{24}{6}\) = \(\frac{65}{6}\) = 10\(\frac{5}{6}\)

Question 25.
10\(\frac{5}{6}\) – 4 =
Answer:
10\(\frac{5}{6}\) – 4 = 6\(\frac{5}{6}\)
Explanation :
10\(\frac{5}{6}\) – 4 = \(\frac{65}{6}\) – \(\frac{24}{6}\) = \(\frac{41}{6}\) = 6\(\frac{5}{6}\)

Question 26.
10\(\frac{5}{6}\) – 6 =
Answer:
10\(\frac{5}{6}\) – 6 = 4\(\frac{5}{6}\)
Explanation :
10\(\frac{5}{6}\) – 6 = \(\frac{65}{6}\) – \(\frac{36}{6}\) = \(\frac{29}{6}\) = 4\(\frac{5}{6}\)

Question 27.
4 + \(\frac{4}{5}\) + 2 =
Answer:
4 + \(\frac{4}{5}\) + 2 = 6\(\frac{4}{5}\)
Explanation :
4 + \(\frac{4}{5}\) + 2 = 6 + \(\frac{4}{5}\) = \(\frac{30}{5}\) + \(\frac{4}{5}\) = \(\frac{34}{5}\) = 6\(\frac{4}{5}\)

Question 28.
6 + \(\frac{7}{8}\) + 3 =
Answer:
6 + \(\frac{7}{8}\) + 3 = 9\(\frac{7}{8}\)
Explanation :
6 + \(\frac{7}{8}\) + 3 = 9 + \(\frac{7}{8}\) = \(\frac{72}{8}\) + \(\frac{7}{8}\) = \(\frac{79}{8}\) = 9\(\frac{7}{8}\)

Question 29.
6 + \(\frac{4}{5}\) – 2 =
Answer:
6 + \(\frac{4}{5}\) – 2 = 4\(\frac{4}{5}\)
Explanation :
6 + \(\frac{4}{5}\) – 2 = 4 + \(\frac{4}{5}\) = \(\frac{20}{5}\)  + \(\frac{4}{5}\)  = \(\frac{24}{5}\) = 4\(\frac{4}{5}\)

Question 30.
9 + \(\frac{5}{12}\) – 4 =
Answer:
9 + \(\frac{5}{12}\) – 4 = 5\(\frac{5}{12}\)
Explanation :
9 + \(\frac{5}{12}\) – 4 = 5 + \(\frac{5}{12}\) = \(\frac{60}{12}\) + \(\frac{5}{12}\) = \(\frac{65}{12}\) = 5\(\frac{5}{12}\)

Question 31.
6 + \(\frac{1}{5}\) + \(\frac{1}{5}\) + 2 =
Answer:
6 + \(\frac{1}{5}\) + \(\frac{1}{5}\) + 2 = 8 \(\frac{2}{5}\)
Explanation :
6 + \(\frac{1}{5}\) + \(\frac{1}{5}\) + 2 = 8 + \(\frac{2}{5}\) = \(\frac{40}{5}\) + \(\frac{2}{5}\) = \(\frac{42}{5}\) = 8\(\frac{2}{5}\)

Question 32.
6 + \(\frac{2}{5}\) + 2 =
Answer:
6 + \(\frac{2}{5}\) + 2 = 8\(\frac{2}{5}\)
Explanation :
6 + \(\frac{2}{5}\) + 2 = 8 + \(\frac{2}{5}\) = \(\frac{40}{5}\) + \(\frac{2}{5}\)  = \(\frac{42}{5}\) = 8\(\frac{2}{5}\)

Question 33.
6 + \(\frac{2}{5}\) + 2 + \(\frac{2}{5}\) =
Answer:
6 + \(\frac{2}{5}\) + 2 + \(\frac{2}{5}\) = 8\(\frac{4}{5}\)
Explanation :
6 + \(\frac{2}{5}\) + 2 + \(\frac{2}{5}\) = 8 + \(\frac{4}{5}\) = \(\frac{40}{5}\) + \(\frac{4}{5}\) = \(\frac{44}{5}\) = 8\(\frac{4}{5}\)

Question 34.
6\(\frac{2}{5}\) + 2\(\frac{2}{5}\) =
Answer:
6\(\frac{2}{5}\) + 2\(\frac{2}{5}\) = 8\(\frac{4}{5}\)
Explanation :
6\(\frac{2}{5}\) + 2\(\frac{2}{5}\) = \(\frac{32}{5}\) + \(\frac{12}{5}\) = \(\frac{44}{5}\)= 8\(\frac{4}{5}\)

Question 35.
5 + \(\frac{1}{3}\) + 1 + \(\frac{1}{3}\) =
Answer:
5 + \(\frac{1}{3}\) + 1 + \(\frac{1}{3}\) = 6\(\frac{2}{3}\)
Explanation :
5 + \(\frac{1}{3}\) + 1 + \(\frac{1}{3}\) = 6 + \(\frac{2}{3}\) = \(\frac{18}{3}\) + \(\frac{2}{3}\) = \(\frac{20}{3}\) = 6\(\frac{2}{3}\)

Question 36.
5\(\frac{1}{3}\) + 1\(\frac{1}{3}\) =
Answer:
5\(\frac{1}{3}\) + 1\(\frac{1}{3}\) = 6\(\frac{2}{3}\)
Explanation :
5\(\frac{1}{3}\) + 1\(\frac{1}{3}\) = \(\frac{16}{3}\) + \(\frac{4}{3}\) = \(\frac{20}{3}\)= 6\(\frac{2}{3}\)

Question 37.
7 + \(\frac{2}{3}\) – 1 =
Answer:
7 + \(\frac{2}{3}\) – 1 = 6\(\frac{2}{3}\)
Explanation :
7 + \(\frac{2}{3}\) – 1 = 6 + \(\frac{2}{3}\) = \(\frac{18}{3}\)  + \(\frac{2}{3}\)  = \(\frac{20}{3}\) = 6\(\frac{2}{3}\)

Question 38.
7\(\frac{2}{3}\) – 1\(\frac{1}{3}\) =
Answer:
7\(\frac{2}{3}\) – 1\(\frac{1}{3}\) = 6\(\frac{1}{3}\)
Explanation :
7\(\frac{2}{3}\) – 1\(\frac{1}{3}\) = \(\frac{23}{3}\) – \(\frac{4}{3}\) = \(\frac{19}{3}\) = 6\(\frac{1}{3}\)

Question 39.
7\(\frac{2}{3}\) – 1\(\frac{2}{3}\) =
Answer:
7\(\frac{2}{3}\) – 1\(\frac{2}{3}\) = 6
Explanation :
7\(\frac{2}{3}\) – 1\(\frac{2}{3}\) = \(\frac{23}{3}\) – \(\frac{5}{3}\) = \(\frac{18}{3}\) = 6

Question 40.
5 + \(\frac{4}{7}\) + 1 + \(\frac{2}{7}\) =
Answer:
5 + \(\frac{4}{7}\) + 1 + \(\frac{2}{7}\) = 6\(\frac{6}{7}\)
Explanation :
5 + \(\frac{4}{7}\) + 1 + \(\frac{2}{7}\) = 6 + \(\frac{6}{7}\) = \(\frac{42}{7}\) + \(\frac{6}{7}\)  = \(\frac{48}{7}\) =6\(\frac{6}{7}\)

Question 41.
5\(\frac{4}{7}\) + 1\(\frac{2}{7}\) =
Answer:
5\(\frac{4}{7}\) + 1\(\frac{2}{7}\) = 6\(\frac{6}{7}\)
Explanation :
5\(\frac{4}{7}\) + 1\(\frac{2}{7}\) = \(\frac{39}{7}\) + \(\frac{9}{7}\) = \(\frac{48}{7}\)
= 6\(\frac{6}{7}\)

Question 42.
6 + \(\frac{4}{5}\) – 2\(\frac{3}{5}\) =
Answer:
6 + \(\frac{4}{5}\) – 2\(\frac{3}{5}\) =  4\(\frac{1}{5}\)
Explanation :
6 + \(\frac{4}{5}\) – 2\(\frac{3}{5}\) = \(\frac{30}{5}\) + \(\frac{4}{5}\) – \(\frac{13}{5}\) = \(\frac{21}{5}\) = 4\(\frac{1}{5}\)

Question 43.
6\(\frac{4}{5}\) – 2\(\frac{3}{5}\) =
Answer:
6\(\frac{4}{5}\) – 2\(\frac{3}{5}\) = 4\(\frac{1}{5}\)
Explanation :
6\(\frac{4}{5}\) – 2\(\frac{3}{5}\) = \(\frac{34}{5}\) – \(\frac{13}{5}\) = \(\frac{21}{5}\)
= 4\(\frac{1}{5}\)

Question 44.
13\(\frac{7}{9}\) – 6\(\frac{5}{9}\) =
Answer:
13\(\frac{7}{9}\) – 6\(\frac{5}{9}\) = 7\(\frac{2}{9}\)
Explanation :
13\(\frac{7}{9}\) – 6\(\frac{5}{9}\) = \(\frac{124}{9}\) – \(\frac{59}{9}\) = \(\frac{65}{9}\) = 7\(\frac{2}{9}\)

Eureka Math Grade 5 Module 3 Lesson 9 Problem Set Answer Key

Question 1.
Add.
a. 2\(\frac{1}{4}\) + 1\(\frac{1}{5}\) =
b. 2\(\frac{3}{4}\) + 1\(\frac{2}{5}\) =
c. 1\(\frac{1}{5}\) + 2\(\frac{1}{3}\) =
d. 4\(\frac{2}{3}\) + 1\(\frac{2}{5}\) =
e. 3\(\frac{1}{3}\) + 4\(\frac{5}{7}\) =
f. 2\(\frac{6}{7}\) + 5\(\frac{2}{3}\) =
g. 15\(\frac{1}{5}\) + 3\(\frac{5}{8}\) =
h. 15\(\frac{5}{8}\) + 5\(\frac{2}{5}\) =
Answer:
a.
2\(\frac{1}{4}\) + 1\(\frac{1}{5}\) =\(\frac{9}{4}\) + \(\frac{6}{5}\)
lcm of 4 and 5 is 20 .
\(\frac{45}{20}\) + \(\frac{24}{20}\) = \(\frac{69}{20}\) = 3\(\frac{9}{20}\)

b.
2\(\frac{3}{4}\) + 1\(\frac{2}{5}\) = \(\frac{11}{4}\) + \(\frac{7}{5}\)
lcm of 4 and 5 is 20 .
\(\frac{55}{20}\) + \(\frac{28}{20}\) =\(\frac{88}{20}\) = \(\frac{22}{5}\) = 4\(\frac{2}{5}\)

c.
1\(\frac{1}{5}\) + 2\(\frac{1}{3}\) =\(\frac{6}{5}\) + \(\frac{7}{3}\)
lcm of 5 and 3 is 15 .
\(\frac{18}{15}\) + \(\frac{35}{15}\) = \(\frac{53}{15}\) =3\(\frac{8}{15}\)

d.
4\(\frac{2}{3}\) + 1\(\frac{2}{5}\) = \(\frac{14}{3}\) + \(\frac{7}{5}\)
lcm of 3 and 5 is 15 .
\(\frac{70}{15}\) + \(\frac{21}{15}\) = \(\frac{91}{15}\) = 6\(\frac{1}{15}\)

e.
3\(\frac{1}{3}\) + 4\(\frac{5}{7}\) = \(\frac{10}{3}\) + \(\frac{33}{7}\)
lcm of 3 and 7 is 21.
\(\frac{70}{21}\) + \(\frac{99}{21}\) = \(\frac{169}{21}\) =8\(\frac{1}{21}\)

f.
2\(\frac{6}{7}\) + 5\(\frac{2}{3}\) = \(\frac{20}{7}\) + \(\frac{17}{3}\)
lcm of 7 and 3 is 21 .
\(\frac{60}{21}\) + \(\frac{139}{21}\) = \(\frac{199}{21}\) = 9\(\frac{10}{21}\)

g.
15\(\frac{1}{5}\) + 3\(\frac{5}{8}\) =\(\frac{76}{5}\) + \(\frac{29}{8}\)
lcm of 5 and 8 is 40 .
\(\frac{608}{40}\) + \(\frac{145}{40}\) = \(\frac{753}{40}\) = 18 \(\frac{33}{40}\)

h.
15\(\frac{5}{8}\) + 5\(\frac{2}{5}\) = \(\frac{125}{8}\) + \(\frac{12}{5}\)
lcm of 8 and 5 is 40 .
\(\frac{625}{40}\) + \(\frac{96}{40}\) = \(\frac{721}{40}\) = 18 \(\frac{1}{40}\)

Question 2.
Erin jogged 2\(\frac{1}{4}\) miles on Monday. Wednesday, she jogged 3\(\frac{1}{3}\) miles, and on Friday, she jogged 2\(\frac{2}{3}\) miles. How far did Erin jog altogether?
Answer:
Fraction of miles jogged on Monday = 2\(\frac{1}{4}\) = \(\frac{9}{4}\)
Fraction of miles jogged on Wednesday = 3\(\frac{1}{3}\) = \(\frac{10}{3}\)
Fraction of miles jogged on Friday = 2\(\frac{2}{3}\) = \(\frac{8}{3}\)
Total Fraction of miles jogged altogether = \(\frac{9}{4}\) + \(\frac{10}{3}\) + \(\frac{8}{3}\) = \(\frac{27}{12}\) + \(\frac{40}{12}\) + \(\frac{32}{12}\) = \(\frac{99}{12}\) =\(\frac{33}{4}\) = 8\(\frac{1}{4}\) .
Therefore, Total Fraction of miles jogged altogether = 8\(\frac{1}{4}\)

Question 3.
Darren bought some paint. He used 2\(\frac{1}{4}\) gallons painting his living room. After that, he had 3\(\frac{5}{6}\) gallons left. How much paint did he buy?
Answer:
Fraction of Quantity of paint used for living room = 2\(\frac{1}{4}\) gallons
Fraction of Quantity of paint left = 3\(\frac{5}{6}\) gallons
Total Fraction of Quantity of Paint = 2\(\frac{1}{4}\) + 3\(\frac{5}{6}\) = \(\frac{9}{4}\) + \(\frac{23}{6}\) = \(\frac{27}{12}\) + \(\frac{46}{12}\) = \(\frac{73}{12}\) .
Therefore, Total Fraction of Quantity of Paint = \(\frac{73}{12}\) .

Question 4.
Clayton says that 2\(\frac{1}{2}\) + 3\(\frac{3}{5}\) will be more than 5 but less than 6 since 2 + 3 is 5. Is Clayton’s reasoning correct? Prove him right or wrong.
Answer:
2\(\frac{1}{2}\) + 3\(\frac{3}{5}\) = \(\frac{5}{2}\) + \(\frac{18}{5}\) = \(\frac{25}{10}\) + \(\frac{36}{10}\) = \(\frac{61}{10}\) = 6\(\frac{1}{10}\) .
Clyton is not correct \(\frac{1}{2}\) + \(\frac{3}{5}\) is more than 1 .

Eureka Math Grade 5 Module 3 Lesson 9 Exit Ticket Answer Key

Add.
Question 1.
3\(\frac{1}{2}\) + 1\(\frac{1}{3}\) =
Answer:
3\(\frac{1}{2}\) + 1\(\frac{1}{3}\) = \(\frac{7}{2}\) + \(\frac{4}{3}\)
lcm of 2 and 3 is 6
\(\frac{21}{6}\) + \(\frac{8}{6}\) = \(\frac{29}{6}\)

Question 2.
4\(\frac{5}{7}\) + 3\(\frac{3}{4}\) =
Answer:
4\(\frac{5}{7}\) + 3\(\frac{3}{4}\) = \(\frac{33}{7}\) + \(\frac{15}{4}\)
lcm of 7 and 4 is 28
\(\frac{132}{28}\) + \(\frac{105}{28}\) = \(\frac{237}{28}\) = 8\(\frac{13}{28}\)

Eureka Math Grade 5 Module 3 Lesson 9 Homework Answer Key

Question 1.
Add.
a.2\(\frac{1}{2}\) + 1\(\frac{1}{5}\) =
b. 2\(\frac{1}{2}\) + 1\(\frac{3}{5}\) =
c. 1\(\frac{1}{5}\) + 3\(\frac{1}{3}\) =
d. 3\(\frac{2}{3}\) + 1\(\frac{3}{5}\) =
e. 2\(\frac{1}{3}\) + 4\(\frac{4}{7}\) =
f. 3\(\frac{5}{7}\) + 4\(\frac{2}{3}\) =
g. 1\(\frac{1}{5}\) + 4\(\frac{3}{8}\) =
h. 18\(\frac{3}{8}\) + 2\(\frac{2}{5}\) =
Answer:
a. 2\(\frac{1}{2}\) + 1\(\frac{1}{5}\) = 3\(\frac{7}{10}\)
Explanation :
2\(\frac{1}{2}\) + 1\(\frac{1}{5}\) = \(\frac{5}{2}\) + \(\frac{6}{5}\)
lcm of 2 and 5 is 10 .
\(\frac{25}{10}\) + \(\frac{12}{10}\) = \(\frac{37}{10}\) = 3\(\frac{7}{10}\)

b. 2\(\frac{1}{2}\) + 1\(\frac{3}{5}\) = 4 \(\frac{1}{10}\)
Explanation :
2\(\frac{1}{2}\) + 1\(\frac{3}{5}\) = \(\frac{5}{2}\) + \(\frac{8}{5}\)
lcm of 2 and 5 is 10
\(\frac{25}{10}\) + \(\frac{16}{10}\) = \(\frac{41}{10}\) = 4 \(\frac{1}{10}\)

c. 1\(\frac{1}{5}\) + 3\(\frac{1}{3}\) =4\(\frac{8}{15}\)
Explanation :
1\(\frac{1}{5}\) + 3\(\frac{1}{3}\) = \(\frac{6}{5}\) + \(\frac{10}{3}\)
lcm of 5 and 3 is 15.
\(\frac{18}{15}\) + \(\frac{50}{15}\) = \(\frac{68}{15}\) = 4\(\frac{8}{15}\)

d. 3\(\frac{2}{3}\) + 1\(\frac{3}{5}\) = 5\(\frac{4}{15}\)
Explanation :
3\(\frac{2}{3}\) + 1\(\frac{3}{5}\) = \(\frac{11}{3}\) + \(\frac{8}{5}\)
lcm of 3 and 5 = 15 .
\(\frac{55}{15}\) + \(\frac{24}{15}\) = \(\frac{79}{15}\) = 5\(\frac{4}{15}\)

e. 2\(\frac{1}{3}\) + 4\(\frac{4}{7}\) = 6\(\frac{19}{21}\)
Explanation :
2\(\frac{1}{3}\) + 4\(\frac{4}{7}\) = \(\frac{7}{3}\) + \(\frac{32}{7}\)
lcm of 3 and 7 is 21
\(\frac{49}{21}\) + \(\frac{96}{21}\) = \(\frac{145}{21}\) = 6\(\frac{19}{21}\)

f. 3\(\frac{5}{7}\) + 4\(\frac{2}{3}\) = 8 \(\frac{8}{21}\)
Explanation :
3\(\frac{5}{7}\) + 4\(\frac{2}{3}\) = \(\frac{26}{7}\) + \(\frac{14}{3}\)
lcm of 7 and 3 is 21
\(\frac{78}{21}\) + \(\frac{98}{21}\) = \(\frac{176}{21}\) = 8 \(\frac{8}{21}\)

g. 1\(\frac{1}{5}\) + 4\(\frac{3}{8}\) = 4 \(\frac{23}{40}\)
Explanation :
1\(\frac{1}{5}\) + 4\(\frac{3}{8}\) = \(\frac{6}{5}\) + \(\frac{27}{8}\)
lcm of 5 and 8 is 40 .
\(\frac{48}{40}\) + \(\frac{135}{40}\) = \(\frac{183}{40}\) = 4 \(\frac{23}{40}\)

h. 18\(\frac{3}{8}\) + 2\(\frac{2}{5}\) =
Explanation :
18\(\frac{3}{8}\) + 2\(\frac{2}{5}\) = \(\frac{147}{8}\) + \(\frac{12}{5}\)
lcm of 8 and 5 is 40 .
\(\frac{735}{40}\) + \(\frac{96}{40}\) = \(\frac{831}{40}\) = 20\(\frac{31}{40}\)

Question 2.
Angela practiced piano for 2\(\frac{1}{2}\) hours on Friday, 2\(\frac{1}{23}\) hours on Saturday, and 3\(\frac{2}{3}\) hours on Sunday. How much time did Angela practice piano during the weekend?
Answer:
Fraction of hours practiced piano on Friday = 2\(\frac{1}{2}\) hours = \(\frac{5}{2}\)
Fraction of hours practiced piano on Saturday = 2\(\frac{1}{3}\) hours = \(\frac{7}{3}\)
Fraction of hours practiced piano on Sunday = 3\(\frac{2}{3}\) hours = \(\frac{11}{3}\)
Total Fraction of hours practice piano during the weekend = \(\frac{5}{2}\) + \(\frac{7}{3}\) + \(\frac{11}{3}\) = \(\frac{15}{6}\) + \(\frac{14}{6}\) + \(\frac{22}{6}\) = \(\frac{51}{6}\) = \(\frac{17}{2}\) = 8 \(\frac{1}{2}\)
Therefore, Total Fraction of hours practice piano during the weekend = 8 \(\frac{1}{2}\)  .

