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\(\frac{3}{4}\)
