## Engage NY Eureka Math 5th Grade Module 6 Lesson 20 Answer Key

### Eureka Math Grade 5 Module 6 Lesson 20 Sprint Answer Key

A
Subtracting Fractions from a Whole Number

Question 1.
4 – $$\frac{1}{2}$$ =
4 – $$\frac{1}{2}$$ = $$\frac{8 – 1 }{2}$$ = $$\frac{7}{2}$$

Question 2.
3 – $$\frac{1}{2}$$ =
3 – $$\frac{1}{2}$$ = $$\frac{6 – 1 }{2}$$ = $$\frac{5}{2}$$

Question 3.
2 – $$\frac{1}{2}$$ =
2 – $$\frac{1}{2}$$ = $$\frac{4-1}{2}$$ = $$\frac{3}{2}$$ = 1$$\frac{1}{2}$$

Question 4.
1 – $$\frac{1}{2}$$ =
1- $$\frac{1}{2}$$ = $$\frac{2 – 1}{2}$$ = $$\frac{1}{2}$$

Question 5.
1 – $$\frac{1}{3}$$ =
1 – $$\frac{1}{3}$$ = $$\frac{3 – 1}{3}$$ = $$\frac{2}{3}$$

Question 6.
2 – $$\frac{1}{3}$$ =
2 – $$\frac{1}{3}$$ = $$\frac{6 – 1}{3}$$ = $$\frac{5}{3}$$ =  1$$\frac{2}{3}$$

Question 7.
4 – $$\frac{1}{3}$$ =
4 – $$\frac{1}{3}$$ = $$\frac{12 – 1}{3}$$ = $$\frac{11}{3}$$= 3$$\frac{2}{3}$$

Question 8.
4 – $$\frac{2}{3}$$ =
4 – $$\frac{2}{3}$$ = $$\frac{12 – 2}{3}$$ = $$\frac{10}{3}$$ = 3$$\frac{1}{3}$$

Question 9.
2 – $$\frac{2}{3}$$ =
2 – $$\frac{2}{3}$$= $$\frac{8 -2}{3}$$

Question 10.
2 – $$\frac{1}{4}$$ =
2 – $$\frac{1}{4}$$ = $$\frac{8 -1}{4}$$ = $$\frac{7}{4}$$ = 1$$\frac{3}{4}$$

Question 11.
2 – $$\frac{3}{4}$$ =
2 – $$\frac{3}{4}$$ = $$\frac{8 – 3}{4}$$= $$\frac{5}{4}$$ = 1$$\frac{1}{4}$$

Question 12.
3 – $$\frac{3}{4}$$ =
3 – $$\frac{3}{4}$$= $$\frac{9 – 3}{4}$$ = $$\frac{6}{4}$$= 1$$\frac{2}{4}$$

Question 13.
3 – $$\frac{1}{4}$$ =
3 – $$\frac{1}{4}$$ = $$\frac{12 – 1}{4}$$= $$\frac{11}{4}$$= 2$$\frac{3}{4}$$

Question 14.
4 – $$\frac{3}{4}$$ =
4 – $$\frac{3}{4}$$ = $$\frac{16 – 3}{4}$$ = $$\frac{13}{4}$$= 3$$\frac{1}{4}$$

Question 15.
2 – $$\frac{1}{10}$$ =
2 – $$\frac{1}{10}$$ = $$\frac{20 – 1}{10}$$ = $$\frac{19}{10}$$ = 1$$\frac{9}{10}$$

Question 16.
3 – $$\frac{9}{10}$$ =
3 – $$\frac{9}{10}$$ = $$\frac{30 – 9}{10}$$ = $$\frac{21}{10}$$ = 2$$\frac{1}{10}$$

Question 17.
2 – $$\frac{7}{10}$$ =
2 – $$\frac{7}{10}$$ = $$\frac{20- 7}{10}$$= $$\frac{13}{10}$$= 1 $$\frac{3}{10}$$

Question 18.
4 – $$\frac{3}{10}$$ =
4 – $$\frac{7}{10}$$= $$\frac{40 – 7}{10}$$ = $$\frac{33}{10}$$= 3 $$\frac{3}{10}$$