Question 3..
String A is 3\(\frac{5}{6}\) meters long. String B is 2\(\frac{1}{4}\) meters long. What’s the total length of both strings?
Answer:
Fraction of length of String A = 3\(\frac{5}{6}\) = \(\frac{23}{6}\) meters
Fraction of length of String B = 2\(\frac{1}{4}\) = \(\frac{9}{4}\) meters
Fraction of total length of both strings = \(\frac{23}{6}\) + \(\frac{9}{4}\) = \(\frac{46}{12}\) + \(\frac{27}{12}\) = \(\frac{73}{12}\) = 6\(\frac{1}{12}\) meters .
Therefore, Fraction of total length of both strings = 6\(\frac{1}{12}\) meters .

Question 4.
Matt says that 5 – 1\(\frac{1}{4}\) will be more than 4, since 5 – 1 is 4. Draw a picture to prove that Matt is wrong.
Answer:
Matt is wrong 5 – 1\(\frac{1}{4}\) = 3\(\frac{3}{4}\) which is less than 4 .
Explanation :
5 – 1\(\frac{1}{4}\) = 5 – \(\frac{5}{4}\)
lcm is 4
5 – \(\frac{5}{4}\) = \(\frac{20}{4}\) – \(\frac{5}{4}\) = \(\frac{15}{4}\) = 3\(\frac{3}{4}\)

Engage NY Eureka Math 5th Grade Module 3 Lesson 9 Answer Key

Eureka Math Grade 5 Module 3 Lesson 9 Sprint Answer Key

A
Add and Subtract Fractions with Like Units

Question 1.
\(\frac{1}{5}\) + \(\frac{1}{5}\) =
Answer:
\(\frac{1}{5}\) + \(\frac{1}{5}\) = \(\frac{2}{5}\)

Question 2.
\(\frac{1}{10}\) + \(\frac{5}{10}\) =
Answer:
\(\frac{1}{10}\) + \(\frac{5}{10}\) = \(\frac{6}{10}\) = \(\frac{3}{5}\)

Question 3.
\(\frac{1}{10}\) + \(\frac{7}{10}\) =
Answer:
\(\frac{1}{10}\) + \(\frac{7}{10}\) = \(\frac{8}{10}\) = \(\frac{4}{5}\)

Question 4.
\(\frac{2}{5}\) + \(\frac{2}{5}\) =
Answer:
\(\frac{2}{5}\) + \(\frac{2}{5}\) = \(\frac{4}{5}\)

Question 5.
\(\frac{5}{10}\) – \(\frac{4}{10}\) =
Answer:
\(\frac{5}{10}\) – \(\frac{4}{10}\) = \(\frac{1}{10}\)

Question 6.
\(\frac{3}{5}\) – \(\frac{1}{5}\) =
Answer:
\(\frac{3}{5}\) – \(\frac{1}{5}\) = \(\frac{2}{5}\)

Question 7.
\(\frac{3}{10}\) + \(\frac{3}{10}\) =
Answer:
\(\frac{3}{10}\) + \(\frac{3}{10}\) = \(\frac{6}{10}\) = \(\frac{3}{5}\)

Question 8.
\(\frac{4}{5}\) – \(\frac{1}{5}\) =
Answer:
\(\frac{4}{5}\) – \(\frac{1}{5}\) = \(\frac{3}{5}\)

Question 9.
\(\frac{1}{4}\) + \(\frac{1}{4}\) =
Answer:
\(\frac{1}{4}\) + \(\frac{1}{4}\) = \(\frac{2}{4}\) = \(\frac{1}{2}\)

Question 10.
\(\frac{1}{4}\) + \(\frac{2}{4}\) =
Answer:
\(\frac{1}{4}\) + \(\frac{2}{4}\) = \(\frac{3}{4}\)

Question 11.
\(\frac{3}{12}\) – \(\frac{2}{12}\) =
Answer:
\(\frac{3}{12}\) – \(\frac{2}{12}\) = \(\frac{1}{12}\)

Question 12.
\(\frac{1}{4}\) + \(\frac{3}{4}\) =
Answer:
\(\frac{1}{4}\) + \(\frac{3}{4}\) = \(\frac{4}{4}\) = 1

Question 13.
\(\frac{1}{12}\) + \(\frac{1}{12}\) =
Answer:
\(\frac{1}{12}\) + \(\frac{1}{12}\) = \(\frac{2}{12}\) = \(\frac{1}{6}\)

Question 14.
\(\frac{1}{3}\) + \(\frac{1}{3}\) =
Answer:
\(\frac{1}{3}\) + \(\frac{1}{3}\) = \(\frac{2}{3}\)

Question 15.
\(\frac{3}{12}\) – \(\frac{2}{12}\) =
Answer:
\(\frac{3}{12}\) – \(\frac{2}{12}\) = \(\frac{1}{12}\)

Question 16.
\(\frac{5}{12}\) + \(\frac{6}{12}\) =
Answer:
\(\frac{5}{12}\) + \(\frac{6}{12}\) = \(\frac{11}{12}\)

Question 17.
\(\frac{7}{12}\) + \(\frac{4}{12}\) =
Answer:
\(\frac{7}{12}\) + \(\frac{4}{12}\) = \(\frac{11}{12}\)

Question 18.
\(\frac{4}{6}\) – \(\frac{1}{6}\) =
Answer:
\(\frac{4}{6}\) – \(\frac{1}{6}\) = \(\frac{3}{6}\) = \(\frac{1}{2}\)

Question 19.
\(\frac{1}{6}\) + \(\frac{2}{6}\) =
Answer:
\(\frac{1}{6}\) + \(\frac{2}{6}\) = \(\frac{3}{6}\) = \(\frac{1}{2}\)

Question 20.
\(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) =
Answer:
\(\frac{1}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) = \(\frac{3}{6}\) =  \(\frac{1}{2}\)

Question 21.
\(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) =
Answer:
\(\frac{1}{3}\) + \(\frac{1}{3}\) + \(\frac{1}{3}\) = \(\frac{3}{3}\) = 1

Question 22.
\(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\) =
Answer:
\(\frac{1}{12}\) + \(\frac{1}{12}\) + \(\frac{1}{12}\) = \(\frac{3}{12}\) = \(\frac{1}{4}\)

Question 23.
\(\frac{1}{9}\) + \(\frac{1}{9}\) + \(\frac{1}{9}\) =
Answer:
\(\frac{1}{9}\) + \(\frac{1}{9}\) + \(\frac{1}{9}\) = \(\frac{3}{9}\) =  \(\frac{1}{3}\)

Question 24.
\(\frac{1}{9}\) + \(\frac{3}{9}\) + \(\frac{1}{9}\) =
Answer:
\(\frac{1}{9}\) + \(\frac{3}{9}\) + \(\frac{1}{9}\) = \(\frac{5}{9}\)

Question 25.
\(\frac{4}{9}\) – \(\frac{1}{9}\) – \(\frac{3}{9}\) =
Answer:
\(\frac{4}{9}\) – \(\frac{1}{9}\) – \(\frac{3}{9}\) = \(\frac{8}{9}\)

Question 26.
\(\frac{1}{4}\) + \(\frac{2}{4}\) + \(\frac{1}{4}\) =
Answer:
\(\frac{1}{4}\) + \(\frac{2}{4}\) + \(\frac{1}{4}\) = \(\frac{4}{4}\) = 1

Question 27.
\(\frac{1}{8}\) + \(\frac{3}{8}\) + \(\frac{2}{8}\) =
Answer:
\(\frac{1}{8}\) + \(\frac{3}{8}\) + \(\frac{2}{8}\) = \(\frac{6}{8}\) = \(\frac{3}{4}\)

Question 28.
\(\frac{5}{12}\) + \(\frac{1}{12}\) + \(\frac{5}{12}\) =
Answer:
\(\frac{5}{12}\) + \(\frac{1}{12}\) + \(\frac{5}{12}\) = \(\frac{11}{12}\)

Question 29.
\(\frac{2}{9}\) + \(\frac{3}{9}\) + \(\frac{2}{9}\) =
Answer:
\(\frac{2}{9}\) + \(\frac{3}{9}\) + \(\frac{2}{9}\) = \(\frac{7}{9}\)

Question 30.
\(\frac{3}{10}\) – \(\frac{3}{10}\) + \(\frac{3}{10}\) =
Answer:
\(\frac{3}{10}\) – \(\frac{3}{10}\) + \(\frac{3}{10}\) = \(\frac{9}{10}\)

Question 31.
\(\frac{3}{5}\) – \(\frac{1}{5}\) – \(\frac{1}{5}\) =
Answer:
\(\frac{3}{5}\) – \(\frac{1}{5}\) – \(\frac{1}{5}\) = \(\frac{3}{5}\) – \(\frac{2}{5}\) = \(\frac{1}{5}\)

Question 32.
\(\frac{1}{6}\) + \(\frac{2}{6}\) =
Answer:
\(\frac{1}{6}\) + \(\frac{2}{6}\) = \(\frac{3}{6}\) = \(\frac{1}{2}\) =\

Question 33.
\(\frac{3}{12}\) + \(\frac{4}{12}\) =
Answer:
\(\frac{3}{12}\) + \(\frac{4}{12}\) = \(\frac{7}{12}\)

Question 34.
\(\frac{3}{12}\) + \(\frac{6}{12}\) =
Answer:
\(\frac{3}{12}\) + \(\frac{6}{12}\) = \(\frac{9}{12}\) = \(\frac{3}{4}\)

Question 35.
\(\frac{4}{8}\) + \(\frac{2}{8}\) =
Answer:
\(\frac{4}{8}\) + \(\frac{2}{8}\) = \(\frac{6}{8}\) = \(\frac{3}{4}\)

Question 36.
\(\frac{4}{12}\) + \(\frac{1}{12}\) =
Answer:
\(\frac{4}{12}\) + \(\frac{1}{12}\) = \(\frac{5}{12}\)

Question 37.
\(\frac{1}{5}\) + \(\frac{3}{5}\) =
Answer:
\(\frac{1}{5}\) + \(\frac{3}{5}\) = \(\frac{4}{5}\)

Question 38.
\(\frac{2}{5}\) + \(\frac{2}{5}\) =
Answer:
\(\frac{2}{5}\) + \(\frac{2}{5}\) = \(\frac{4}{5}\)

Question 39.
\(\frac{1}{6}\) + \(\frac{2}{6}\) =
Answer:
\(\frac{1}{6}\) + \(\frac{2}{6}\) = \(\frac{3}{6}\) = \(\frac{1}{2}\)

Question 40.
\(\frac{5}{12}\) – \(\frac{3}{12}\) =
Answer:
\(\frac{5}{12}\) – \(\frac{3}{12}\) = \(\frac{2}{12}\) = \(\frac{1}{6}\)

Question 41.
\(\frac{7}{15}\) – \(\frac{2}{15}\) =
Answer:
\(\frac{7}{15}\) – \(\frac{2}{15}\) = \(\frac{5}{15}\) = \(\frac{1}{3}\)

Question 42.
\(\frac{7}{15}\) – \(\frac{3}{15}\) =
Answer:
\(\frac{7}{15}\) – \(\frac{3}{15}\) = \(\frac{4}{15}\)

Question 43.
\(\frac{11}{15}\) – \(\frac{2}{15}\) =
Answer:
\(\frac{11}{15}\) – \(\frac{2}{15}\) = \(\frac{9}{15}\)

Question 44.
\(\frac{2}{15}\) + \(\frac{4}{15}\) =
Answer:
\(\frac{2}{15}\) + \(\frac{4}{15}\) = \(\frac{6}{15}\) = \(\frac{2}{5}\)

B
Add and Subtract Fractions with Like Units

Question 1.
\(\frac{1}{2}\) + \(\frac{1}{2}\) =
Answer:
\(\frac{1}{2}\) + \(\frac{1}{2}\) = \(\frac{2}{2}\) = 1

Question 2.
\(\frac{2}{8}\) + \(\frac{1}{8}\) =
Answer:
\(\frac{2}{8}\) + \(\frac{1}{8}\) = \(\frac{3}{8}\)

Question 3.
\(\frac{2}{8}\) + \(\frac{3}{8}\) =
Answer:
\(\frac{2}{8}\) + \(\frac{3}{8}\) = \(\frac{5}{8}\)

Question 4.
\(\frac{2}{12}\) – \(\frac{1}{12}\) =
Answer:
\(\frac{2}{12}\) – \(\frac{1}{12}\) = \(\frac{1}{12}\)

Question 5.
\(\frac{5}{12}\) + \(\frac{2}{12}\) =
Answer:
\(\frac{5}{12}\) + \(\frac{2}{12}\) = \(\frac{7}{12}\)

Question 6.
\(\frac{4}{8}\) – \(\frac{3}{8}\) =
Answer:
\(\frac{4}{8}\) – \(\frac{3}{8}\) = \(\frac{1}{8}\)

Question 7.
\(\frac{4}{8}\) – \(\frac{3}{8}\) =
Answer:
\(\frac{4}{8}\) – \(\frac{3}{8}\) = \(\frac{1}{8}\)

Question 8.
\(\frac{1}{8}\) + \(\frac{5}{8}\) =
Answer:
\(\frac{1}{8}\) + \(\frac{5}{8}\) = \(\frac{6}{8}\) = \(\frac{3}{4}\)

Question 9.
\(\frac{3}{4}\) – \(\frac{1}{4}\) =
Answer:
\(\frac{3}{4}\) – \(\frac{1}{4}\) = \(\frac{2}{4}\) = \(\frac{1}{2}\)

Question 10.
\(\frac{3}{6}\) – \(\frac{3}{6}\) =
Answer:
\(\frac{3}{6}\) – \(\frac{3}{6}\) = 0

Question 11.
\(\frac{3}{9}\) + \(\frac{3}{9}\) =
Answer:
\(\frac{3}{9}\) + \(\frac{3}{9}\) = \(\frac{6}{9}\) = \(\frac{2}{3}\)

Question 12.
\(\frac{2}{3}\) + \(\frac{1}{3}\) =
Answer:
\(\frac{2}{3}\) + \(\frac{1}{3}\) = \(\frac{3}{3}\) = 1

Question 13.
\(\frac{6}{9}\) – \(\frac{4}{9}\) =
Answer:
\(\frac{6}{9}\) – \(\frac{4}{9}\) = \(\frac{2}{9}\)

Question 14.
\(\frac{5}{9}\) – \(\frac{3}{9}\) =
Answer:
\(\frac{5}{9}\) – \(\frac{3}{9}\) = \(\frac{2}{9}\)

Question 15.
\(\frac{2}{9}\) + \(\frac{2}{9}\) =
Answer:
\(\frac{2}{9}\) + \(\frac{2}{9}\) = \(\frac{4}{9}\)

Question 16.
\(\frac{1}{12}\) + \(\frac{3}{12}\) =
Answer:
\(\frac{1}{12}\) + \(\frac{3}{12}\) = \(\frac{4}{12}\) = \(\frac{1}{4}\)

Question 17.
\(\frac{5}{12}\) – \(\frac{4}{12}\) =
Answer:
\(\frac{5}{12}\) – \(\frac{4}{12}\) = \(\frac{1}{12}\)

Question 18.
\(\frac{9}{12}\) – \(\frac{6}{12}\) =
Answer:
\(\frac{9}{12}\) – \(\frac{6}{12}\) = \(\frac{3}{12}\) = \(\frac{1}{4}\)

Question 19.
\(\frac{6}{10}\) – \(\frac{4}{10}\) =
Answer:
\(\frac{6}{10}\) – \(\frac{4}{10}\) = \(\frac{2}{10}\) = \(\frac{1}{5}\)

Question 20.
\(\frac{2}{8}\) + \(\frac{2}{8}\) + \(\frac{2}{8}\) =
Answer:
\(\frac{2}{8}\) + \(\frac{2}{8}\) + \(\frac{2}{8}\) = \(\frac{6}{8}\) = \(\frac{3}{4}\)

Question 21.
\(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) =
Answer:
\(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) = \(\frac{3}{10}\) +

Question 22.
\(\frac{7}{12}\) – \(\frac{2}{10}\) – \(\frac{4}{10}\) =
Answer:
\(\frac{7}{12}\) – \(\frac{2}{10}\) – \(\frac{4}{10}\) = \(\frac{7}{12}\) – \(\frac{6}{10}\) = \(\frac{1}{10}\)

Question 23.
\(\frac{1}{12}\) + \(\frac{6}{12}\) + \(\frac{2}{12}\) =
Answer:
\(\frac{1}{12}\) + \(\frac{6}{12}\) + \(\frac{2}{12}\) = \(\frac{9}{12}\) = \(\frac{3}{4}\)

Question 24.
\(\frac{4}{12}\) + \(\frac{3}{12}\) + \(\frac{3}{12}\) =
Answer:
\(\frac{4}{12}\) + \(\frac{3}{12}\) + \(\frac{3}{12}\) = \(\frac{10}{12}\) = \(\frac{5}{6}\)

