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