## 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.
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.
$$\frac{3}{8}$$ – $$\frac{1}{6}$$ = $$\frac{3}{8}$$ – $$\frac{1}{6}$$
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?)
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?
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$$\frac{1}{3}$$ =
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$$\frac{1}{3}$$ =
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?
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?
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?
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 = $$\frac{13}{15}$$
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?
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$$\frac{1}{6}$$ .