Question 25.
\(\frac{8}{12}\) – \(\frac{4}{12}\) – \(\frac{4}{12}\) =
Answer:
\(\frac{8}{12}\) – \(\frac{4}{12}\) – \(\frac{4}{12}\) = \(\frac{8}{12}\) – \(\frac{8}{12}\) = 0

Question 26.
\(\frac{1}{10}\) + \(\frac{2}{10}\) + \(\frac{4}{10}\) =
Answer:
\(\frac{1}{10}\) + \(\frac{2}{10}\) + \(\frac{4}{10}\) = \(\frac{7}{10}\)

Question 27.
\(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{6}{10}\) =
Answer:
\(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{6}{10}\) = \(\frac{8}{10}\) = \(\frac{4}{5}\)

Question 28.
\(\frac{4}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) =
Answer:
\(\frac{4}{6}\) + \(\frac{1}{6}\) + \(\frac{1}{6}\) = \(\frac{6}{6}\) = 1

Question 29.
\(\frac{2}{12}\) + \(\frac{3}{12}\) + \(\frac{4}{12}\) =
Answer:
\(\frac{2}{12}\) + \(\frac{3}{12}\) + \(\frac{4}{12}\) = \(\frac{9}{12}\) = \(\frac{3}{4}\)

Question 30.
\(\frac{2}{10}\) + \(\frac{4}{10}\) + \(\frac{4}{10}\) =
Answer:
\(\frac{2}{10}\) + \(\frac{4}{10}\) + \(\frac{4}{10}\) = \(\frac{10}{10}\) = 1

Question 31.
\(\frac{3}{10}\) + \(\frac{1}{10}\) + \(\frac{2}{10}\) =
Answer:
\(\frac{3}{10}\) + \(\frac{1}{10}\) + \(\frac{2}{10}\) = \(\frac{6}{10}\) = \(\frac{3}{5}\)

Question 32.
\(\frac{4}{6}\) – \(\frac{2}{6}\) =
Answer:
\(\frac{4}{6}\) – \(\frac{2}{6}\) = \(\frac{2}{6}\) = \(\frac{1}{3}\)

Question 33.
\(\frac{3}{12}\) – \(\frac{2}{12}\) =
Answer:
\(\frac{3}{12}\) – \(\frac{2}{12}\) = \(\frac{1}{12}\)

Question 34.
\(\frac{2}{3}\) + \(\frac{1}{3}\) =
Answer:
\(\frac{2}{3}\) + \(\frac{1}{3}\) = \(\frac{3}{3}\) = 1

Question 35.
\(\frac{2}{4}\) + \(\frac{1}{4}\) =
Answer:
\(\frac{2}{4}\) + \(\frac{1}{4}\) = \(\frac{3}{4}\)

Question 36.
\(\frac{3}{12}\) + \(\frac{2}{12}\) =
Answer:
\(\frac{3}{12}\) + \(\frac{2}{12}\) = \(\frac{5}{12}\)

Question 37.
\(\frac{1}{5}\) + \(\frac{2}{5}\) =
Answer:
\(\frac{1}{5}\) + \(\frac{2}{5}\) = \(\frac{3}{5}\)

Question 38.
\(\frac{4}{5}\) – \(\frac{4}{5}\) =
Answer:
\(\frac{4}{5}\) – \(\frac{4}{5}\) = 0

Question 39.
\(\frac{5}{12}\) – \(\frac{1}{12}\) =
Answer:
\(\frac{5}{12}\) – \(\frac{1}{12}\) = \(\frac{4}{12}\) = \(\frac{1}{3}\)

Question 40.
\(\frac{6}{8}\) + \(\frac{2}{8}\) =
Answer:
\(\frac{6}{8}\) + \(\frac{2}{8}\) = \(\frac{8}{8}\) = 1

Question 41.
\(\frac{2}{8}\) + \(\frac{2}{8}\) + \(\frac{2}{8}\) =
Answer:
\(\frac{2}{8}\) + \(\frac{2}{8}\) + \(\frac{2}{8}\) = \(\frac{6}{8}\) = \(\frac{3}{4}\)

Question 42.
\(\frac{9}{10}\) – \(\frac{7}{10}\) – \(\frac{1}{10}\) =
Answer:
\(\frac{9}{10}\) – \(\frac{7}{10}\) – \(\frac{1}{10}\) = \(\frac{9}{10}\) – \(\frac{8}{10}\) = \(\frac{1}{10}\) =

Question 43.
\(\frac{2}{10}\) + \(\frac{5}{10}\) + \(\frac{2}{10}\) =
Answer:
\(\frac{2}{10}\) + \(\frac{5}{10}\) + \(\frac{2}{10}\) = \(\frac{9}{10}\)

Question 44.
\(\frac{9}{12}\) – \(\frac{1}{12}\) – \(\frac{4}{12}\) =
Answer:
\(\frac{9}{12}\) – \(\frac{1}{12}\) – \(\frac{4}{12}\) = \(\frac{9}{12}\) – \(\frac{5}{12}\) = \(\frac{4}{12}\) = \(\frac{1}{3}\)  .

Eureka Math Grade 5 Module 3 Lesson 9 Problem Set Answer Key

Question 1.
First make like units, and then add.
a. \(\frac{3}{4}\) + \(\frac{1}{7}\) =
b. \(\frac{1}{4}\) + \(\frac{9}{8}\) =
c. \(\frac{3}{8}\) + \(\frac{3}{7}\) =
d. \(\frac{4}{9}\) + \(\frac{4}{7}\) =
e. \(\frac{1}{5}\) + \(\frac{2}{3}\) =
f. \(\frac{3}{4}\) + \(\frac{5}{6}\) =
g. \(\frac{2}{3}\) + \(\frac{1}{11}\) =
h. \(\frac{3}{4}\) + 1\(\frac{1}{10}\) =
Answer:
a.
\(\frac{3}{4}\) + \(\frac{1}{7}\)
lcm of 4 and 7 is 28
=\(\frac{21}{28}\) + \(\frac{4}{28}\) = \(\frac{25}{28}\)
b.
\(\frac{1}{4}\) + \(\frac{9}{8}\)
lcm of 4 and 8 is 8
\(\frac{2}{8}\) + \(\frac{9}{8}\) =\(\frac{11}{8}\) = 1\(\frac{3}{8}\)
c.
\(\frac{3}{8}\) + \(\frac{3}{7}\)
lcm of 8 and 7 is 56
\(\frac{21}{56}\) + \(\frac{24}{56}\) = \(\frac{45}{56}\)
d.
\(\frac{4}{9}\) + \(\frac{4}{7}\)
lcm of 9 and 7 is 63
\(\frac{28}{63}\) + \(\frac{36}{63}\) = \(\frac{64}{63}\) = 1\(\frac{1}{63}\)
e.
\(\frac{1}{5}\) + \(\frac{2}{3}\)
lcm of 5 and 3 is 15 .
\(\frac{3}{15}\) + \(\frac{10}{15}\) = \(\frac{13}{15}\)
f.
\(\frac{3}{4}\) + \(\frac{5}{6}\)
lcm of 4 and 6 is 12.
\(\frac{9}{12}\) + \(\frac{10}{12}\) = \(\frac{19}{12}\) =1 \(\frac{7}{12}\)
g.
\(\frac{2}{3}\) + \(\frac{1}{11}\)
lcm of 3 and 11 is 33
\(\frac{22}{33}\) + \(\frac{3}{33}\) = \(\frac{25}{33}\)
h.
\(\frac{3}{4}\) + 1\(\frac{1}{10}\) = \(\frac{3}{4}\) + \(\frac{11}{10}\)
lcm of 4 and 10 is 20.
\(\frac{15}{20}\) + \(\frac{22}{10}\) = \(\frac{37}{20}\) = 1\(\frac{17}{20}\)

Question 2.
Whitney says that to add fractions with different denominators, you always have to multiply the denominators to find the common unit; for example:
\(\frac{1}{4}+\frac{1}{6}=\frac{6}{24}+\frac{4}{24}\)
Show Whitney how she could have chosen a denominator smaller than 24, and solve the problem.
Answer:
multiples of 4 and 6 are
4 : 4, 8, 12, 16, 20, 24
6: 6, 12, 18, 24, 30 .
12 and 24 are the common multiplies of 4 and 6. smaller than 24 we get 12 multiple .
(\(\frac{1 × 3}{4 × 3}\)) + (\(\frac{1 × 2}{6 × 2}\)) = \(\frac{3}{12}\) + \(\frac{2}{12}\) = \(\frac{5}{12}\)

Question 3.
Jackie brought \(\frac{3}{4}\) of a gallon of iced tea to the party. Bill brought \(\frac{7}{8}\) of a gallon of iced tea to the same party. How much iced tea did Jackie and Bill bring to the party?
Answer:
Fraction of iced tea brought by Jackie = \(\frac{3}{4}\)
Fraction of iced tea brought by Bill = \(\frac{7}{8}\)
Total Fraction of iced tea brought to party = \(\frac{3}{4}\) + \(\frac{7}{8}\)  = \(\frac{6}{8}\) + \(\frac{7}{8}\) = \(\frac{13}{8}\) = 1\(\frac{5}{8}\)
Therefore, Total Fraction of iced tea brought to party = \(\frac{13}{8}\) = 1\(\frac{5}{8}\) .

Question 4.
Madame Curie made some radium in her lab. She used \(\frac{2}{5}\) kg of the radium in an experiment and had 1\(\frac{1}{4}\) kg left. How much radium did she have at first? (Extension: If she performed the experiment twice, how much radium would she have left?)
Answer:
Quantity of Radium made by Madam Curie = x kgs
Fraction of Quantity of Radium used by Experiment = \(\frac{2}{5}\) kg
Fraction of Quantity of Radium left = 1\(\frac{1}{4}\) kg = \(\frac{5}{4}\) kg
Quantity of Radium made by Madam Curie = \(\frac{2}{5}\) + \(\frac{5}{4}[/latex
lcm of 5 and 4 is 20 .
[latex]\frac{8}{20}\)  + \(\frac{25}{20}\) = \(\frac{33}{20}\) =1\(\frac{13}{20}\) .
Therefore if the experiment is done once the Total Quantity = \(\frac{33}{20}\) =1\(\frac{13}{20}\)
If the Experiment if done twiced .
Total Quantity – Quantity Used for Experiment twice = left Quantity .
\(\frac{33}{20}\) – 2 × \(\frac{2}{5}\) = \(\frac{33}{20}\) –  \(\frac{4}{5}\) = \(\frac{33}{20}\) – \(\frac{16}{20}\) = \(\frac{17}{20}\)
Therefore if the experiment is done once the Total Quantity = \(\frac{17}{20}\)

Eureka Math Grade 5 Module 3 Lesson 9 Exit Ticket Answer Key

Make like units, and then add.
a. \(\frac{1}{6}\) + \(\frac{3}{4}\) =
b. 1\(\frac{1}{2}\) + \(\frac{2}{5}\) =
Answer:
a.
\(\frac{1}{6}\) + \(\frac{3}{4}\)
lcm of 6 and 4 is 12
\(\frac{2}{12}\) + \(\frac{9}{12}\) = \(\frac{11}{12}\)
b.
1\(\frac{1}{2}\) + \(\frac{2}{5}\) = \(\frac{3}{2}\) + \(\frac{2}{5}\)
lcm of 2 and 5 is 10.
\(\frac{15}{10}\) + \(\frac{4}{10}\) =\(\frac{19}{10}\) = 1\(\frac{9}{10}\)

Eureka Math Grade 5 Module 3 Lesson 9 Homework Answer Key

Question 1.
Make like units, and then add.
a. \(\frac{3}{5}\) + \(\frac{1}{3}\) =
b. \(\frac{3}{5}\) + \(\frac{1}{11}\) =
c. \(\frac{2}{9}\) + \(\frac{5}{6}\) =
d. \(\frac{2}{5}\) + \(\frac{1}{4}\) + \(\frac{1}{10}\) =
e. \(\frac{1}{3}\) + \(\frac{7}{5}\) =
f. \(\frac{5}{8}\) + \(\frac{7}{12}\) =
g. 1\(\frac{1}{3}\) + \(\frac{3}{4}\) =
h. \(\frac{5}{6}\) + 1\(\frac{1}{4}\) =
Answer:
a.
\(\frac{3}{5}\) + \(\frac{1}{3}\)
lcm of 5 and 3 is 15
\(\frac{9}{15}\) + \(\frac{5}{15}\) = \(\frac{14}{15}\)
b.
\(\frac{3}{5}\) + \(\frac{1}{11}\)
lcm of 5 and 11 is 55
\(\frac{33}{55}\) + \(\frac{5}{55}\) = \(\frac{38}{55}\)
c.
\(\frac{2}{9}\) + \(\frac{5}{6}\)
lcm of 9 and 6 is 18 .
\(\frac{4}{18}\) + \(\frac{15}{18}\) = \(\frac{19}{18}\) = 1 \(\frac{1}{18}\)
d.
\(\frac{2}{5}\) + \(\frac{1}{4}\) + \(\frac{1}{10}\)
lcm of 5 , 4 and 10 is 20 .
\(\frac{8}{20}\) + \(\frac{5}{20}\) + \(\frac{2}{20}\) = \(\frac{15}{20}\)= \(\frac{3}{4}\)
e.
\(\frac{1}{3}\) + \(\frac{7}{5}\)
lcm of 3 and 5 is 15 .
\(\frac{5}{15}\) + \(\frac{21}{15}\) =\(\frac{26}{3}\) =1\(\frac{11}{15}\)
f.
\(\frac{5}{8}\) + \(\frac{7}{12}\)
lcm of 8 and 12 is 24.
\(\frac{15}{24}\) + \(\frac{14}{24}\) = \(\frac{29}{24}\) = 1\(\frac{5}{24}\)
g.
1\(\frac{1}{3}\) + \(\frac{3}{4}\) = \(\frac{4}{3}\) + \(\frac{3}{4}\)
lcm of 3 and 4  is 12
\(\frac{16}{12}\) + \(\frac{9}{12}\) = \(\frac{25}{12}\) = 2 \(\frac{1}{12}\)
h.
\(\frac{5}{6}\) + 1\(\frac{1}{4}\) =\(\frac{5}{6}\) + \(\frac{5}{4}\)
lcm of 4 and 6 is 12 .
\(\frac{10}{12}\) + \(\frac{15}{12}\) = \(\frac{25}{12}\) = 2\(\frac{1}{12}\)

Question 2.
On Monday, Ka practiced guitar for \(\frac{2}{3}\) of one hour. When she finished, she practiced piano for \(\frac{3}{4}\) of one hour. How much time did Ka spend practicing instruments on Monday?
Answer:
Fraction of Time spent in playing guitar of one hour = \(\frac{2}{3}\)
Fraction of Time spent in playing guitar when finished = \(\frac{3}{4}\)
Total Time taken for practicing = \(\frac{2}{3}\) + \(\frac{3}{4}\) = \(\frac{8}{12}\) + \(\frac{9}{12}\) = \(\frac{17}{12}\) = 1\(\frac{5}{12}\) hour .
Therefore, Total Time taken in practicing = \(\frac{17}{12}\) = 1\(\frac{5}{12}\) hour

Question 3.
Ms. How bought a bag of rice for dinner. She used \(\frac{3}{5}\) kg of the rice and still had 2\(\frac{1}{4}\) kg left. How heavy was the bag of rice that Ms. How bought?
Answer:
Fraction of Quantity of rice used = \(\frac{3}{5}\) kg
Fraction of Quantity of rice left = 2\(\frac{1}{4}\) kg
Total Quantity of rice = \(\frac{3}{5}\)  + 2\(\frac{1}{4}\)  = \(\frac{3}{5}\) + \(\frac{9}{4}\)
= \(\frac{12}{20}\) + \(\frac{45}{20}\) =\(\frac{57}{20}\) = 2\(\frac{17}{20}\)
Therefore, Total Quantity of rice = \(\frac{57}{20}\) = 2\(\frac{17}{20}\) .

Question 4.
Joe spends \(\frac{2}{5}\) of his money on a jacket and \(\frac{3}{8}\) of his money on a shirt. He spends the rest on a pair of pants. What fraction of his money does he use to buy the pants?
Answer:
Money spent on jacket = \(\frac{2}{5}\)
Money spent on a shirt = \(\frac{3}{8}\)
Money spent on pair of pants = x
1 = \(\frac{2}{5}\) + \(\frac{3}{8}\)  + x
lcm of 5 and 8 is 40.
\(\frac{40}{40}\)  = \(\frac{16}{40}\) + \(\frac{10}{40}\) +x
\(\frac{40}{40}\)  = \(\frac{26}{40}\) + x
x = \(\frac{40}{40}\)  – \(\frac{13}{40}\)
x = \(\frac{27}{40}\)

Engage NY Eureka Math 5th Grade Module 3 Lesson 8 Answer Key

Eureka Math Grade 5 Module 3 Lesson 8 Problem Set Answer Key

Question 1.
Add or subtract.
a. 2 + 1\(\frac{1}{5}\) =
b. 2 – 1\(\frac{3}{8}\) =
c. 5\(\frac{2}{5}\) + 2\(\frac{3}{5}\)=
d. 4 – 2\(\frac{2}{7}\) =
e. 9\(\frac{3}{4}\) + 8 =
f. 17 – 15\(\frac{2}{3}\) =
g. 15 + 17 \(\frac{2}{3}\) =
h. 100 – 20\(\frac{7}{8}\) =
Answer:
a.
2 + 1\(\frac{1}{5}\) = 2 + \(\frac{6}{5}\)
lcm of 5 and 1 is 5
\(\frac{10}{5}\)  + \(\frac{6}{5}\)
\(\frac{16}{5}\)
3\(\frac{1}{5}\)

b.
2 – 1\(\frac{3}{8}\)
2 – \(\frac{11}{8}\)
lcm is 8
2 – \(\frac{11}{8}\)
\(\frac{16}{8}\) – \(\frac{11}{8}\)
\(\frac{5}{8}\)

c.
5\(\frac{2}{5}\) + 2\(\frac{3}{5}\)
\(\frac{27}{5}\) + \(\frac{13}{5}\)
\(\frac{40}{5}\) = 8

d.
4 – 2\(\frac{2}{7}\) = 4 – \(\frac{16}{7}\)
lcm of 1 and 7 is 7
\(\frac{28}{7}\) – \(\frac{16}{7}\) =\(\frac{12}{7}\)
e.
9\(\frac{3}{4}\) + 8 = \(\frac{39}{4}\) + 8
lcm of 1 and 4 is 4 .
\(\frac{39}{4}\) + \(\frac{32}{4}\)  = \(\frac{71}{4}\) =17 \(\frac{2}{4}\)
f.
17 – 15\(\frac{2}{3}\) = 17 – \(\frac{47}{3}\)
lcm is 3
\(\frac{51}{3}\) – \(\frac{47}{3}\) = \(\frac{4}{3}\)
g.
15 + 17 \(\frac{2}{3}\) = 15 + \(\frac{53}{3}\)
lcm is 3
\(\frac{45}{3}\) + \(\frac{53}{3}\) = \(\frac{98}{3}\) = 32\(\frac{1}{3}\)
h.
100 – 20\(\frac{7}{8}\) = 100 – \(\frac{167}{8}\)
lcm is 8
\(\frac{800}{8}\) – \(\frac{167}{8}\) = \(\frac{733}{8}\) = 91\(\frac{5}{8}\)

Question 2.
Calvin had 30 minutes in time-out. For the first 23\(\frac{1}{3}\) minutes, Calvin counted spots on the ceiling. For the rest of the time, he made faces at his stuffed tiger. How long did Calvin spend making faces at his tiger?
Answer:
Number of Minutes of Time-out =30 minutes .
Fraction of Minutes did calvin counted spots on ceiling = 23\(\frac{1}{3}\) minutes
Fraction of Minutes did calvin did faces at his stuffed tiger = x
30 minutes = 23\(\frac{1}{3}\) + x
lcm is 3
30 minutes = \(\frac{70}{3}\) + x
\(\frac{90}{3}\) = \(\frac{70}{3}\) + x
x = \(\frac{90}{3}\) – \(\frac{70}{3}\)
x = \(\frac{20}{3}\)
Therefore, Fraction of Minutes did calvin did faces at his stuffed tiger = x = \(\frac{20}{3}\) .