Question 19.
3 – $$\frac{1}{5}$$ =
3 – $$\frac{1}{5}$$ = $$\frac{15 – 1}{5}$$ = $$\frac{14}{5}$$= 2 $$\frac{4}{5}$$

Question 20.
3 – $$\frac{2}{5}$$ =
3 – $$\frac{2}{5}$$ = $$\frac{15 – 2}{5}$$ = $$\frac{13}{5}$$=2$$\frac{3}{5}$$

Question 21.
3 – $$\frac{4}{5}$$ =
3 – $$\frac{4}{5}$$ = $$\frac{15 – 4}{5}$$ = $$\frac{11}{5}$$= 2$$\frac{1}{5}$$

Question 22.
3 – $$\frac{3}{5}$$ =
3 – $$\frac{3}{5}$$ = $$\frac{15 – 3}{5}$$ = $$\frac{12}{5}$$=2 $$\frac{2}{5}$$

Question 23.
3 – $$\frac{1}{8}$$ =
3 – $$\frac{1}{8}$$= $$\frac{24 – 1}{8}$$= $$\frac{23}{8}$$ =2$$\frac{7}{8}$$

Question 24.
3 – $$\frac{3}{8}$$ =
3 – $$\frac{3}{8}$$ = $$\frac{24 -3}{8}$$ = $$\frac{21}{8}$$ = 2$$\frac{5}{8}$$

Question 25.
3 – $$\frac{5}{8}$$ =
3 – $$\frac{5}{8}$$ = $$\frac{24 – 5}{8}$$ =$$\frac{19}{8}$$ = 2$$\frac{3}{8}$$

Question 26.
3 – $$\frac{7}{8}$$ =
3 – $$\frac{7}{8}$$ =$$\frac{24 – 7}{8}$$ = $$\frac{23}{8}$$ =2 $$\frac{7}{8}$$

Question 27.
2 – $$\frac{7}{8}$$ =
2 – $$\frac{7}{8}$$ = $$\frac{16 – 7}{8}$$ = $$\frac{9}{8}$$ = 1$$\frac{1}{8}$$

Question 28.
4 – $$\frac{1}{7}$$ =
4 – $$\frac{1}{7}$$ = $$\frac{32 -1}{7}$$ = $$\frac{31}{7}$$ = 4$$\frac{3}{7}$$

Question 29.
3 – $$\frac{6}{7}$$ =
3 – $$\frac{6}{7}$$ =$$\frac{21 – 6}{7}$$ =$$\frac{15}{7}$$ = 2 $$\frac{1}{7}$$

Question 30.
2 – $$\frac{3}{7}$$ =
2 – $$\frac{6}{7}$$ = $$\frac{14 – 6}{7}$$ = $$\frac{8}{7}$$ = 1$$\frac{1}{7}$$

Question 31.
4 – $$\frac{4}{7}$$ =
4 – $$\frac{4}{7}$$ = $$\frac{28 – 4}{7}$$ = $$\frac{24}{7}$$ = 3$$\frac{3}{7}$$

Question 32.
3 – $$\frac{5}{7}$$ =
3 – $$\frac{5}{7}$$ = $$\frac{21 – 5}{7}$$ = $$\frac{16}{7}$$ = 2$$\frac{2}{7}$$

Question 33.
4 – $$\frac{3}{4}$$ =
4 – $$\frac{3}{4}$$ = $$\frac{16 – 3 }{4}$$ = $$\frac{13}{4}$$ = 3$$\frac{1}{4}$$

Question 34.
2 – $$\frac{5}{8}$$ =
2 – $$\frac{5}{8}$$ = $$\frac{16 – 5 }{8}$$ = $$\frac{11}{8}$$ = 1$$\frac{3}{8}$$

Question 35.
3 – $$\frac{3}{10}$$ =
3 – $$\frac{3}{10}$$ = $$\frac{30 – 3}{10}$$ = $$\frac{27}{10}$$= 2 $$\frac{7}{10}$$

Question 36.
4 – $$\frac{2}{5}$$ =
4 – $$\frac{2}{5}$$ = $$\frac{20 – 2}{5}$$ = $$\frac{18}{5}$$ = 3$$\frac{3}{5}$$

