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

Question 2.
3 + $$\frac{1}{2}$$ =
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 =
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 =
3 – 1 = 2
Explanation :
subtracting 1 from 3 we get 2 .

Question 5.
3$$\frac{1}{2}$$ – 1 =
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 =
4 – 2 = 2
Explanation :
Subtracting 2 from 4 we get difference as 2.

Question 7.
4$$\frac{1}{2}$$ – 2 =
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 =
5 – 2 = 3
Explanation :
Subtracting 2 from 5 we get difference as 3.

Question 9.
5$$\frac{1}{3}$$ – 2 =
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 =
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 =
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 =
6 + 2 = 8
Explanation :
Adding 2 to 6 we get sum as 8 .

Question 13.
6 + $$\frac{3}{4}$$ =
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 =
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 =
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 =
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 =
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 =
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$$\frac{3}{4}$$ – $$\frac{3}{4}$$ =
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 =
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 =
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 =
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 =
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 =
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 =
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 =
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 =
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 =
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 =
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 =
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
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 =
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 + $$\frac{2}{5}$$ =
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$$\frac{2}{5}$$ =
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 + $$\frac{1}{3}$$ =
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$$\frac{1}{3}$$ =
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 =
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$$\frac{1}{3}$$ =
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$$\frac{2}{3}$$ =
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 + $$\frac{2}{7}$$ =
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$$\frac{2}{7}$$ =
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$$\frac{3}{5}$$ =
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$$\frac{2}{5}$$ =
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$$\frac{5}{9}$$ =
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 =
2 + 1 = 3
Explanation :
adding 1 to 2 we get sum as 3 .

Question 2.
2 + $$\frac{1}{2}$$ =
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 =
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 =
2 – 1 = 1
Explanation :
Subtracting 1 from 2 we get 1as difference .

Question 5.
2$$\frac{1}{2}$$ – 1 =
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 =
5 – 2 = 3
Explanation :
subtract 2 from 5 we get 3 as difference .

Question 7.
5$$\frac{1}{2}$$ – 2 =
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 =
6 – 2 = 4
Explanation :
subtract 2 from 6 we get 4 as difference .

Question 9.
6$$\frac{1}{3}$$ – 2 =
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 =
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 =
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 =
7 + 2 = 9
Explanation:
Adding 2 to 7 we get sum as 9

Question 13.
7 + $$\frac{3}{4}$$ =
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 =
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 =
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 =
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 =
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 =
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$$\frac{3}{4}$$ – $$\frac{3}{4}$$ =
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 =
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 =
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 =
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 =
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 =
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 =
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 =
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 =
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 =
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 =
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 =
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 =
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 =
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 + $$\frac{2}{5}$$ =
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$$\frac{2}{5}$$ =
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 + $$\frac{1}{3}$$ =
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$$\frac{1}{3}$$ =
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 =
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$$\frac{1}{3}$$ =
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$$\frac{2}{3}$$ =
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 + $$\frac{2}{7}$$ =
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$$\frac{2}{7}$$ =
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$$\frac{3}{5}$$ =
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$$\frac{3}{5}$$ =
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$$\frac{5}{9}$$ =
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.
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$$\frac{2}{5}$$ =
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?
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?
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.
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

Question 1.
3$$\frac{1}{2}$$ + 1$$\frac{1}{3}$$ =
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$$\frac{3}{4}$$ =
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.
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$$\frac{2}{5}$$ =
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?
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?
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 .
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.
Matt is wrong 5 – 1$$\frac{1}{4}$$ = 3$$\frac{3}{4}$$ which is less than 4 .
5 – 1$$\frac{1}{4}$$ = 5 – $$\frac{5}{4}$$
5 – $$\frac{5}{4}$$ = $$\frac{20}{4}$$ – $$\frac{5}{4}$$ = $$\frac{15}{4}$$ = 3$$\frac{3}{4}$$