Question 3.
Linda planned to spend 9 hours practicing piano this week. By Tuesday, she had spent 2\(\frac{1}{2}\) hours practicing. How much longer does she need to practice to reach her goal?
Answer:
Number of Hours required to practice = 9 hours .
Fraction of hours practiced till Tuesday = 2\(\frac{1}{2}\) hours.
Fraction of hours needed to practice to reach goal = x
9 hours = 2\(\frac{1}{2}\)  + x
lcm is 2
9 = \(\frac{5}{2}\) + x
\(\frac{18}{2}\) = \(\frac{5}{2}\) + x
x = \(\frac{18}{2}\) – \(\frac{5}{2}\)
x = \(\frac{13}{2}\) .
Therefore Fraction of hours needed to practice to reach goal =x = \(\frac{13}{2}\) .

Question 4.
Gary says that 3-1\(\frac{1}{3}\) will be more than 2, since 3 – 1 is 2. Draw a picture to prove that Gary is wrong.
Answer:
Gray is wrong
Explanation :
3-1\(\frac{1}{3}\) = 3 – \(\frac{4}{3}\)
lcm is 3
\(\frac{9}{3}\) – \(\frac{4}{3}\)  = \(\frac{5}{3}\)

Eureka Math Grade 5 Module 3 Lesson 8 Exit Ticket Answer Key

Add or subtract.
a. 5 + 1\(\frac{7}{8}\) =
b. 3 – 1\(\frac{3}{4}\) =
c. 7\(\frac{3}{8}\) + 4=
d. 4 – 2\(\frac{3}{7}\) =
Answer:
a.
5 + 1\(\frac{7}{8}\) = 5 + \(\frac{15}{8}\)
lcm of 1 and 8 is 8
\(\frac{40}{8}\) + \(\frac{15}{8}\)  = \(\frac{55}{8}\) = 6\(\frac{7}{8}\) .
b.
3 – 1\(\frac{3}{4}\) = 3 – \(\frac{7}{4}\)
lcm is 4
\(\frac{12}{4}\) – \(\frac{7}{4}\) = \(\frac{5}{4}\) =1\(\frac{1}{4}\)
c.
7\(\frac{3}{8}\) + 4= \(\frac{59}{8}\) + 4
lcm of 1 and 8 is 8
\(\frac{59}{8}\) +\(\frac{32}{8}\) = \(\frac{91}{8}\) =11\(\frac{3}{8}\) .
d.
4 – 2\(\frac{3}{7}\) = 4 – \(\frac{17}{7}\)
lcm of 1 and 7 is 7
\(\frac{28}{7}\) – \(\frac{17}{7}\) = \(\frac{11}{7}\) =1\(\frac{4}{7}\) .

Eureka Math Grade 5 Module 3 Lesson 8 Homework Answer Key

Question 1.
Add or subtract.
a. 3 + 1\(\frac{1}{4}\) =
b. 2 – 1\(\frac{5}{8}\) =
c. 5\(\frac{2}{5}\) + 2 \(\frac{3}{5}\) =
d. 4 – 2\(\frac{5}{7}\) =
e. 8\(\frac{4}{5}\) + 7 =
f. 18 – 15\(\frac{3}{4}\) =
g. 16 + 18\(\frac{5}{6}\) =
h. 100 -50\(\frac{3}{8}\) =
Answer:
a.
3 + 1\(\frac{1}{4}\) = 3 + \(\frac{5}{4}\)
lcm of 1 and 4 is 4
\(\frac{12}{4}\) + \(\frac{5}{4}\) = \(\frac{17}{4}\) = 4\(\frac{1}{4}\) .
b.
2 – 1\(\frac{5}{8}\) = 2 – \(\frac{13}{8}\)
lcm is 8
\(\frac{16}{8}\)  – \(\frac{13}{8}\) =\(\frac{3}{8}\) .
c.
5\(\frac{2}{5}\) + 2 \(\frac{3}{5}\) = \(\frac{27}{5}\) + \(\frac{13}{5}\) = \(\frac{40}{5}\) = 8.
d.
4 – 2\(\frac{5}{7}\) = 4 – \(\frac{19}{7}\)
lcm of 1 and 7 is 7 .
\(\frac{28}{7}\)  – \(\frac{19}{7}\) = \(\frac{9}{7}\) =1\(\frac{2}{7}\)
e.
8\(\frac{4}{5}\) + 7 = \(\frac{44}{5}\) + 7
lcm of  5 and 7 is  35.
\(\frac{308}{35}\) + \(\frac{245}{35}\) = \(\frac{553}{35}\) =15 \(\frac{28}{35}\)
f.
18 – 15\(\frac{3}{4}\) = 18 – \(\frac{63}{4}\)
lcm of 1 and 4 is 4.
18 – \(\frac{63}{4}\)  = \(\frac{72}{4}\) – \(\frac{63}{4}\)  = \(\frac{9}{4}\) =2\(\frac{1}{4}\)
g.
16 + 18\(\frac{5}{6}\) = 16 + \(\frac{113}{6}\)
lcm is 6
\(\frac{96}{6}\) + \(\frac{113}{6}\)  = \(\frac{209}{6}\) = 34\(\frac{5}{6}\)
h.
100 -50\(\frac{3}{8}\) = 100 –\(\frac{403}{8}\)
lcm of 1 and 8 is 8 .
\(\frac{800}{8}\) – \(\frac{403}{8}\) = \(\frac{397}{8}\) = 49\(\frac{5}{8}\) .

Question 2.
The total length of two ribbons is 13 meters. If one ribbon is 7\(\frac{5}{8}\) meters long, what is the length of the other ribbon?
Answer:
The total length of two ribbons = 13 meters.
Fraction of length of one ribbon = 7\(\frac{5}{8}\)
Fraction of length of other ribbon = x
13 = 7\(\frac{5}{8}\) + x
13 = \(\frac{61}{8}\) + x
lcm of 1 and 8 is 8
\(\frac{104}{8}\) = \(\frac{61}{8}\) + x
x = \(\frac{104}{8}\) – \(\frac{61}{8}\)
x = \(\frac{43}{8}\) = 5 \(\frac{3}{8}\)
Therefore, Fraction of length of other ribbon = x  = \(\frac{43}{8}\) = 5 \(\frac{3}{8}\) .

Question 3.
It took Sandy two hours to jog 13 miles. She ran 7\(\frac{1}{2}\) miles in the first hour. How far did she run during the second hour?
Answer:
Distance traveled by sandy in 2 hours = 13 miles.
Distance traveled in one hour = 7\(\frac{1}{2}\) miles
Distance traveled in second hour = x
13 miles = 7\(\frac{1}{2}\) + x miles.
13 = \(\frac{15}{2}\) + x
lcm of 1 and 2 is 2 .
\(\frac{26}{2}\) = \(\frac{15}{2}\) + x
x = \(\frac{26}{2}\) – \(\frac{15}{2}\)
x = \(\frac{11}{2}\) = 5\(\frac{1}{2}\) .
Therefore, Distance traveled in second hour = x = \(\frac{11}{2}\) = 5\(\frac{1}{2}\)

Question 4.
Andre says that 5\(\frac{3}{4}\) + 2\(\frac{1}{4}\) = 7\(\frac{1}{2}\) because 7\(\frac{4}{8}\) = 7 \(\frac{1}{2}\). Identify his mistake. Draw a picture to prove that he is wrong.
Answer:
5\(\frac{3}{4}\) + 2\(\frac{1}{4}\) = 7\(\frac{1}{2}\)
5\(\frac{3}{4}\) + 2\(\frac{1}{4}\) = \(\frac{23}{4}\) + \(\frac{9}{4}\) = \(\frac{32}{4}\) = 8
that means andre subtracted \(\frac{3}{4}\) and \(\frac{1}{4}\) instead of adding

Engage NY Eureka Math 5th Grade Module 3 Lesson 7 Answer Key

Eureka Math Grade 5 Module 3 Lesson 7 Sprint Answer Key

A
Circle the Equivalent Fraction

Question 1.
\(\frac{2}{4}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{2}{4}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{2}{4}\) when its numerator and denominator is divided by 2 we get \(\frac{1}{2}\)

Question 2.
\(\frac{2}{6}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{2}{6}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{2}{6}\) when its numerator and denominator is divided by 2 we get \(\frac{1}{3}\)

Question 3.
\(\frac{2}{8}\) = \(\frac{1}{2}\) \(\frac{1}{4}\)
Answer:
\(\frac{2}{8}\) = \(\frac{1}{4}\)
Explanation :
\(\frac{2}{8}\) when its numerator and denominator is divided by 2 we get \(\frac{1}{4}\)

Question 4.
\(\frac{5}{10}\) = \(\frac{1}{2}\) \(\frac{1}{4}\)
Answer:
\(\frac{5}{10}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{5}{10}\) when its numerator and denominator is divided by 5 we get \(\frac{1}{2}[/latex

Question 5.
[latex]\frac{5}{15}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{5}{15}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{5}{15}\) when its numerator and denominator is divided by 5 we get \(\frac{1}{3}\)

Question 6.
\(\frac{5}{20}\) = \(\frac{1}{2}\) \(\frac{1}{4}\)
Answer:
\(\frac{5}{20}\) = \(\frac{1}{4}\)
Explanation :
\(\frac{5}{20}\) when its numerator and denominator is divided by 5 we get \(\frac{1}{4}\)

Question 7.
\(\frac{4}{8}\) = \(\frac{1}{2}\) \(\frac{1}{4}\)
Answer:
\(\frac{4}{8}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{4}{8}\) when its numerator and denominator is divided by 4 we get \(\frac{1}{2}\)

Question 8.
\(\frac{4}{12}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{4}{12}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{4}{12}\) when its numerator and denominator is divided by 4 we get \(\frac{1}{3}\)

Question 9.
\(\frac{4}{16}\) = \(\frac{1}{2}\) \(\frac{1}{4}\)
Answer:
\(\frac{4}{16}\) = \(\frac{1}{4}\)
Explanation :
\(\frac{4}{16}\) when its numerator and denominator is divided by 4 we get \(\frac{1}{4}\)

Question 10.
\(\frac{3}{6}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{3}{6}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{3}{6}\) when its numerator and denominator is divided by 3 we get \(\frac{1}{2}\)

Question 11.
\(\frac{3}{9}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{3}{9}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{3}{9}\) when its numerator and denominator is divided by 3 we get \(\frac{1}{3}\)

Question 12.
\(\frac{3}{12}\) = \(\frac{1}{2}\) \(\frac{1}{4}\)
Answer:
\(\frac{3}{12}\) = \(\frac{1}{4}\)
Explanation :
\(\frac{3}{12}\) when its numerator and denominator is divided by 3 we get \(\frac{1}{4}\)

Question 13.
\(\frac{4}{6}\) = \(\frac{2}{3}\) \(\frac{1}{3}\)
Answer:
\(\frac{4}{6}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{4}{6}\) when its numerator and denominator is divided by 2 we get \(\frac{2}{3}\)

Question 14.
\(\frac{6}{12}\) = \(\frac{2}{3}\) \(\frac{1}{2}\)
Answer:
\(\frac{6}{12}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{6}{12}\) when its numerator and denominator is divided by 6 we get \(\frac{1}{2}\)

Question 15.
\(\frac{6}{18}\) = \(\frac{2}{3}\) \(\frac{1}{3}\)
Answer:
\(\frac{6}{18}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{6}{18}\) when its numerator and denominator is divided by 6 we get \(\frac{1}{3}\)

Question 16.
\(\frac{6}{30}\) = \(\frac{1}{5}\) \(\frac{1}{3}\)
Answer:
\(\frac{6}{30}\) = \(\frac{1}{5}\)
Explanation :
\(\frac{6}{30}\) when its numerator and denominator is divided by 6 we get \(\frac{1}{5}\)

Question 17.
\(\frac{6}{9}\) = \(\frac{2}{3}\) \(\frac{1}{3}\)
Answer:
\(\frac{6}{9}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{6}{9}\) when its numerator and denominator is divided by 3 we get \(\frac{2}{3}\)

Question 18.
\(\frac{7}{14}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{7}{14}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{7}{14}\) when its numerator and denominator is divided by 7 we get \(\frac{1}{2}\)

Question 19.
\(\frac{7}{21}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{7}{21}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{7}{21}\) when its numerator and denominator is divided by 7 we get \(\frac{1}{3}\)

Question 20.
\(\frac{7}{42}\) = \(\frac{1}{6}\) \(\frac{1}{7}\)
Answer:
\(\frac{7}{42}\) = \(\frac{1}{6}\)
Explanation :
\(\frac{7}{42}\) when its numerator and denominator is divided by 7 we get \(\frac{1}{6}\)

Question 21.
\(\frac{8}{12}\) = \(\frac{2}{3}\) \(\frac{3}{4}\)
Answer:
\(\frac{8}{12}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{8}{12}\) when its numerator and denominator is divided by 4 we get \(\frac{2}{3}\)

Question 22.
\(\frac{9}{18}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{9}{18}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{9}{18}\) when its numerator and denominator is divided by 9 we get \(\frac{1}{2}\)

Question 23.
\(\frac{9}{27}\) = \(\frac{2}{3}\) \(\frac{1}{3}\) \(\frac{1}{4}\)
Answer:
\(\frac{9}{27}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{9}{27}\) when its numerator and denominator is divided by 9 we get \(\frac{1}{3}\)

Question 24.
\(\frac{9}{63}\) = \(\frac{1}{6}\) \(\frac{1}{7}\) \(\frac{1}{8}\)
Answer:
\(\frac{9}{63}\) = \(\frac{1}{7}\)
Explanation :
\(\frac{9}{63}\) when its numerator and denominator is divided by 9 we get \(\frac{1}{7}\)

Question 25.
\(\frac{8}{12}\) = \(\frac{2}{3}\) \(\frac{3}{4}\) \(\frac{4}{5}\)
Answer:
\(\frac{8}{12}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{8}{12}\) when its numerator and denominator is divided by 4 we get \(\frac{2}{3}\)

Question 26.
\(\frac{8}{16}\) = \(\frac{1}{2}\) \(\frac{1}{3}\) \(\frac{1}{4}\)
Answer:
\(\frac{8}{16}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{8}{16}\) when its numerator and denominator is divided by 8 we get \(\frac{1}{2}\)

Question 27.
\(\frac{8}{24}\) = \(\frac{1}{2}\) \(\frac{1}{3}\) \(\frac{1}{4}\)
Answer:
\(\frac{8}{24}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{8}{24}\) when its numerator and denominator is divided by 8 we get \(\frac{1}{3}\)

Question 28.
\(\frac{8}{64}\) = \(\frac{1}{7}\) \(\frac{1}{8}\) \(\frac{1}{9}\)
Answer:
\(\frac{8}{64}\) = \(\frac{1}{8}\)
Explanation :
\(\frac{8}{64}\) when its numerator and denominator is divided by 8 we get \(\frac{1}{8}\)

Question 29.
\(\frac{12}{18}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{12}{18}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{12}{18}\) when its numerator and denominator is divided by 6 we get \(\frac{2}{3}\)

Question 30.
\(\frac{12}{16}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{12}{16}\) = \(\frac{3}{4}\)
Explanation :
\(\frac{12}{16}\) when its numerator and denominator is divided by 4 we get \(\frac{3}{4}\)

Question 31.
\(\frac{9}{12}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{9}{12}\) = \(\frac{3}{4}\)
Explanation :
\(\frac{9}{12}\) when its numerator and denominator is divided by 3 we get \(\frac{3}{4}\)

Question 32.
\(\frac{6}{8}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{6}{8}\) = \(\frac{3}{4}\)
Explanation :
\(\frac{6}{8}\) when its numerator and denominator is divided by 2 we get \(\frac{3}{4}\)

Question 33.
\(\frac{10}{12}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{10}{12}\) = \(\frac{5}{6}\)
Explanation :
\(\frac{10}{12}\) when its numerator and denominator is divided by 2 we get \(\frac{5}{6}\)

Question 34.
\(\frac{15}{18}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{15}{18}\) = \(\frac{5}{6}\)
Explanation :
\(\frac{15}{18}\) when its numerator and denominator is divided by 3 we get \(\frac{5}{6}\)

Question 35.
\(\frac{8}{10}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{8}{10}\) = \(\frac{4}{5}\)
Explanation :
\(\frac{8}{10}\) when its numerator and denominator is divided by 2 we get \(\frac{4}{5}\)

Question 36.
\(\frac{16}{20}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{16}{20}\) = \(\frac{4}{5}\)
Explanation :
\(\frac{16}{20}\) when its numerator and denominator is divided by 4 we get \(\frac{4}{5}\)

Question 37.
\(\frac{12}{15}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{12}{15}\) = \(\frac{4}{5}\)
Explanation :
\(\frac{12}{15}\) when its numerator and denominator is divided by 3 we get \(\frac{4}{5}\)

Question 38.
\(\frac{18}{27}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{18}{27}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{18}{27}\) when its numerator and denominator is divided by 9 we get \(\frac{2}{3}\)

Question 39.
\(\frac{27}{36}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{27}{36}\) = \(\frac{3}{4}\)
Explanation :
\(\frac{27}{36}\) when its numerator and denominator is divided by 9 we get \(\frac{3}{4}\)

Question 40.
\(\frac{32}{40}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{32}{40}\) = \(\frac{4}{5}\)
Explanation :
\(\frac{32}{40}\) when its numerator and denominator is divided by 8 we get \(\frac{4}{5}\)

Question 41.
\(\frac{45}{54}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{5}{6}\)
Answer:
\(\frac{45}{54}\) = \(\frac{5}{6}\)
Explanation :
\(\frac{45}{54}\) when its numerator and denominator is divided by 9 we get \(\frac{5}{6}\)

Question 42.
\(\frac{24}{36}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{24}{36}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{24}{36}\) when its numerator and denominator is divided by 12 we get \(\frac{2}{3}\)