Question 37.
4 – $$\frac{3}{7}$$ =
4 – $$\frac{3}{7}$$ = $$\frac{28 – 3}{7}$$ = $$\frac{25}{7}$$ = 3$$\frac{4}{7}$$

Question 38.
3 – $$\frac{7}{10}$$ =
3 – $$\frac{7}{10}$$ = $$\frac{30 – 7}{10}$$ = $$\frac{21}{10}$$ = 2$$\frac{1}{10}$$

Question 39.
3 – $$\frac{5}{10}$$ =
3 – $$\frac{5}{10}$$ = $$\frac{30 – 5}{10}$$ = $$\frac{25}{10}$$ = $$\frac{5}{2}$$

Question 40.
4 – $$\frac{2}{8}$$ =
4 – $$\frac{2}{8}$$ = $$\frac{32 – 2}{8}$$ = $$\frac{30}{8}$$ = $$\frac{15}{4}$$

Question 41.
2 – $$\frac{9}{12}$$ =
2 – $$\frac{9}{12}$$ = $$\frac{24 – 9}{12}$$ = $$\frac{15}{12}$$ = $$\frac{5}{4}$$

Question 42.
4 – $$\frac{2}{12}$$ =
4 – $$\frac{2}{12}$$ = $$\frac{48 – 2}{12}$$ = $$\frac{46}{12}$$ = $$\frac{23}{6}$$

Question 43.
3 – $$\frac{2}{6}$$ =
3 – $$\frac{2}{6}$$ = $$\frac{18 – 2}{6}$$ = $$\frac{16}{6}$$ = $$\frac{8}{3}$$

Question 44.
2 – $$\frac{8}{12}$$ =
2 – $$\frac{8}{12}$$ = 2 – $$\frac{2}{3}$$ = $$\frac{6 – 2}{3}$$ = $$\frac{4}{3}$$

B
Subtracting Fractions from a Whole Number

Question 1.
1 – $$\frac{1}{2}$$ =
1 – $$\frac{1}{2}$$ = $$\frac{2 – 1}{2}$$ = $$\frac{1}{2}$$

Question 2.
2 – $$\frac{1}{2}$$ =
2 – $$\frac{1}{2}$$  = $$\frac{4 -1}{2}$$ = $$\frac{3}{2}$$ =1$$\frac{1}{2}$$

Question 3.
3 – $$\frac{1}{2}$$ =
3 – $$\frac{1}{2}$$ = $$\frac{6 – 1}{2}$$ = $$\frac{5}{2}$$ = 2$$\frac{1}{2}$$

Question 4.
4 – $$\frac{1}{2}$$ =
4 – $$\frac{1}{2}$$  = $$\frac{8 -1}{2}$$ = $$\frac{7}{2}$$ =3$$\frac{1}{2}$$

Question 5.
1 – $$\frac{1}{4}$$ =
1 – $$\frac{1}{4}$$ = $$\frac{4 – 1}{4}$$ = $$\frac{3}{4}$$

Question 6.
2 – $$\frac{1}{4}$$ =
2 – $$\frac{1}{4}$$ = $$\frac{8 – 1}{4}$$ = $$\frac{1}{4}$$

Question 7.
4 – $$\frac{1}{4}$$ =
4 – $$\frac{1}{4}$$  = $$\frac{16 – 1}{4}$$ = $$\frac{15}{4}$$ = 3$$\frac{3}{4}$$

Question 8.
4 – $$\frac{3}{4}$$ =
4 – $$\frac{1}{4}$$  = $$\frac{16 – 3}{4}$$ = $$\frac{13}{4}$$ =3$$\frac{1}{4}$$

Question 9.
2 – $$\frac{3}{4}$$ =
2 – $$\frac{3}{4}$$ = $$\frac{8 – 3}{4}$$= $$\frac{5}{4}$$= 1$$\frac{1}{4}$$

Question 10.
2 – $$\frac{1}{3}$$ =
2 – $$\frac{1}{3}$$  = $$\frac{6 – 1}{3}$$ = $$\frac{5}{3}$$ = 1$$\frac{2}{3}$$

Question 11.
2 – $$\frac{2}{3}$$ =
2 – $$\frac{2}{3}$$ = $$\frac{6 – 2}{3}$$ = $$\frac{4}{3}$$= 1$$\frac{1}{3}$$