Question 43.
\(\frac{60}{72}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{60}{72}\) = \(\frac{5}{6}\)
Explanation :
\(\frac{60}{72}\) when its numerator and denominator is divided by 12 we get \(\frac{5}{6}\)

Question 44.
\(\frac{48}{60}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{5}{6}\)
Answer:
\(\frac{48}{60}\) = \(\frac{4}{5}\)
Explanation :
\(\frac{48}{60}\) when its numerator and denominator is divided by 12 we get \(\frac{4}{5}\)

B
Circle the Equivalent Fraction

Question 1.
\(\frac{5}{10}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{5}{10}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{5}{10}\) when its numerator and denominator is divided by 5 we get \(\frac{1}{2}\)

Question 2.
\(\frac{5}{15}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{5}{15}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{5}{15}\) when its numerator and denominator is divided by 5 we get \(\frac{1}{3}\)

Question 3.
\(\frac{5}{20}\) = \(\frac{1}{2}\) \(\frac{1}{4}\)
Answer:
\(\frac{5}{20}\) = \(\frac{1}{4}\)
Explanation :
\(\frac{5}{20}\) when its numerator and denominator is divided by 5 we get \(\frac{1}{4}\)

Question 4.
\(\frac{2}{4}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{2}{4}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{2}{4}\) when its numerator and denominator is divided by 2 we get \(\frac{1}{2}\)

Question 5.
\(\frac{2}{6}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{2}{6}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{2}{6}\) when its numerator and denominator is divided by 2 we get \(\frac{1}{3}\)

Question 6.
\(\frac{2}{8}\) = \(\frac{1}{2}\) \(\frac{1}{4}\)
Answer:
\(\frac{2}{8}\) = \(\frac{1}{4}\)
Explanation :
\(\frac{2}{8}\) when its numerator and denominator is divided by 2 we get \(\frac{1}{4}\)

Question 7.
\(\frac{3}{6}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{3}{6}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{3}{6}\) when its numerator and denominator is divided by 3 we get \(\frac{1}{2}\)

Question 8.
\(\frac{3}{9}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{3}{9}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{3}{9}\) when its numerator and denominator is divided by 3 we get \(\frac{1}{3}\)

Question 9.
\(\frac{3}{12}\) = \(\frac{1}{4}\) \(\frac{1}{3}\)
Answer:
\(\frac{3}{12}\) = \(\frac{1}{4}\)
Explanation :
\(\frac{3}{12}\) when its numerator and denominator is divided by 3 we get \(\frac{1}{4}\)

Question 10.
\(\frac{4}{8}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{4}{8}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{4}{8}\) when its numerator and denominator is divided by 4 we get \(\frac{1}{2}\)

Question 11.
\(\frac{4}{12}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{4}{12}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{4}{12}\) when its numerator and denominator is divided by 4 we get \(\frac{1}{3}\)

Question 12.
\(\frac{4}{16}\) = \(\frac{1}{4}\) \(\frac{1}{3}\)
Answer:
\(\frac{4}{16}\) = \(\frac{1}{4}\)
Explanation :
\(\frac{4}{16}\) when its numerator and denominator is divided by 4 we get \(\frac{1}{4}\)

Question 13.
\(\frac{4}{6}\) = \(\frac{2}{3}\) \(\frac{1}{2}\)
Answer:
\(\frac{4}{6}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{4}{6}\) when its numerator and denominator is divided by 2 we get \(\frac{2}{3}\)

Question 14.
\(\frac{7}{14}\) = \(\frac{2}{3}\) \(\frac{1}{2}\)
Answer:
\(\frac{7}{14}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{7}{14}\) when its numerator and denominator is divided by 7 we get \(\frac{1}{2}\)

Question 15.
\(\frac{7}{21}\) = \(\frac{1}{5}\) \(\frac{1}{3}\)
Answer:
\(\frac{7}{21}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{7}{21}\) when its numerator and denominator is divided by 7 we get \(\frac{1}{3}\)

Question 16.
\(\frac{7}{35}\) = \(\frac{1}{5}\) \(\frac{1}{3}\)
Answer:
\(\frac{7}{35}\) = \(\frac{1}{5}\)
Explanation :
\(\frac{7}{35}\) when its numerator and denominator is divided by 7 we get \(\frac{1}{5}\)

Question 17.
\(\frac{6}{9}\) = \(\frac{2}{3}\) \(\frac{1}{3}\)
Answer:
\(\frac{6}{9}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{6}{9}\) when its numerator and denominator is divided by 3 we get \(\frac{2}{3}\)

Question 18.
\(\frac{6}{12}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{6}{12}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{6}{12}\) when its numerator and denominator is divided by 6 we get \(\frac{1}{2}\)

Question 19.
\(\frac{6}{18}\) = \(\frac{1}{6}\) \(\frac{1}{3}\)
Answer:
\(\frac{6}{18}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{6}{18}\) when its numerator and denominator is divided by 6 we get \(\frac{1}{3}\)

Question 20.
\(\frac{6}{36}\) = \(\frac{1}{6}\) \(\frac{1}{3}\)
Answer:
\(\frac{6}{36}\) = \(\frac{1}{6}\)
Explanation :
\(\frac{6}{36}\) when its numerator and denominator is divided by 6 we get \(\frac{1}{6}\)

Question 21.
\(\frac{8}{12}\) = \(\frac{2}{3}\) \(\frac{3}{4}\)
Answer:
\(\frac{8}{12}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{8}{12}\) when its numerator and denominator is divided by 4 we get \(\frac{2}{3}\)

Question 22.
\(\frac{8}{16}\) = \(\frac{1}{2}\) \(\frac{1}{3}\)
Answer:
\(\frac{8}{16}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{8}{16}\) when its numerator and denominator is divided by 8 we get \(\frac{1}{2}\)

Question 23.
\(\frac{8}{24}\) = \(\frac{2}{3}\) \(\frac{1}{3}\) \(\frac{1}{4}\)
Answer:
\(\frac{8}{24}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{8}{24}\) when its numerator and denominator is divided by 8 we get \(\frac{1}{3}\)

Question 24.
\(\frac{8}{56}\) = \(\frac{1}{6}\) \(\frac{1}{7}\) \(\frac{1}{8}\)
Answer:
\(\frac{8}{24}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{8}{56}\) when its numerator and denominator is divided by 8 we get \(\frac{1}{7}\)

Question 25.
\(\frac{8}{12}\) = \(\frac{2}{3}\) \(\frac{3}{4}\) \(\frac{4}{5}\)
Answer:
\(\frac{8}{12}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{8}{12}\) when its numerator and denominator is divided by 4 we get \(\frac{2}{3}\)

Question 26.
\(\frac{9}{18}\) = \(\frac{1}{2}\) \(\frac{1}{3}\) \(\frac{1}{4}\)
Answer:
\(\frac{9}{18}\) = \(\frac{1}{2}\)
Explanation :
\(\frac{9}{18}\) when its numerator and denominator is divided by 9 we get \(\frac{1}{2}\)

Question 27.
\(\frac{9}{27}\) = \(\frac{1}{2}\) \(\frac{1}{3}\) \(\frac{1}{4}\)
Answer:
\(\frac{9}{27}\) = \(\frac{1}{3}\)
Explanation :
\(\frac{9}{27}\) when its numerator and denominator is divided by 9 we get \(\frac{1}{3}\)

Question 28.
\(\frac{9}{72}\) = \(\frac{1}{7}\) \(\frac{1}{8}\) \(\frac{1}{9}\)
Answer:
\(\frac{9}{72}\) = \(\frac{1}{8}\)
Explanation :
\(\frac{9}{72}\) when its numerator and denominator is divided by 9 we get \(\frac{1}{8}\)

Question 29.
\(\frac{12}{18}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{12}{18}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{12}{18}\) when its numerator and denominator is divided by 6 we get \(\frac{2}{3}\)

Question 30.
\(\frac{6}{8}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{6}{8}\) = \(\frac{3}{4}\)
Explanation :
\(\frac{6}{8}\) when its numerator and denominator is divided by 2 we get \(\frac{3}{4}\)

Question 31.
\(\frac{9}{12}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{9}{12}\) = \(\frac{3}{4}\)
Explanation :
\(\frac{9}{12}\) when its numerator and denominator is divided by 3 we get \(\frac{3}{4}\)

Question 32.
\(\frac{12}{16}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{12}{16}\) = \(\frac{3}{4}\)
Explanation :
\(\frac{12}{16}\) when its numerator and denominator is divided by 4 we get \(\frac{3}{4}\)

Question 33.
\(\frac{8}{10}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{8}{10}\) = \(\frac{4}{5}\)
Explanation :
\(\frac{8}{10}\) when its numerator and denominator is divided by 2 we get \(\frac{4}{5}\)

Question 34.
\(\frac{16}{20}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{16}{20}\) = \(\frac{4}{5}\)
Explanation :
\(\frac{16}{20}\) when its numerator and denominator is divided by 4 we get \(\frac{4}{5}\)

Question 35.
\(\frac{12}{15}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{12}{15}\) = \(\frac{4}{5}\)
Explanation :
\(\frac{12}{15}\) when its numerator and denominator is divided by 3 we get \(\frac{4}{5}\)

Question 36.
\(\frac{10}{12}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{5}{6}\)
Answer:
\(\frac{10}{12}\) = \(\frac{5}{6}\)
Explanation :
\(\frac{10}{12}\) when its numerator and denominator is divided by 2 we get \(\frac{5}{6}\)

Question 37.
\(\frac{15}{18}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{15}{18}\) = \(\frac{5}{6}\)
Explanation :
\(\frac{15}{18}\) when its numerator and denominator is divided by 3 we get \(\frac{5}{6}\)

Question 38.
\(\frac{16}{24}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{16}{24}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{16}{24}\) when its numerator and denominator is divided by 8 we get \(\frac{2}{3}\)

Question 39.
\(\frac{24}{32}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{24}{32}\) = \(\frac{3}{4}\)
Explanation :
\(\frac{24}{32}\) when its numerator and denominator is divided by 12 we get \(\frac{3}{4}\)

Question 40.
\(\frac{36}{45}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{36}{45}\) = \(\frac{4}{5}\)
Explanation :
\(\frac{36}{45}\) when its numerator and denominator is divided by 9 we get \(\frac{4}{5}\)

Question 41.
\(\frac{40}{48}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{5}{6}\)
Answer:
\(\frac{40}{48}\) = \(\frac{5}{6}\)
Explanation :
\(\frac{40}{48}\) when its numerator and denominator is divided by 8 we get \(\frac{5}{}\)

Question 42.
\(\frac{24}{36}\) = \(\frac{3}{4}\) \(\frac{4}{5}\) \(\frac{2}{3}\)
Answer:
\(\frac{24}{36}\) = \(\frac{2}{3}\)
Explanation :
\(\frac{24}{36}\) when its numerator and denominator is divided by 12 we get \(\frac{2}{3}\)

Question 43.
\(\frac{48}{60}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{4}{5}\)
Answer:
\(\frac{48}{60}\) = \(\frac{4}{5}\)
Explanation :
\(\frac{48}{60}\) when its numerator and denominator is divided by 12 we get \(\frac{4}{5}\)

Question 44.
\(\frac{60}{72}\) = \(\frac{3}{4}\) \(\frac{5}{6}\) \(\frac{2}{3}\)
Answer:
\(\frac{60}{72}\) = \(\frac{5}{6}\)
Explanation :
\(\frac{60}{72}\) when its numerator and denominator is divided by 12 we get \(\frac{5}{6}\)

Eureka Math Grade 5 Module 3 Lesson 7 Problem Set Answer Key

Solve the word problems using the RDW strategy. Show all of your work.
Question 1.
George weeded \(\frac{1}{5}\) of the garden, and Summer weeded some, too. When they were finished, \(\frac{2}{3}\) of the garden still needed to be weeded. What fraction of the garden did Summer weed?
Answer:
Total Garden = 1 whole .
Fraction of garden weeded by George = \(\frac{1}{5}\)
Fraction of garden needed to be weeded = \(\frac{2}{3}\)
Fraction of garden weeded by summer = x
1 = \(\frac{1}{5}\) + x + \(\frac{2}{3}\)
x = 1 – \(\frac{1}{5}\) – \(\frac{2}{3}\)
lcm of 5 and 3 is 15.
x = \(\frac{15}{15}\)  – \(\frac{3}{15}\) – \(\frac{10}{15}\)
x = \(\frac{15}{15}\)  – \(\frac{13}{15}\)
x = \(\frac{2}{15}\)
Therefore , Fraction of garden weeded by summer = x = \(\frac{2}{15}\)

Question 2.
Jing spent \(\frac{1}{3}\) of her money on a pack of pens, \(\frac{1}{2}\) of her money on a pack of markers, and \(\frac{1}{8}\) of her money on a pack of pencils. What fraction of her money is left?
Answer:
Total Money = 1
Money spent on pack of pens = \(\frac{1}{3}\)
Money spent on pack of markers = \(\frac{1}{2}\)
Money spent on pack of pencils = \(\frac{1}{8}\)
Fraction of Money left = x
1 = \(\frac{1}{3}\) + \(\frac{1}{2}\) + \(\frac{1}{8}\) + x
lcm of 3, 2 and 8 is 24
\(\frac{24}{24}\) = \(\frac{8}{24}\) + \(\frac{12}{24}\) + \(\frac{3}{24}\) + x
\(\frac{24}{24}\) = \(\frac{23}{24}\) + x
x = \(\frac{24}{24}\) – \(\frac{23}{24}\)
x = \(\frac{1}{24}\) .
Therefore, Fraction of Money left = \(\frac{1}{24}\)

Question 3.
Shelby bought a 2-ounce tube of blue paint. She used \(\frac{2}{3}\) ounce to paint the water, \(\frac{3}{5}\) ounce to paint the sky, and some to paint a flag. After that, she has \(\frac{2}{15}\) ounce left. How much paint did Shelby use to paint her flag?
Answer:
Quantity of Blue paint = 2 – ounce
Fraction of blue paint used for painting water = \(\frac{2}{3}\)
Fraction of blue paint used for painting sky = \(\frac{3}{5}\)
Fraction of blue paint used for painting flag = x
Fraction of blue paint left = \(\frac{2}{15}\)
2 = \(\frac{2}{3}\) + \(\frac{3}{5}\) + x + \(\frac{2}{15}\)
lcm of 3, 5 and 15 is 15 .
\(\frac{30}{15}\) = \(\frac{10}{15}\) + \(\frac{9}{15}\) + x + \(\frac{2}{15}\)
\(\frac{30}{15}\) = \(\frac{21}{15}\) + x
x = \(\frac{30}{15}\) – \(\frac{21}{15}\)
x = \(\frac{9}{15}\) = \(\frac{3}{5}\)
Therefore , Fraction of blue paint used for painting flag = x = \(\frac{9}{15}\) = \(\frac{3}{5}\) .ounce

Question 4.
Jim sold \(\frac{3}{4}\) gallon of lemonade. Dwight sold some lemonade, too. Together, they sold 1\(\frac{5}{12}\) gallons. Who sold more lemonade, Jim or Dwight? How much more?
Answer:
Fraction of lemonade sold by Jim = \(\frac{3}{4}\) gallon
Fraction of lemonade sold by Dwight = x gallon
Fraction of lemonade sold by Jim and Dwight = 1\(\frac{5}{12}\) gallon
1\(\frac{5}{12}\) = \(\frac{3}{4}\) + x
x = 1\(\frac{5}{12}\) – \(\frac{3}{4}\)
lcm of 12 and 4 is 12 .
x = \(\frac{17}{12}\) – \(\frac{9}{12}\)
x = \(\frac{8}{12}\) = \(\frac{2}{3}\)
Therefore, Fraction of lemonade sold by Dwight = x = \(\frac{8}{12}\) = \(\frac{2}{3}\) gallon .

Question 5.
Leonard spent \(\frac{1}{4}\) of his money on a sandwich. He spent 2 times as much on a gift for his brother as on some comic books. He had \(\frac{3}{8}\) of his money left. What fraction of his money did he spend on the comic books?
Answer:
Fraction of Money spent on sandwich = \(\frac{1}{4}\)
Fraction of money left with him = \(\frac{3}{8}\)
Total Money = 1
1 = \(\frac{1}{4}\) + \(\frac{3}{8}\) + x .
Lcm of 4 and 8 is 8.
\(\frac{8}{8}\) = \(\frac{2}{8}\) + \(\frac{3}{8}\) + x
\(\frac{8}{8}\) = \(\frac{5}{8}\) + x
x = \(\frac{8}{8}\) – \(\frac{5}{8}\)
x = \(\frac{3}{8}\)
Fraction of Money spent on his brother = \(\frac{2}{8}\) = \(\frac{1}{4}\)
Fraction of Money spent on Comic books = \(\frac{1}{8}\) .

Eureka Math Grade 5 Module 3 Lesson 7 Exit Ticket Answer Key

Solve the word problem using the RDW strategy. Show all of your work.
Mr. Pham mowed \(\frac{2}{7}\) of his lawn. His son mowed \(\frac{1}{4}\) of it. Who mowed the most? How much of the lawn still needs to be mowed?
Answer:
Fraction Of Lawn mowed by Mr.Pham = \(\frac{2}{7}\)
Fraction Of Lawn mowed by his Son = \(\frac{1}{4}\)
lcm of 7 and 4 is 28 .
\(\frac{2}{7}\) = \(\frac{8}{28}\)
\(\frac{1}{4}\) = \(\frac{7}{28}\)
\(\frac{8}{28}\) > \(\frac{7}{28}\)
Mr. Pham mowed most than his son .
Fraction of lawn still needed to mowed = x
1= \(\frac{8}{28}\) + \(\frac{7}{28}\)  + x
\(\frac{28}{28}\) = \(\frac{15}{28}\) + x
x = \(\frac{28}{28}\) – \(\frac{15}{28}\)
x = \(\frac{13}{28}\)
Therefore, Fraction of lawn still needed to mowed = x = \(\frac{13}{28}\) .

Eureka Math Grade 5 Module 3 Lesson 7 Homework Answer Key

Solve the word problems using the RDW strategy. Show all of your work.
Question 1.
Christine baked a pumpkin pie. She ate \(\frac{1}{6}\) of the pie. Her brother ate \(\frac{1}{6}\) of it and gave the leftovers to his friends. What fraction of the pie did he give to his friends?
Answer:
Total pie = 1 .
Fraction of pie ate by Christine = \(\frac{1}{6}\)
Fraction of pie ate by her Brother =\(\frac{1}{6}\)
Fraction of pie leftover to her friends = x
1 = \(\frac{1}{6}\) + \(\frac{1}{6}\) + x
lcm is 6
\(\frac{6}{6}\) = \(\frac{2}{6}\) + x
x = \(\frac{6}{6}\) – \(\frac{2}{6}\)
x = \(\frac{4}{6}\) = \(\frac{2}{3}\)
Therefore, Fraction of pie leftover to her friends = x = \(\frac{4}{6}\) = \(\frac{2}{3}\) .

Question 2.
Liang went to the bookstore. He spent \(\frac{1}{3}\) of his money on a pen and \(\frac{4}{7}\) of it on books. What fraction of his money did he have left?
Answer:
Total money = 1
Fraction of Money spent on Pen =\(\frac{1}{3}\)
Fraction of Money spent on Books =\(\frac{4}{7}\)
Fraction of Money left = x
1 = \(\frac{1}{3}\) + \(\frac{4}{7}\) + x
lcm of 3 and 7 is 21 .
\(\frac{21}{21}\) = \(\frac{7}{21}\) + \(\frac{12}{21}\) + x
\(\frac{21}{21}\) = \(\frac{19}{21}\) + x
x = \(\frac{3}{21}\) = \(\frac{1}{7}\) .
Therefore, Fraction of Money left = x = \(\frac{3}{21}\) = \(\frac{1}{7}\) .

Question 3.
Tiffany bought \(\frac{2}{5}\) kg of cherries. Linda bought \(\frac{1}{10}\) kg of cherries less than Tiffany. How many kilograms of cherries did they buy altogether?
Answer:
Fraction of Quantity of Cherries bought by Tiffany = \(\frac{2}{5}\) kg
Fraction of Quantity of Cherries bought by Linda = x kg
Fraction of Quantity of cherries Linda bought \(\frac{1}{10}\) kg of cherries less than Tiffany.
Fraction of Quantity of Cherries bought by Linda = x = \(\frac{2}{5}\) – \(\frac{1}{10}\)
lcm of 2 and 5 is 10 .
x = \(\frac{4}{10}\) – \(\frac{1}{10}\)
x = \(\frac{3}{10}\)
Fraction of Quantity of cherries bought by both = \(\frac{2}{5}\)  + \(\frac{3}{10}\)  =  \(\frac{4}{10}\) + \(\frac{3}{10}\)  = \(\frac{7}{10}\)
Therefore, Fraction of Quantity of cherries bought by both = \(\frac{7}{10}\)

Question 4.
Mr. Rivas bought a can of paint. He used \(\frac{3}{8}\) of it to paint a bookshelf. He used \(\frac{1}{4}\) of it to paint a wagon. He used some of it to paint a birdhouse and has \(\frac{1}{8}\) of the paint left. How much paint did he use for the birdhouse?
Answer:
Fraction of paint used to paint a bookshelf = \(\frac{3}{8}\)
Fraction of paint used to paint a wagon = \(\frac{1}{4}\)
Fraction of paint used to paint a birdhouse = x
Fraction of paint left = \(\frac{1}{8}\)
Total paint = 1 .
1 = \(\frac{3}{8}\) + \(\frac{1}{4}\) + x + \(\frac{1}{8}\)
lcm of 4 and 8 is 8 .
\(\frac{8}{8}\) = \(\frac{3}{8}\) +\(\frac{2}{8}\) + x + \(\frac{1}{8}\)
\(\frac{8}{8}\) = \(\frac{6}{8}\) + x
x = \(\frac{8}{8}\) – \(\frac{6}{8}\)
x = \(\frac{2}{8}\) = \(\frac{1}{4}\) .
Therefore, Fraction of paint used to paint a bird house = x = \(\frac{2}{8}\) = \(\frac{1}{4}\)

Question 5.
Ribbon A is \(\frac{1}{3}\) m long. It is \(\frac{2}{5}\) m shorter than Ribbon B. What’s the total length of the two ribbons?
Answer:
Fraction of length of Ribbon A = \(\frac{1}{3}\) m
Fraction of length of Ribbon A = Fraction of length of Ribbon B – \(\frac{2}{5}\) m
Fraction of length of Ribbon B = \(\frac{1}{3}\) + \(\frac{2}{5}\)
lcm of 3 and 5 is 15 .
Fraction of length of Ribbon B = \(\frac{1}{3}\) + \(\frac{2}{5}\) = \(\frac{5}{15}\) + \(\frac{6}{15}\) = \(\frac{11}{15}\)
Fraction of Total Length of two ribbons = \(\frac{1}{3}\) + \(\frac{11}{15}\) = \(\frac{5}{15}\) + \(\frac{11}{15}\) = \(\frac{16}{15}\) m .
Therefore, Fraction of Total Length of two ribbons =\(\frac{16}{15}\) m

Engage NY Eureka Math 5th Grade Module 3 Lesson 6 Answer Key

Eureka Math Grade 5 Module 3 Lesson 6 Problem Set Answer Key

Question 1.
For the following problems, draw a picture using the rectangular fraction model and write the answer. Simplify your answer, if possible.
a. 1\(\frac{1}{4}\) – \(\frac{1}{3}\) =
b. 1\(\frac{1}{5}\) – \(\frac{1}{3}\) =
c. 1\(\frac{3}{8}\) – \(\frac{1}{2}\) =
d. 1\(\frac{2}{5}\) – \(\frac{1}{2}\) =
e. 1\(\frac{2}{7}\) – \(\frac{1}{3}\) =
f. 1\(\frac{2}{3}\) – \(\frac{3}{5}\) =
Answer:
a.
1\(\frac{1}{4}\) – \(\frac{1}{3}\) = \(\frac{5}{4}\) – \(\frac{1}{3}\)
lcm of 4 and 3 is 12 .
\(\frac{15}{12}\) – \(\frac{4}{12}\) = \(\frac{11}{12}\).

Explanation :
The Rectangle is divided into 4 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{1}{4}\) .
1\(\frac{1}{4}\) and  \(\frac{1}{3}\) have lcm 12 so, the rectangle is divided into 12 parts by drawing 2 horizontal lines . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts represent the difference of the given fraction to its total parts .

b.
1\(\frac{1}{5}\) – \(\frac{1}{3}\) = \(\frac{6}{5}\) – \(\frac{1}{3}\)
lcm of 5 and 3 is 15 .
\(\frac{18}{15}\) – \(\frac{5}{15}\) = \(\frac{13}{15}\)

Explanation :
The Rectangle is divided into 5 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{1}{5}\) .
1\(\frac{1}{5}\) and  \(\frac{1}{3}\) have lcm 15 so, the rectangle is divided into 15 parts by drawing 2 horizontal lines . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts represent the difference of the given fraction to its total parts .

c.
1\(\frac{3}{8}\) – \(\frac{1}{2}\) = \(\frac{11}{8}\) – \(\frac{1}{2}\)
lcm of 8 and 2 is 8 .
\(\frac{11}{8}\) – \(\frac{4}{8}\) =\(\frac{7}{8}\) .

Explanation :
The Rectangle is divided into 8 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{3}{8}\) .
1\(\frac{3}{8}\) and  \(\frac{1}{2}\) have lcm 8 so, the rectangle is divided into 8 parts . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts represent the difference of the given fraction to its total parts .

d.
1\(\frac{2}{5}\) – \(\frac{1}{2}\) = \(\frac{7}{5}\) – \(\frac{1}{2}\)
lcm of 5 and 2 is 10.
\(\frac{14}{10}\) – \(\frac{5}{10}\) = \(\frac{9}{10}\)

Explanation :
The Rectangle is divided into 5 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{2}{5}\) .
1\(\frac{2}{5}\) and  \(\frac{1}{2}\) have lcm 10 so, the rectangle is divided into 10 parts by drawing 1 horizontal lines . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts represent the difference of the given fraction to its total parts .

e.
1\(\frac{2}{7}\) – \(\frac{1}{3}\) = \(\frac{9}{7}\) – \(\frac{1}{3}\)
lcm of 7 and 3 is 21 .
\(\frac{27}{21}\) – \(\frac{7}{21}\) = \(\frac{20}{21}\) .

Explanation :
The Rectangle is divided into 7 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{2}{7}\) .
1\(\frac{2}{7}\) and  \(\frac{1}{3}\) have lcm 21 so, the rectangle is divided into 21 parts by drawing 2 horizontal lines . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts represent the difference of the given fraction to its total parts .

f.
1\(\frac{2}{3}\) – \(\frac{3}{5}\) = \(\frac{5}{3}\) – \(\frac{3}{5}\)
lcm of 3 and 5 is 15 .
\(\frac{25}{15}\) – \(\frac{9}{15}\) = \(\frac{16}{15}\)

Explanation :
The Rectangle is divided into 5 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{2}{3}\) .
1\(\frac{2}{3}\) and  \(\frac{3}{5}\) have lcm 15 so, the rectangle is divided into 15 parts by drawing 4 horizontal lines . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts represent the difference of the given fraction to its total parts .

Question 2.
Jean-Luc jogged around the lake in 1\(\frac{1}{4}\) hour. William jogged the same distance in \(\frac{5}{6}\) hour. How much longer did Jean-Luc take than William in hours?
Answer:
Time taken to jog for Jean-Luc = 1\(\frac{1}{4}\) hour .
Time taken to jog for William = \(\frac{5}{6}\) hour .
Time taken by Jean-Luc than William = 1\(\frac{1}{4}\) – \(\frac{5}{6}\)  = \(\frac{5}{4}\) – \(\frac{5}{6}\)  = \(\frac{30}{24}\)  – \(\frac{20}{24}\) = \(\frac{10}{24}\) = \(\frac{5}{12}\) hour .

Question 3.
Is it true that 1\(\frac{2}{5}\) – \(\frac{3}{4}\) = \(\frac{1}{4}\) + \(\frac{2}{5}\)? Prove your answer.
Answer:
Yes , 1\(\frac{2}{5}\) – \(\frac{3}{4}\) = \(\frac{1}{4}\) + \(\frac{2}{5}\)
Explanation :
1\(\frac{2}{5}\) – \(\frac{3}{4}\) = \(\frac{7}{5}\) – \(\frac{3}{4}\) = \(\frac{28}{20}\) – \(\frac{15}{20}\) = \(\frac{13}{20}\) .
\(\frac{1}{4}\) + \(\frac{2}{5}\) = \(\frac{5}{20}\) + \(\frac{8}{20}\) = \(\frac{13}{20}\)
Therefore, 1\(\frac{2}{5}\) – \(\frac{3}{4}\) = \(\frac{1}{4}\) + \(\frac{2}{5}\) = \(\frac{13}{20}\)  .

Eureka Math Grade 5 Module 3 Lesson 6 Exit Ticket Answer Key

For the following problems, draw a picture using the rectangular fraction model and write the answer. Simplify your answer, if possible.
a. 1\(\frac{1}{5}\) – \(\frac{1}{2}\) =
b. 1\(\frac{1}{3}\) – \(\frac{5}{6}\) =
Answer:
a.
1\(\frac{1}{5}\) – \(\frac{1}{2}\) = \(\frac{6}{5}\) – \(\frac{1}{2}\)
lcm of 5 and 2 is 10 .
\(\frac{12}{10}\) – \(\frac{5}{10}\) = \(\frac{7}{10}\)

Explanation :
The Rectangle is divided into 5 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{2}{5}\) .
1\(\frac{2}{5}\) and  \(\frac{1}{2}\) have lcm 10 so, the rectangle is divided into 10 parts by drawing 1 horizontal line . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts represent the difference of the given fraction to its total parts .

b.
1\(\frac{1}{3}\) – \(\frac{5}{6}\) = \(\frac{4}{3}\) – \(\frac{5}{6}\)
lcm of 3 and 6 is  6 .
\(\frac{8}{6}\) – \(\frac{5}{6}\) = \(\frac{3}{6}\) = \(\frac{1}{2}\)

Explanation :
The Rectangle is divided into 3 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{1}{3}\) .
1\(\frac{1}{3}\) and  \(\frac{5}{6}\) have lcm 6 so, the rectangle is divided into 6 parts by drawing 2 horizontal lines . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts represent the difference of the given fraction to its total parts .

Eureka Math Grade 5 Module 3 Lesson 6 Homework Answer Key

Question 1.
For the following problems, draw a picture using the rectangular fraction model and write the answer. Simplify your answer, if possible.
a. 1 – \(\frac{5}{6}\) =
b. \(\frac{3}{2}\) – \(\frac{5}{6}\) =
c. \(\frac{4}{3}\) – \(\frac{5}{7}\) =
d. 1\(\frac{1}{8}\) – \(\frac{3}{5}\) =
e. 1\(\frac{2}{5}\) – \(\frac{3}{4}\) =
f. 1\(\frac{5}{6}\) – \(\frac{7}{8}\) =
g. \(\frac{9}{7}\) – \(\frac{3}{4}\) =
h. 1\(\frac{3}{12}\) – \(\frac{2}{3}\) =
Answer:
a.
1 – \(\frac{5}{6}\)
lcm of 1 and 6 is 6 .
\(\frac{6}{6}\) – \(\frac{5}{6}\) = \(\frac{1}{6}\) .

Explanation :
The Rectangle is divided into 6 parts using vertical lines and shaded to represent the fraction \(\frac{6}{6}\) .
1 and  \(\frac{5}{6}\) have lcm 6 . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts without x marks represent the difference of the given fraction to its total parts .

b.
\(\frac{3}{2}\) – \(\frac{5}{6}\)
lcm of 2 and 6 is  6 .
\(\frac{9}{6}\) – \(\frac{5}{6}\) = \(\frac{4}{6}\) = \(\frac{2}{3}\)

Explanation :
The Rectangle is divided into 2 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{1}{2}\) .
1\(\frac{1}{2}\) and  \(\frac{5}{6}\) have lcm 6 so, the rectangle is divided into 6 parts by drawing 2 horizontal lines . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts without x marks represent the difference of the given fraction to its total parts .
c.
\(\frac{4}{3}\) – \(\frac{5}{7}\)
lcm of 3 and 7 is 21 .
\(\frac{28}{21}\) – \(\frac{15}{21}\) = \(\frac{13}{21}\)

Explanation :
The Rectangle is divided into 3 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{1}{3}\) .
1\(\frac{1}{3}\) and  \(\frac{5}{7}\) have lcm 21 so, the rectangle is divided into 21 parts by drawing 6 horizontal lines . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts without x marks represent the difference of the given fraction to its total parts .

d.
1\(\frac{1}{8}\) – \(\frac{3}{5}\) = \(\frac{9}{8}\) – \(\frac{3}{5}\)
lcm of 8 and 5 is 40
\(\frac{45}{40}\) – \(\frac{24}{40}\) = \(\frac{21}{40}\)

Explanation :
The Rectangle is divided into 8 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{1}{8}\) .
1\(\frac{1}{8}\) and  \(\frac{3}{5}\) have lcm 40 so, the rectangle is divided into 40 parts by drawing 4 horizontal lines . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts without x marks represent the difference of the given fraction to its total parts .

e.
1\(\frac{2}{5}\) – \(\frac{3}{4}\) = \(\frac{7}{5}\) – \(\frac{3}{4}\)
lcm of 5 and 4 is 20 .
\(\frac{28}{20}\) – \(\frac{15}{20}\) = \(\frac{13}{20}\) .

Explanation :
The Rectangle is divided into 5 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{2}{5}\) .
1\(\frac{2}{5}\) and  \(\frac{3}{4}\) have lcm 20 so, the rectangle is divided into 20 parts by drawing 3 horizontal lines . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts without x marks represent the difference of the given fraction to its total parts .

f.
1\(\frac{5}{6}\) – \(\frac{7}{8}\) = \(\frac{11}{6}\) – \(\frac{7}{8}\)
lcm of 6 and 8 is 24 .
\(\frac{44}{24}\) – \(\frac{21}{24}\) = \(\frac{23}{24}\) .

Explanation :
The Rectangle is divided into 6 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{5}{6}\) .
1\(\frac{5}{6}\) and  \(\frac{7}{8}\) have lcm 24 so, the rectangle is divided into 24 parts by drawing 3 horizontal lines . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts without x marks represent the difference of the given fraction to its total parts .

g.
\(\frac{9}{7}\) – \(\frac{3}{4}\)
lcm of 7 and 4 is 28 .
\(\frac{36}{28}\) – \(\frac{21}{28}\) = \(\frac{15}{28}\)

Explanation :
The Rectangle is divided into 7 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{2}{7}\) .
1\(\frac{2}{7}\) and  \(\frac{3}{4}\) have lcm 28 so, the rectangle is divided into 28 parts by drawing 3 horizontal lines . after making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts without x marks represent the difference of the given fractions to its total parts .

h.
1\(\frac{3}{12}\) – \(\frac{2}{3}\) = \(\frac{15}{12}\) – \(\frac{2}{3}\)
lcm of 12 and 3 is 12 .
\(\frac{15}{12}\) – \(\frac{8}{12}\) = \(\frac{7}{12}\)

Explanation :
The Rectangle is divided into 12 parts using vertical lines and 2 rectangles are drawn and shaded to represent the fraction 1\(\frac{3}{12}\) .
1\(\frac{3}{12}\) and  \(\frac{2}{3}\) have lcm 12 . After making lcm equal then subtraction is done and subtraction is done by showing x-mark on the shaded parts.
The left over shaded parts without x marks represent the difference of the given fractions to its total parts .

Question 2.
Sam had 1\(\frac{1}{2}\) m of rope. He cut off \(\frac{5}{8}\) m and used it for a project. How much rope does Sam have left?
Answer:
Length of Rope with Sam = 1\(\frac{1}{2}\) m
Length of rope used for project = \(\frac{5}{8}\) m
Length of Rope left = 1\(\frac{1}{2}\) – \(\frac{5}{8}\) = \(\frac{3}{2}\) – \(\frac{5}{8}\) =
\(\frac{12}{8}\) – \(\frac{5}{8}\) = \(\frac{7}{8}\) .
Therefore, Length of rope left with sam = \(\frac{7}{8}\) m .