Question 12.
3 – $$\frac{2}{3}$$ =
3 – $$\frac{2}{3}$$ = $$\frac{9 -2}{3}$$ =$$\frac{7}{3}$$ = 2$$\frac{1}{3}$$

Question 13.
3 – $$\frac{1}{3}$$ =
3 – $$\frac{1}{3}$$ = $$\frac{9 – 1}{3}$$= $$\frac{8}{3}$$= 2$$\frac{2}{3}$$

Question 14.
4 – $$\frac{2}{3}$$ =
4 – $$\frac{2}{3}$$ = $$\frac{12 – 2}{3}$$= $$\frac{10}{3}$$ = 3$$\frac{1}{3}$$

Question 15.
3 – $$\frac{1}{10}$$ =
3 – $$\frac{1}{10}$$ = $$\frac{30 – 1}{10}$$ = $$\frac{29}{10}$$

Question 16.
2 – $$\frac{9}{10}$$ =
2 – $$\frac{9}{10}$$  = $$\frac{20 – 9}{10}$$ = $$\frac{11}{10}$$ = 1$$\frac{1}{10}$$

Question 17.
4 – $$\frac{7}{10}$$ =
4 – $$\frac{7}{10}$$ = $$\frac{40 – 7}{10}$$ = $$\frac{33}{10}$$ = 3$$\frac{3}{10}$$

Question 18.
3 – $$\frac{3}{10}$$ =
3 – $$\frac{3}{10}$$ = $$\frac{30 – 3}{10}$$= $$\frac{27}{10}$$= 2$$\frac{7}{10}$$

Question 19.
2 – $$\frac{1}{5}$$ =
2 – $$\frac{1}{5}$$ = $$\frac{10 – 1}{5}$$ = $$\frac{9}{5}$$ = 1$$\frac{4}{5}$$

Question 20.
2 – $$\frac{2}{5}$$ =
2 – $$\frac{2}{5}$$ = $$\frac{10 – 2}{5}$$ = $$\frac{8}{5}$$ = 1$$\frac{3}{5}$$

Question 21.
2 – $$\frac{4}{5}$$ =
2 – $$\frac{4}{5}$$ = $$\frac{10 – 2}{5}$$ = $$\frac{8}{5}$$ = 1$$\frac{3}{5}$$

Question 22.
3 – $$\frac{3}{5}$$ =
3 – $$\frac{3}{5}$$ = $$\frac{15 – 3}{5}$$ = $$\frac{12}{5}$$ = 2$$\frac{2}{5}$$

Question 23.
2 – $$\frac{1}{8}$$ =
2 – $$\frac{1}{8}$$  = $$\frac{16 – 1}{8}$$ = $$\frac{15}{8}$$ = 1 $$\frac{7}{8}$$

Question 24.
2 – $$\frac{3}{8}$$ =
2 – $$\frac{3}{8}$$  = $$\frac{16 – 3}{8}$$ = $$\frac{13}{8}$$ = 1$$\frac{5}{8}$$

Question 25.
2 – $$\frac{5}{8}$$ =
2 – $$\frac{5}{8}$$  = $$\frac{16 -5}{8}$$ = $$\frac{11}{8}$$ = 1$$\frac{3}{8}$$

Question 26.
2 – $$\frac{7}{8}$$ =
2 – $$\frac{7}{8}$$ = $$\frac{16 – 7}{8}$$ = $$\frac{9}{8}$$ =1$$\frac{1}{8}$$

Question 27.
4 – $$\frac{7}{8}$$ =
4 – $$\frac{7}{8}$$ = $$\frac{28 – 7}{8}$$ = $$\frac{21}{8}$$ = 2$$\frac{5}{8}$$

Question 28.
3 – $$\frac{1}{7}$$ =
3 – $$\frac{1}{7}$$ = $$\frac{21 – 1}{7}$$ = $$\frac{20}{7}$$ = 2$$\frac{6}{7}$$

Question 29.
2 – $$\frac{6}{7}$$ =
2 – $$\frac{6}{7}$$ = $$\frac{14 – 6}{7}$$ = $$\frac{8}{7}$$ =1$$\frac{1}{7}$$