Question 3.
Jackson had 1\(\frac{3}{8}\) kg of fertilizer. He used some to fertilize a flower bed, and he only had \(\frac{2}{3}\) kg left. How much fertilizer was used in the flower bed?
Answer:
Quantity of fertilizers with Jackson = 1\(\frac{3}{8}\) kg
Quantity of fertilizers left = \(\frac{2}{3}\) kg .
Quantity of Fertilizers used for flower bed  = 1\(\frac{3}{8}\) kg  – \(\frac{2}{3}\) kg = \(\frac{11}{8}\) – \(\frac{2}{3}\) = \(\frac{33}{24}\) – \(\frac{16}{24}\) = \(\frac{17}{24}\) .
Therefore, Quantity of Fertilizers used for flower bed  =\(\frac{17}{24}\)

Engage NY Eureka Math 5th Grade Module 3 Lesson 5 Answer Key

Eureka Math Grade 5 Module 3 Lesson 5 Sprint Answer Key

A
Subtracting Fractions from a Whole Number

Question 1.
4 – \(\frac{1}{2}\) =
Answer:
4 – \(\frac{1}{2}\) = 3\(\frac{1}{2}\)
Explanation :
4 – \(\frac{1}{2}\) = \(\frac{8}{2}\) – \(\frac{1}{2}\) = \(\frac{7}{2}\) = 3\(\frac{1}{2}\)

Question 2.
3 – \(\frac{1}{2}\) =
Answer:
3 – \(\frac{1}{2}\) = 2\(\frac{1}{2}\)
Explanation :
3 – \(\frac{1}{2}\) = \(\frac{6}{2}\) – \(\frac{1}{2}\) = \(\frac{5}{2}\) = 2\(\frac{1}{2}\)

Question 3.
2 – \(\frac{1}{2}\) =
Answer:
2 – \(\frac{1}{2}\) = 1\(\frac{1}{2}\)
Explanation :
2 – \(\frac{1}{2}\) = \(\frac{4}{2}\) – \(\frac{1}{2}\) = \(\frac{3}{2}\) = 1\(\frac{1}{2}\)

Question 4.
1 – \(\frac{1}{2}\) =
Answer:
1 – \(\frac{1}{2}\) = \(\frac{1}{2}\)
Explanation :
1 – \(\frac{1}{2}\) = \(\frac{2}{2}\) – \(\frac{1}{2}\) = \(\frac{1}{2}\)

Question 5.
1 – \(\frac{1}{3}\) =
Answer:
1 – \(\frac{1}{3}\) = \(\frac{2}{3}\)
Explanation :
1 – \(\frac{1}{3}\) = \(\frac{3}{3}\) – \(\frac{1}{3}\) = \(\frac{2}{3}\)

Question 6.
2 – \(\frac{1}{3}\) =
Answer:
2 – \(\frac{1}{3}\) = 1\(\frac{2}{3}\)
Explanation :
2 – \(\frac{1}{3}\) = \(\frac{6}{3}\) – \(\frac{1}{3}\) = \(\frac{5}{3}\) = 1\(\frac{2}{3}\)

Question 7.
4 – \(\frac{1}{3}\) =
Answer:
4 – \(\frac{1}{3}\) = 3\(\frac{2}{3}\)
Explanation :
4 – \(\frac{1}{3}\) = \(\frac{12}{3}\) – \(\frac{1}{3}\) = \(\frac{11}{3}\) = 3\(\frac{2}{3}\)

Question 8.
4 – \(\frac{2}{3}\) =
Answer:
4 – \(\frac{2}{3}\) = 3\(\frac{1}{3}\)
Explanation :
4 – \(\frac{2}{3}\) = \(\frac{12}{3}\) – \(\frac{2}{3}\) = \(\frac{10}{3}\) = 3\(\frac{1}{3}\)

Question 9.
2 – \(\frac{2}{3}\) =
Answer:
2 – \(\frac{1}{3}\) = 1\(\frac{2}{3}\)
Explanation :
2 – \(\frac{1}{3}\) = \(\frac{6}{3}\) – \(\frac{1}{3}\) = \(\frac{5}{3}\) = 1\(\frac{2}{3}\)

Question 10.
2 – \(\frac{1}{4}\) =
Answer:
2 – \(\frac{1}{4}\) = 1\(\frac{3}{4}\)
Explanation :
2 – \(\frac{1}{4}\) = \(\frac{8}{4}\) – \(\frac{1}{4}\) = \(\frac{7}{4}\) = 1\(\frac{3}{4}\)

Question 11.
2 – \(\frac{3}{4}\) =
Answer:
2 – \(\frac{3}{4}\) = 1\(\frac{1}{4}\)
Explanation :
2 – \(\frac{3}{4}\) = \(\frac{8}{4}\) – \(\frac{3}{4}\) = \(\frac{5}{4}\) = 1\(\frac{1}{4}\)

Question 12.
3 – \(\frac{3}{4}\) =
Answer:
3 – \(\frac{3}{4}\) = 2\(\frac{1}{4}\)
Explanation :
3 – \(\frac{3}{4}\) = \(\frac{12}{4}\) – \(\frac{3}{4}\) = \(\frac{9}{4}\) = 2\(\frac{1}{4}\)

Question 13.
3 – \(\frac{1}{4}\) =
Answer:
3 – \(\frac{1}{4}\) = 2\(\frac{3}{4}\)
Explanation :
3 – \(\frac{1}{4}\) = \(\frac{12}{4}\) – \(\frac{1}{4}\) = \(\frac{11}{4}\) = 2\(\frac{3}{4}\)

Question 14.
4 – \(\frac{3}{4}\) =
Answer:
4 – \(\frac{3}{4}\) = 3\(\frac{1}{4}\)
Explanation :
4 – \(\frac{3}{4}\) = \(\frac{16}{4}\) – \(\frac{3}{4}\) = \(\frac{13}{4}\) = 3\(\frac{1}{4}\)

Question 15.
2 – \(\frac{1}{10}\) =
Answer:
2 – \(\frac{1}{10}\) = 1\(\frac{9}{10}\)
Explanation :
2 – \(\frac{1}{10}\) = \(\frac{20}{10}\) – \(\frac{1}{10}\) = \(\frac{19}{10}\) = 1\(\frac{9}{10}\)

Question 16.
3 – \(\frac{9}{10}\) =
Answer:
3 – \(\frac{9}{10}\) = 2\(\frac{1}{10}\)
Explanation :
3 – \(\frac{9}{10}\) = \(\frac{30}{10}\) – \(\frac{9}{10}\) = \(\frac{21}{10}\) = 2\(\frac{1}{10}\)

Question 17.
2 – \(\frac{7}{10}\) =
Answer:
Answer:
2 – \(\frac{7}{10}\) = 1\(\frac{3}{10}\)
Explanation :
2 – \(\frac{7}{10}\) = \(\frac{20}{10}\) – \(\frac{7}{10}\) = \(\frac{13}{10}\) = 1\(\frac{3}{10}\)

Question 18.
4 – \(\frac{3}{10}\) =
Answer:
4 – \(\frac{1}{10}\) = 3\(\frac{9}{10}\)
Explanation :
4 – \(\frac{1}{10}\) = \(\frac{40}{10}\) – \(\frac{1}{10}\) = \(\frac{39}{10}\) = 3\(\frac{9}{10}\)

Question 19.
3 – \(\frac{1}{5}\) =
Answer:
3 – \(\frac{1}{5}\) = 2\(\frac{4}{5}\)
Explanation :
3 – \(\frac{1}{5}\) = \(\frac{15}{5}\) – \(\frac{1}{5}\) = \(\frac{14}{5}\) = 2\(\frac{4}{5}\)

Question 20.
3 – \(\frac{2}{5}\) =
Answer:
3 – \(\frac{2}{5}\) = 2\(\frac{3}{5}\)
Explanation :
3 – \(\frac{2}{5}\) = \(\frac{15}{5}\) – \(\frac{2}{5}\) = \(\frac{13}{5}\) = 2\(\frac{3}{5}\)

Question 21.
3 – \(\frac{4}{5}\) =
Answer:
3 – \(\frac{4}{5}\) = 2\(\frac{1}{5}\)
Explanation :
3 – \(\frac{4}{5}\) = \(\frac{15}{5}\) – \(\frac{4}{5}\) = \(\frac{11}{5}\) = 2\(\frac{1}{5}\)

Question 22.
3 – \(\frac{3}{5}\) =
Answer:
3 – \(\frac{3}{5}\) = 2\(\frac{2}{5}\)
Explanation :
3 – \(\frac{3}{5}\) = \(\frac{15}{5}\) – \(\frac{3}{5}\) = \(\frac{12}{5}\) = 2\(\frac{2}{5}\)

Question 23.
3 – \(\frac{1}{8}\) =
Answer:
3 – \(\frac{1}{8}\) = 2\(\frac{7}{8}\)
Explanation :
3 – \(\frac{1}{8}\) = \(\frac{24}{8}\) – \(\frac{1}{8}\) = \(\frac{23}{8}\) = 2\(\frac{7}{8}\)

Question 24.
3 – \(\frac{3}{8}\) =
Answer:
3 – \(\frac{3}{8}\) = 2\(\frac{5}{8}\)
Explanation :
3 – \(\frac{3}{8}\) = \(\frac{24}{8}\) – \(\frac{3}{8}\) = \(\frac{21}{8}\) = 2\(\frac{5}{8}\)

Question 25.
3 – \(\frac{5}{8}\) =
Answer:
3 – \(\frac{5}{8}\) = 2\(\frac{3}{8}\)
Explanation :
3 – \(\frac{5}{8}\) = \(\frac{24}{8}\) – \(\frac{5}{8}\) = \(\frac{19}{8}\) = 2\(\frac{3}{8}\)

Question 26.
3 – \(\frac{7}{8}\) =
Answer:
3 – \(\frac{7}{8}\) = 2\(\frac{1}{8}\)
Explanation :
3 – \(\frac{7}{8}\) = \(\frac{24}{8}\) – \(\frac{7}{8}\) = \(\frac{17}{8}\) = 2\(\frac{1}{8}\)

Question 27.
2 – \(\frac{7}{8}\) =
Answer:
2 – \(\frac{7}{8}\) = 1\(\frac{1}{8}\)
Explanation :
2 – \(\frac{7}{8}\) = \(\frac{16}{8}\) – \(\frac{7}{8}\) = \(\frac{9}{8}\) = 1\(\frac{1}{8}\)

Question 28.
4 – \(\frac{1}{7}\) =
Answer:
4 – \(\frac{1}{7}\) = 3\(\frac{6}{7}\)
Explanation :
4 – \(\frac{1}{7}\) = \(\frac{28}{7}\) – \(\frac{1}{7}\) = \(\frac{27}{7}\) = 3\(\frac{6}{7}\)

Question 29.
3 – \(\frac{6}{7}\) =
Answer:
3 – \(\frac{6}{7}\) = 2\(\frac{1}{7}\)
Explanation :
3 – \(\frac{6}{7}\) = \(\frac{21}{7}\) – \(\frac{6}{7}\) = \(\frac{15}{7}\) = 2\(\frac{1}{7}\)

Question 30.
2 – \(\frac{3}{7}\) =
Answer:
2 – \(\frac{3}{7}\) =
Answer:
2 – \(\frac{3}{7}\) = 1\(\frac{4}{7}\)
Explanation :
2 – \(\frac{3}{7}\) = \(\frac{14}{7}\) – \(\frac{3}{7}\) = \(\frac{11}{7}\) = 1\(\frac{4}{7}\)

Question 31.
4 – \(\frac{4}{7}\) =
Answer:
4 – \(\frac{4}{7}\) =
Answer:
4 – \(\frac{4}{7}\) = 3\(\frac{3}{7}\)
Explanation :
4 – \(\frac{4}{7}\) = \(\frac{28}{7}\) – \(\frac{4}{7}\) = \(\frac{24}{7}\) = 3\(\frac{3}{7}\)

Question 32.
3 – \(\frac{5}{7}\) =
Answer:
3 – \(\frac{5}{7}\) = 2\(\frac{2}{7}\)
Explanation :
3 – \(\frac{5}{7}\) = \(\frac{21}{7}\) – \(\frac{5}{7}\) = \(\frac{16}{7}\) = 2\(\frac{2}{7}\)

Question 33.
4 – \(\frac{3}{4}\) =
Answer:
4 – \(\frac{3}{4}\) = 3\(\frac{1}{4}\)
Explanation :
4 – \(\frac{3}{4}\) = \(\frac{16}{4}\) – \(\frac{3}{4}\) = \(\frac{13}{4}\) = 3\(\frac{1}{4}\)

Question 34.
2 – \(\frac{5}{8}\) =
Answer:
2 – \(\frac{5}{8}\) = 1\(\frac{3}{8}\)
Explanation :
2 – \(\frac{5}{8}\) = \(\frac{16}{8}\) – \(\frac{5}{8}\) = \(\frac{11}{8}\) = 1\(\frac{3}{8}\)

Question 35.
3 – \(\frac{3}{10}\) =
Answer:
3 – \(\frac{3}{10}\) = 2\(\frac{7}{10}\)
Explanation :
3 – \(\frac{3}{10}\) = \(\frac{30}{10}\) – \(\frac{3}{10}\) = \(\frac{27}{10}\) = 2\(\frac{7}{10}\)

Question 36.
4 – \(\frac{2}{5}\) =
Answer:
4 – \(\frac{2}{5}\) = 3\(\frac{3}{5}\)
Explanation :
4 – \(\frac{2}{5}\) = \(\frac{20}{5}\) – \(\frac{2}{5}\) = \(\frac{18}{5}\) = 3\(\frac{3}{5}\)

Question 37.
4 – \(\frac{3}{7}\) =
Answer:
4 – \(\frac{3}{7}\) =
Answer:
4 – \(\frac{3}{7}\) = 3\(\frac{4}{7}\)
Explanation :
4 – \(\frac{3}{7}\) = \(\frac{28}{7}\) – \(\frac{3}{7}\) = \(\frac{25}{7}\) = 3\(\frac{4}{7}\)

Question 38.
3 – \(\frac{7}{10}\) =
Answer:
3 – \(\frac{7}{10}\) = 2\(\frac{3}{10}\)
Explanation :
3 – \(\frac{7}{10}\) = \(\frac{30}{10}\) – \(\frac{7}{10}\) = \(\frac{23}{10}\) = 2\(\frac{3}{10}\)

Question 39.
3 – \(\frac{5}{10}\) =
Answer:
3 – \(\frac{5}{10}\) = 2\(\frac{5}{10}\)
Explanation :
3 – \(\frac{5}{10}\) = \(\frac{30}{10}\) – \(\frac{5}{10}\) = \(\frac{25}{10}\) = 2\(\frac{5}{10}\)

Question 40.
4 – \(\frac{2}{8}\) =
Answer:
4 – \(\frac{2}{8}\) = 3\(\frac{6}{8}\)
Explanation :
4 – \(\frac{2}{8}\) = \(\frac{32}{8}\) – \(\frac{2}{8}\) = \(\frac{30}{8}\) = 3\(\frac{6}{8}\)

Question 41.
2 – \(\frac{9}{12}\) =
Answer:
2 – \(\frac{9}{12}\) = 2 – \(\frac{3}{4}\) = 1\(\frac{1}{4}\)
Explanation :
2 – \(\frac{3}{4}\) = \(\frac{8}{4}\) – \(\frac{3}{4}\) = \(\frac{5}{4}\) = 1\(\frac{1}{4}\)

Question 42.
4 – \(\frac{2}{12}\) = 3\(\frac{5}{6}\)
Answer:
4 – \(\frac{2}{12}\) = 4 – \(\frac{1}{6}\) = 3\(\frac{5}{6}\)
Explanation :
4 – \(\frac{1}{6}\) = \(\frac{24}{6}\) – \(\frac{1}{6}\) = \(\frac{23}{6}\) = 3\(\frac{5}{6}\)

Question 43.
3 – \(\frac{2}{6}\) =
Answer:
3 – \(\frac{2}{6}\) = 3 – \(\frac{1}{3}\) = 2\(\frac{2}{3}\)
Explanation :
3 – \(\frac{1}{3}\) = \(\frac{9}{3}\) – \(\frac{1}{3}\) = \(\frac{8}{3}\) = 2\(\frac{2}{3}\)

Question 44.
2 – \(\frac{8}{12}\) =
Answer:
2 – \(\frac{8}{12}\) = 2 – \(\frac{2}{3}\) = 1\(\frac{1}{3}\)
Explanation :
2 – \(\frac{2}{3}\) = \(\frac{6}{3}\) – \(\frac{2}{3}\) = \(\frac{4}{3}\) = 2\(\frac{1}{3}\)

B
Subtracting Fractions from a Whole Number

Question 1.
1 – \(\frac{1}{2}\) =
Answer:
1 – \(\frac{1}{2}\) = \(\frac{1}{2}\)
Explanation :
1 – \(\frac{1}{2}\) = \(\frac{2}{2}\) – \(\frac{1}{2}\) = \(\frac{1}{2}\)

Question 2.
2 – \(\frac{1}{2}\) =
Answer:
2 – \(\frac{1}{2}\) = 1\(\frac{1}{2}\)
Explanation :
2 – \(\frac{1}{2}\) = \(\frac{4}{2}\) – \(\frac{1}{2}\) = \(\frac{3}{2}\) = 1\(\frac{1}{2}\)

Question 3.
3 – \(\frac{1}{2}\) =
Answer:
3 – \(\frac{1}{2}\) = 2\(\frac{1}{2}\)
Explanation :
3 – \(\frac{1}{2}\) = \(\frac{6}{2}\) – \(\frac{1}{2}\) = \(\frac{5}{2}\) = 2\(\frac{1}{2}\)

Question 4.
4 – \(\frac{1}{2}\) =
Answer:
4 – \(\frac{1}{2}\) = 3\(\frac{1}{2}\)
Explanation :
4 – \(\frac{1}{2}\) = \(\frac{8}{2}\) – \(\frac{1}{2}\) = \(\frac{7}{2}\) = 3\(\frac{1}{2}\)

Question 5.
1 – \(\frac{1}{4}\) =
Answer:
1 – \(\frac{1}{4}\) = \(\frac{3}{4}\)
Explanation :
1 – \(\frac{1}{4}\) = \(\frac{4}{4}\) – \(\frac{1}{4}\) = \(\frac{3}{4}\)

Question 6.
2 – \(\frac{1}{4}\) =
Answer:
2 – \(\frac{1}{4}\) = 1\(\frac{3}{4}\)
Explanation :
2 – \(\frac{1}{4}\) = \(\frac{8}{4}\) – \(\frac{1}{4}\) = \(\frac{7}{4}\) = 1\(\frac{3}{4}\)

Question 7.
4 – \(\frac{1}{4}\) =
Answer:
4 – \(\frac{1}{4}\) = 3\(\frac{3}{4}\)
Explanation :
4 – \(\frac{1}{4}\) = \(\frac{16}{4}\) – \(\frac{1}{4}\) = \(\frac{15}{4}\) = 3\(\frac{3}{4}\)

Question 8.
4 – \(\frac{3}{4}\) =
Answer:
4 – \(\frac{3}{4}\) = 3\(\frac{1}{4}\)
Explanation :
4 – \(\frac{3}{4}\) = \(\frac{16}{4}\) – \(\frac{3}{4}\) = \(\frac{13}{4}\) = 3\(\frac{1}{4}\)

Question 9.
2 – \(\frac{3}{4}\) =
Answer:
2 – \(\frac{3}{4}\) = 1\(\frac{1}{4}\)
Explanation :
2 – \(\frac{3}{4}\) = \(\frac{8}{4}\) – \(\frac{3}{4}\) = \(\frac{5}{4}\) = 1\(\frac{1}{4}\)

Question 10.
2 – \(\frac{1}{3}\) =
Answer:
2 – \(\frac{1}{3}\) = 1\(\frac{2}{3}\)
Explanation :
2 – \(\frac{1}{3}\) = \(\frac{6}{3}\) – \(\frac{1}{3}\) = \(\frac{5}{3}\) = 1\(\frac{2}{3}\)

Question 11.
2 – \(\frac{2}{3}\) =
Answer:
2 – \(\frac{2}{3}\) = 1\(\frac{1}{3}\)
Explanation :
2 – \(\frac{2}{3}\) = \(\frac{6}{3}\) – \(\frac{2}{3}\) = \(\frac{4}{3}\) = 1\(\frac{1}{3}\)

Question 12.
3 – \(\frac{2}{3}\) =
Answer:
3 – \(\frac{2}{3}\) = 2\(\frac{1}{3}\)
Explanation :
3 – \(\frac{2}{3}\) = \(\frac{9}{3}\) – \(\frac{2}{3}\) = \(\frac{7}{3}\) = 2\(\frac{1}{3}\)

Question 13.
3 – \(\frac{1}{3}\) =
Answer:
3 – \(\frac{1}{3}\) = 2\(\frac{2}{3}\)
Explanation :
3 – \(\frac{1}{3}\) = \(\frac{9}{3}\) – \(\frac{1}{3}\) = \(\frac{8}{3}\) = 2\(\frac{2}{3}\)

Question 14.
4 – \(\frac{2}{3}\) =
Answer:
4 – \(\frac{2}{3}\) = 3\(\frac{1}{3}\)
Explanation :
4 – \(\frac{2}{3}\) = \(\frac{12}{3}\) – \(\frac{2}{3}\) = \(\frac{10}{3}\) = 3\(\frac{1}{3}\)

Question 15.
3 – \(\frac{1}{10}\) =
Answer:
3 – \(\frac{1}{10}\) = 2\(\frac{9}{10}\)
Explanation :
3 – \(\frac{1}{10}\) = \(\frac{30}{10}\) – \(\frac{9}{10}\) = \(\frac{21}{10}\) = 2\(\frac{1}{10}\)

Question 16.
2 – \(\frac{9}{10}\) =
Answer:
2 – \(\frac{9}{10}\) = 1\(\frac{1}{10}\)
Explanation :
2 – \(\frac{9}{10}\) = \(\frac{20}{10}\) – \(\frac{9}{10}\) = \(\frac{11}{10}\) = 1\(\frac{1}{10}\)

Question 17.
4 – \(\frac{7}{10}\) =
Answer:
4 – \(\frac{7}{10}\) = 3\(\frac{3}{10}\)
Explanation :
4 – \(\frac{7}{10}\) = \(\frac{40}{10}\) – \(\frac{7}{10}\) = \(\frac{33}{10}\) = 3\(\frac{3}{10}\)

Question 18.
3 – \(\frac{3}{10}\) =
Answer:
3 – \(\frac{3}{10}\) = 2\(\frac{7}{10}\)
Explanation :
3 – \(\frac{3}{10}\) = \(\frac{30}{10}\) – \(\frac{3}{10}\) = \(\frac{27}{10}\) = 2\(\frac{7}{10}\)

Question 19.
2 – \(\frac{1}{5}\) =
Answer:
2 – \(\frac{1}{5}\) = 1\(\frac{4}{5}\)
Explanation :
2 – \(\frac{1}{5}\) = \(\frac{10}{5}\) – \(\frac{1}{5}\) = \(\frac{9}{5}\) = 1\(\frac{4}{5}\)

Question 20.
2 – \(\frac{2}{5}\) =
Answer:
2 – \(\frac{2}{5}\) = 1\(\frac{3}{5}\)
Explanation :
2 – \(\frac{2}{5}\) = \(\frac{10}{5}\) – \(\frac{2}{5}\) = \(\frac{8}{5}\) = 1\(\frac{3}{5}\)

Question 21.
2 – \(\frac{4}{5}\) =
Answer:
2 – \(\frac{4}{5}\) = 1\(\frac{1}{5}\)
Explanation :
2 – \(\frac{1}{5}\) = \(\frac{10}{5}\) – \(\frac{4}{5}\) = \(\frac{6}{5}\) = 1\(\frac{1}{5}\)

Question 22.
3 – \(\frac{3}{5}\) =
Answer:
3 – \(\frac{3}{5}\) = 2\(\frac{2}{5}\)
Explanation :
3 – \(\frac{3}{5}\) = \(\frac{15}{5}\) – \(\frac{3}{5}\) = \(\frac{12}{5}\) = 2\(\frac{2}{5}\)

Question 23.
2 – \(\frac{1}{8}\) =
Answer:
2 – \(\frac{1}{8}\) = 1\(\frac{7}{8}\)
Explanation :
2 – \(\frac{1}{8}\) = \(\frac{16}{8}\) – \(\frac{1}{8}\) = \(\frac{15}{8}\) = 1\(\frac{7}{8}\)

Question 24.
2 – \(\frac{3}{8}\) =
Answer:
2 – \(\frac{3}{8}\) = 1\(\frac{5}{8}\)
Explanation :
2 – \(\frac{3}{8}\) = \(\frac{16}{8}\) – \(\frac{3}{8}\) = \(\frac{13}{8}\) = 1\(\frac{4}{8}\)

Question 25.
2 – \(\frac{5}{8}\) =
Answer:
2 – \(\frac{5}{8}\) = 1\(\frac{3}{8}\)
Explanation :
2 – \(\frac{5}{8}\) = \(\frac{16}{8}\) – \(\frac{5}{8}\) = \(\frac{11}{8}\) = 1\(\frac{3}{8}\)

Question 26.
2 – \(\frac{7}{8}\) =
Answer:
2 – \(\frac{7}{8}\) = 1\(\frac{1}{8}\)
Explanation :
2 – \(\frac{7}{8}\) = \(\frac{16}{8}\) – \(\frac{7}{8}\) = \(\frac{9}{8}\) = 1\(\frac{1}{8}\)

Question 27.
4 – \(\frac{7}{8}\) =
Answer:
4 – \(\frac{7}{8}\) = 3\(\frac{1}{8}\)
Explanation :
4 – \(\frac{7}{8}\) = \(\frac{32}{8}\) – \(\frac{3}{8}\) = \(\frac{13}{8}\) = 1\(\frac{4}{8}\)

Question 28.
3 – \(\frac{1}{7}\) =
Answer:
3 – \(\frac{1}{7}\) = 2\(\frac{6}{7}\)
Explanation :
3 – \(\frac{1}{7}\) = \(\frac{21}{7}\) – \(\frac{1}{7}\) = \(\frac{20}{7}\) = 2\(\frac{6}{7}\)

Question 29.
2 – \(\frac{6}{7}\) =
Answer:
2 – \(\frac{6}{7}\) = 1\(\frac{1}{7}\)
Explanation :
2 – \(\frac{6}{7}\) = \(\frac{14}{7}\) – \(\frac{6}{7}\) = \(\frac{8}{7}\) = 1\(\frac{1}{7}\)

Question 30.
4 – \(\frac{3}{7}\) =
Answer:
4 – \(\frac{3}{7}\) = 3\(\frac{4}{7}\)
Explanation :
4 – \(\frac{3}{7}\) = \(\frac{28}{7}\) – \(\frac{3}{7}\) = \(\frac{25}{7}\) = 3\(\frac{4}{7}\)

Question 31.
3 – \(\frac{4}{7}\) =
Answer:
3 – \(\frac{4}{7}\) = 2\(\frac{3}{7}\)
Explanation :
3 – \(\frac{4}{7}\) = \(\frac{21}{7}\) – \(\frac{4}{7}\) = \(\frac{17}{7}\) = 2\(\frac{3}{7}\)

Question 32.
2 – \(\frac{5}{7}\) =
Answer:
2 – \(\frac{5}{7}\) = 1\(\frac{2}{7}\)
Explanation :
2 – \(\frac{5}{7}\) = \(\frac{14}{7}\) – \(\frac{5}{7}\) = \(\frac{9}{7}\) = 1\(\frac{2}{7}\)

Question 33.
3 – \(\frac{3}{4}\) =
Answer:
3 – \(\frac{3}{4}\) = 2\(\frac{1}{4}\)
Explanation :
3 – \(\frac{3}{4}\) = \(\frac{12}{4}\) – \(\frac{3}{4}\) = \(\frac{9}{4}\) = 2\(\frac{1}{4}\)

Question 34.
4 – \(\frac{5}{8}\) =
Answer:
4 – \(\frac{5}{8}\) = 3\(\frac{3}{8}\)
Explanation :
4 – \(\frac{5}{8}\) = \(\frac{32}{8}\) – \(\frac{5}{8}\) = \(\frac{27}{8}\) = 3\(\frac{3}{8}\)

Question 35.
2 – \(\frac{3}{10}\) =
Answer:
2 – \(\frac{3}{10}\) = 1\(\frac{7}{10}\)
Explanation :
2 – \(\frac{3}{10}\) = \(\frac{20}{10}\) – \(\frac{3}{10}\) = \(\frac{17}{10}\) = 1\(\frac{7}{10}\)

Question 36.
3 – \(\frac{2}{5}\) =
Answer:
3 – \(\frac{2}{5}\) = 2\(\frac{3}{5}\)
Explanation :
3 – \(\frac{2}{5}\) = \(\frac{15}{5}\) – \(\frac{2}{5}\) = \(\frac{13}{5}\) = 2\(\frac{3}{5}\)

Question 37.
3 – \(\frac{3}{7}\) =
Answer:
3 – \(\frac{3}{7}\) = 2\(\frac{4}{7}\)
Explanation :
3 – \(\frac{3}{7}\) = \(\frac{21}{7}\) – \(\frac{3}{7}\) = \(\frac{18}{7}\) = 2\(\frac{4}{7}\)

Question 38.
2 – \(\frac{7}{10}\) =
Answer:
2 – \(\frac{7}{10}\) = 1\(\frac{3}{10}\)
Explanation :
2 – \(\frac{7}{10}\) = \(\frac{20}{10}\) – \(\frac{7}{10}\) = \(\frac{13}{10}\) = 1\(\frac{3}{10}\)

Question 39.
2 – \(\frac{5}{10}\) =
Answer:
2 – \(\frac{5}{10}\) = 1\(\frac{1}{2}\)
Explanation :
2 – \(\frac{5}{10}\) = \(\frac{20}{10}\) – \(\frac{5}{10}\) = \(\frac{15}{10}\) = \(\frac{3}{2}\) = 1\(\frac{1}{2}\)

Question 40.
3 – \(\frac{6}{8}\) =
Answer:
3 – \(\frac{6}{8}\) = 2\(\frac{1}{4}\)
Explanation :
3 – \(\frac{6}{8}\) = \(\frac{24}{8}\) – \(\frac{6}{8}\) = \(\frac{18}{8}\) = 2\(\frac{1}{4}\)

Question 41.
4 – \(\frac{3}{12}\) =
Answer:
4 – \(\frac{3}{12}\) = 4 – \(\frac{1}{4}\) = 3\(\frac{3}{4}\)
Explanation :
4 – \(\frac{1}{4}\) = \(\frac{16}{4}\) – \(\frac{1}{4}\) = \(\frac{15}{4}\) = 3\(\frac{3}{4}\)

Question 42.
3 – \(\frac{10}{12}\) =
Answer:
3 – \(\frac{10}{12}\) = 3 – \(\frac{5}{6}\) = 2\(\frac{1}{6}\)
Explanation :
3 – \(\frac{5}{6}\) = \(\frac{18}{6}\) – \(\frac{5}{6}\) = \(\frac{13}{6}\) = 2\(\frac{1}{6}\)

Question 43.
2 – \(\frac{4}{6}\) =
Answer:
2 – \(\frac{4}{6}\) = 2 – \(\frac{2}{3}\) = 1\(\frac{1}{3}\)
Explanation :
2 – \(\frac{2}{3}\) = \(\frac{6}{3}\) – \(\frac{2}{3}\) = \(\frac{4}{3}\) = 1\(\frac{1}{3}\)

Question 44.
4 – \(\frac{4}{12}\) =
Answer:
4 – \(\frac{4}{12}\) = 4 – \(\frac{1}{3}\) = 3\(\frac{2}{3}\)
Explanation :
4 – \(\frac{1}{3}\) = \(\frac{12}{3}\) – \(\frac{1}{3}\) = \(\frac{11}{3}\) = 3\(\frac{2}{3}\)

Eureka Math Grade 5 Module 3 Lesson 5 Problem Set Answer Key

Question 1.
For the following problems, draw a picture using the rectangular fraction model and write the answer. Simplify your answer, if possible.
a. \(\frac{1}{3}\) – \(\frac{1}{4}\) =
b. \(\frac{2}{3}\) – \(\frac{1}{2}\) =
c. \(\frac{5}{6}\) – \(\frac{1}{4}\) =
d. \(\frac{2}{3}\) – \(\frac{1}{7}\) =
e. \(\frac{3}{4}\) – \(\frac{3}{8}\) =
f. \(\frac{3}{4}\) – \(\frac{2}{7}\) =
Answer:
a.
\(\frac{1}{3}\) – \(\frac{1}{4}\)
L.c.m of 3 and 4 is 12
\(\frac{4}{12}\) – \(\frac{3}{12}\) = \(\frac{1}{12}\)

b.
\(\frac{2}{3}\) – \(\frac{1}{2}\)
lcm of 3 and 2 is 6
\(\frac{4}{6}\) – \(\frac{3}{6}\) = \(\frac{1}{6}\)

c.
\(\frac{5}{6}\) – \(\frac{1}{4}\)
lcm of 6 and 4 is 12
\(\frac{10}{12}\) – \(\frac{3}{12}\) = \(\frac{7}{12}\)

d.
\(\frac{2}{3}\) – \(\frac{1}{7}\)
lcm of 3 and 7 is 21 .
\(\frac{14}{21}\) – \(\frac{3}{21}\)  = \(\frac{11}{21}\)

e.
\(\frac{3}{4}\) – \(\frac{3}{8}\)
lcm of 4 and 8 is 8
\(\frac{6}{8}\) – \(\frac{3}{8}\) = \(\frac{3}{8}\)

f.
\(\frac{3}{4}\) – \(\frac{2}{7}\)
lcm of 4 and 7 is 28
\(\frac{21}{28}\) – \(\frac{8}{28}\) = \(\frac{13}{28}\)

Question 2.
Mr. Penman had \(\frac{2}{3}\) liter of salt water. He used \(\frac{1}{5}\) of a liter for an experiment. How much salt water does Mr. Penman have left?
Answer:
Quantity of salt water = \(\frac{2}{3}\)
Quantity of salt water used = \(\frac{1}{5}\)
Quantity of salt water left = \(\frac{2}{3}\) – \(\frac{1}{5}\) = \(\frac{10}{15}\) – \(\frac{3}{15}\)
= \(\frac{7}{15}\) .

Question 3.
Sandra says that \(\frac{4}{7}\) – \(\frac{1}{3}\) = \(\frac{3}{4}\) because all you have to do is subtract the numerators and subtract the denominators. Convince Sandra that she is wrong. You may draw a rectangular fraction model to support your thinking.
Answer:
No, \(\frac{4}{7}\) – \(\frac{1}{3}\) = \(\frac{5}{21}\) not \(\frac{3}{4}\)

Explanation :
\(\frac{4}{7}\) – \(\frac{1}{3}\) = \(\frac{12}{21}\) – \(\frac{7}{21}\) =  \(\frac{5}{21}\)
no, first find the l.c.m of the denominators that is lcm of 7 and 3 is 21 . then multiply the denominators to make 21 and and also multiply same number with the numerator . then after making denominators equal subtract the numerators .

Eureka Math Grade 5 Module 3 Lesson 5 Exit Ticket Answer Key

For the following problems, draw a picture using the rectangular fraction model and write the answer. Simplify your answer, if possible.
a. \(\frac{1}{2}\) – \(\frac{1}{7}\) =
b. \(\frac{3}{5}\) – \(\frac{1}{2}\) =
Answer:
a.
\(\frac{1}{2}\) – \(\frac{1}{7}\)
lcm of 2 and 7 is 14
\(\frac{7}{14}\) – \(\frac{2}{14}\) = \(\frac{5}{14}\)

b.
\(\frac{3}{5}\) – \(\frac{1}{2}\)
lcm of 5 and 2 is 10 .
\(\frac{6}{10}\) – \(\frac{5}{10}\) = \(\frac{1}{10}\)

Eureka Math Grade 5 Module 3 Lesson 5 Homework Answer Key

Question 1.
The picture below shows \(\frac{3}{4}\) of the rectangle shaded. Use the picture to show how to create an equivalent fraction for \(\frac{3}{4}\), and then subtract \(\frac{1}{3}\).
\(\frac{3}{4}\) – \(\frac{1}{3}\) =

Answer:

Explanation :
\(\frac{3}{4}\) – \(\frac{1}{3}\)
l.c.m of 4 and 3 is 12
\(\frac{9}{12}\) – \(\frac{4}{12}\) = \(\frac{5}{12}\)

Question 2.
Find the difference. Use a rectangular fraction model to find common denominators. Simplify your answer, if possible.
a. \(\frac{5}{6}\) – \(\frac{1}{3}\) =
b. \(\frac{2}{3}\) – \(\frac{1}{2}\) =
c. \(\frac{5}{6}\) – \(\frac{1}{4}\) =
d. \(\frac{4}{5}\) – \(\frac{1}{2}\) =
e. \(\frac{2}{3}\) – \(\frac{2}{5}\) =
f. \(\frac{5}{7}\) – \(\frac{2}{3}\) =
Answer:
a.

\(\frac{5}{6}\) – \(\frac{1}{3}\)
Lcm of 6 and 3 is 6 .
\(\frac{5}{6}\) – \(\frac{2}{6}\) = \(\frac{3}{6}\) = \(\frac{1}{2}\)

b.
\(\frac{2}{3}\) – \(\frac{1}{2}\)
lcm of 3 and 2 is 6
\(\frac{4}{6}\) – \(\frac{3}{6}\) = \(\frac{2}{6}\) = \(\frac{1}{3}\)

c.
\(\frac{5}{6}\) – \(\frac{1}{4}\)
lcm of 6 and 4
\(\frac{10}{12}\) – \(\frac{3}{12}\) = \(\frac{7}{12}\)

d.
\(\frac{4}{5}\) – \(\frac{1}{2}\)
lcm of 5 and 2 is 10
\(\frac{8}{10}\) – \(\frac{5}{10}\) = \(\frac{3}{10}\)

e.
\(\frac{2}{3}\) – \(\frac{2}{5}\)
lcm of 3 and 5 is 15
\(\frac{10}{15}\) – \(\frac{6}{15}\)= \(\frac{4}{15}\)

f.
\(\frac{5}{7}\) – \(\frac{2}{3}\)
lcm of 7 and 3 is 21.
\(\frac{15}{21}\) – \(\frac{14}{21}\) = \(\frac{1}{21}\)

Question 3.
Robin used \(\frac{1}{4}\) of a pound of butter to make a cake. Before she started, she had \(\frac{7}{8}\) of a pound of butter. How much butter did Robin have when she was done baking? Give your answer as a fraction of a pound.
Answer:
Quantity of butter used to make cake = \(\frac{1}{4}\)  pound
Quantity of butter with Robin before baking cake = \(\frac{7}{8}\)  pound .
Total Quantity of butter with Robin after baking = \(\frac{7}{8}\)  – \(\frac{1}{4}\) pound  = \(\frac{7}{8}\)  – \(\frac{2}{8}\) = \(\frac{5}{8}\) pound
Therefore, Robin have \(\frac{5}{8}\) pound  when she was done baking .

Question 4.
Katrina needs \(\frac{3}{5}\) kilogram of flour for a recipe. Her mother has \(\frac{3}{7}\) kilogram of flour in her pantry. Is this enough flour for the recipe? If not, how much more will she need?
Answer:
Quantity of Flour Required for Recipe = \(\frac{3}{5}\)
Quantity of Flour with her mother = \(\frac{3}{7}\)
Quantity of Flour Enough or not = \(\frac{3}{7}\) – \(\frac{3}{5}\)  = \(\frac{15}{35}\) – \(\frac{21}{35}\) = – \(\frac{6}{35}\) that means negative indicate doenot enough.
She needs more \(\frac{6}{35}\) Quantity of Flour for the Recipe .