Question 30.
4 – $$\frac{3}{7}$$ =
4 – $$\frac{3}{7}$$ = $$\frac{28 -3}{7}$$ = $$\frac{25}{7}$$ =3$$\frac{4}{7}$$

Question 31.
3 – $$\frac{4}{7}$$ =
3 – $$\frac{4}{7}$$  = $$\frac{21 – 4}{7}$$ = $$\frac{17}{7}$$ =2$$\frac{3}{7}$$

Question 32.
2 – $$\frac{5}{7}$$ =
2 – $$\frac{5}{7}$$  = $$\frac{14 – 5}{7}$$ = $$\frac{9}{7}$$ =1$$\frac{2}{7}$$

Question 33.
3 – $$\frac{3}{4}$$ =
3 – $$\frac{3}{4}$$ = $$\frac{12 – 3}{4}$$ = $$\frac{9}{4}$$= 2$$\frac{1}{4}$$

Question 34.
4 – $$\frac{5}{8}$$ =
4 – $$\frac{5}{8}$$ = $$\frac{32 – 5}{8}$$ = $$\frac{27}{8}$$ = 3$$\frac{3}{8}$$

Question 35.
2 – $$\frac{3}{10}$$ =
2 – $$\frac{3}{10}$$  = $$\frac{20 -3}{10}$$ = $$\frac{17}{10}$$ = 1$$\frac{7}{10}$$

Question 36.
3 – $$\frac{2}{5}$$ =
3 – $$\frac{2}{5}$$  = $$\frac{15 – 2}{5}$$ = $$\frac{13}{5}$$ = 2$$\frac{3}{5}$$

Question 37.
3 – $$\frac{3}{7}$$ =
3 – $$\frac{3}{7}$$ = $$\frac{21 – 3}{7}$$ = $$\frac{18}{7}$$ = 2$$\frac{4}{7}$$.

Question 38.
2 – $$\frac{7}{10}$$ =
2 – $$\frac{7}{10}$$  = $$\frac{20 – 7}{10}$$ = $$\frac{14}{10}$$ = $$\frac{7}{5}$$ =1$$\frac{2}{5}$$

Question 39.
2 – $$\frac{5}{10}$$ =
2 – $$\frac{5}{10}$$ = $$\frac{20 – 5}{10}$$ = $$\frac{15}{10}$$= $$\frac{3}{2}$$ = 1$$\frac{1}{2}$$

Question 40.
4 – $$\frac{6}{8}$$ =
4 – $$\frac{6}{8}$$ = $$\frac{32 – 6}{8}$$ = $$\frac{28}{8}$$ = $$\frac{7}{2}$$=3$$\frac{1}{2}$$

Question 41.
4 – $$\frac{3}{12}$$ =
4 – $$\frac{3}{12}$$ = $$\frac{48 – 3}{12}$$ = $$\frac{45}{12}$$ = $$\frac{15}{4}$$ = 3$$\frac{3}{4}$$

Question 42.
3 – $$\frac{10}{12}$$ =
3 – $$\frac{10}{12}$$  = $$\frac{36 -10}{12}$$ = $$\frac{26}{12}$$ = $$\frac{13}{6}$$ = 2$$\frac{1}{6}$$

Question 43.
2 – $$\frac{4}{6}$$ =
2 – $$\frac{4}{6}$$  = $$\frac{12 -4}{6}$$ = $$\frac{8}{6}$$ = $$\frac{2}{3}$$

Question 44.
4 – $$\frac{4}{12}$$ =
4 – $$\frac{4}{12}$$  = $$\frac{48 -4}{12}$$ = $$\frac{42}{12}$$ = $$\frac{7}{2}$$ =3$$\frac{1}{2}$$

### Eureka Math Grade 5 Module 6 Lesson 20 Problem Set Answer Key

Question 1.
The line graph below tracks the total tomato production for one tomato plant. The total tomato production is plotted at the end of each of 8 weeks. Use the information in the graph to answer the questions that follow.

a. How many pounds of tomatoes did this plant produce at the end of 13 weeks?
b. How many pounds of tomatoes did this plant produce from Week 7 to Week 11? Explain how you know.
c. Which one-week period showed the greatest change in tomato production? The least? Explain how you know.
d. During Weeks 6–8, Jason fed the tomato plant just water. During Weeks 8–10, he used a mixture of water and Fertilizer A, and in Weeks 10–13, he used water and Fertilizer B on the tomato plant. Compare the tomato production for these periods of time.
a. 10 pounds of Tomatoes were produced at the end of 13 week .
b. Number of pounds of tomatoes produced from Week 7 to Week 11 = week 11 production – week 7 production = 9 – 3 = 6 pounds.
c. Week 9 to 10 the line is steeper that means the greatest change in tomato production. In week 11- 12 the line is flat that means no        production taken place . so, least production .
d. The Water helped make tomatoes , But the fertilizer A seemed to make more tomatoes than just water. Fertilizer B didnot seem to help at all because the production in week 10-13 plant hardly increased production .

Question 2.
Use the story context below to sketch a line graph. Then, answer the questions that follow.
The number of fifth-grade students attending Magnolia School has changed over time. The school opened in 2006 with 156 students in the fifth grade. The student population grew the same amount each year before reaching its largest class of 210 students in 2008. The following year, Magnolia lost one-seventh of its fifth graders. In 2010, the enrollment dropped to 154 students and remained constant in 2011. For the next two years, the enrollment grew by 7 students each year.

a. How many more fifth-grade students attended Magnolia in 2009 than in 2013?
b. Between which two consecutive years was there the greatest change in student population?
c. If the fifth-grade population continues to grow in the same pattern as in 2012 and 2013, in what year will the number of students match 2008’s enrollment?

a.  Number of students attended in 2009 = 180
Number of students attended in 2013 = 168 .
Number of more students attended in 2009 than 2013 = 180 -168 = 12
12 more students attended in 2009 than 2013 .
b. Between 2008 – 2009 there is greatest change in student population that is from 210 to 180 = 30 students.
c. The number students in 2008 = 210 ,
In 2012 and 2013 the number of students increased =  7 students
For one year there is a increase in 7 students
At 2013 the number of students = 168
Number of more students required = 210 – 168 = 42
Number of years required = 42  ÷  7 = 6 years
It requires more 6 years from 2013 that means by 2019 .

### Eureka Math Grade 5 Module 6 Lesson 20 Exit Ticket Answer Key

Use the following information to complete the line graph below. Then, answer the questions that follow.
Harry runs a hot dog stand at the county fair. When he arrived on Wednesday, he had 38 dozen hot dogs for his stand. The graph shows the number of hot dogs (in dozens) that remained unsold at the end of each day of sales.

a. How many dozen hot dogs did Harry sell on Wednesday? How do you know?
b. Between which two-day period did the number of hot dogs sold change the most? Explain how you determined your answer.
c. During which three days did Harry sell the most hot dogs?
d. How many dozen hot dogs were sold on these three days?
a. The number of hot dogs = 38 dozens .
On Wednesday number of hot dogs left = 30 that means 38 – 30 = 8 dozens are sold .
b. Saturday and Sunday because on Saturday he started 22 and ended at 14  = 8 dozens are sold and On Sunday he started at 14 and        ended at 4 that means 10 dozens are sold .
c. Friday, Saturday and Sunday .
Friday he started at 27 and ended at 22 that means 5 dozens .
Saturday he started 22 and ended at 14  = 8 dozens are sold .
On Sunday he started at 14 and ended at 4 that means 10 dozens are sold .
d. Friday = 5
Saturday = 8
Sunday = 10
Total = 5 + 8 + 10 = 23 dozens .

### Eureka Math Grade 5 Module 6 Lesson 20 Homework Answer Key

Use the graph to answer the questions.
Johnny left his home at 6 a.m. and kept track of the number of kilometers he traveled at the end of each hour of his trip. He recorded the data in a line graph.

a. How far did Johnny travel in all? How long did it take?
b. Johnny took a one-hour break to have a snack and take some pictures. What time did he stop? How do you know?
c. Did Johnny cover more distance before his break or after? Explain.
d. Between which two hours did Johnny ride 4 kilometers?
e. During which hour did Johnny ride the fastest? Explain how you know.