## Engage NY Eureka Math 5th Grade Module 3 Lesson 15 Answer Key

### Eureka Math Grade 5 Module 3 Lesson 15 Sprint Answer Key

A
Circle the Smaller Fraction

Question 1.
$$\frac{1}{2}$$ $$\frac{1}{4}$$

Question 2.
$$\frac{1}{2}$$ $$\frac{3}{4}$$

Question 3.
$$\frac{1}{2}$$ $$\frac{5}{8}$$

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

Question 5.
$$\frac{1}{2}$$ $$\frac{1}{10}$$

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

Question 7.
$$\frac{1}{2}$$ $$\frac{5}{12}$$

Question 8.
$$\frac{1}{2}$$ $$\frac{11}{12}$$

Question 9.
$$\frac{1}{2}$$ $$\frac{7}{10}$$

Question 10.
$$\frac{1}{5}$$ $$\frac{9}{10}$$

Question 11.
$$\frac{2}{5}$$ $$\frac{1}{10}$$

Question 12.
$$\frac{2}{5}$$ $$\frac{3}{10}$$

Question 13.
$$\frac{3}{5}$$ $$\frac{3}{10}$$

Question 14.
$$\frac{3}{5}$$ $$\frac{7}{10}$$

Question 15.
$$\frac{4}{5}$$ $$\frac{1}{10}$$

Question 16.
$$\frac{4}{5}$$ $$\frac{9}{10}$$

Question 17.
$$\frac{1}{3}$$ $$\frac{1}{9}$$

Question 18.
$$\frac{1}{3}$$ $$\frac{2}{9}$$

Question 19.
$$\frac{1}{3}$$ $$\frac{4}{9}$$

Question 20.
$$\frac{1}{3}$$ $$\frac{8}{9}$$

Question 21.
$$\frac{1}{3}$$ $$\frac{1}{12}$$

Question 22.
$$\frac{1}{3}$$ $$\frac{5}{12}$$

Question 23.
$$\frac{1}{4}$$ $$\frac{1}{8}$$

Question 24.
$$\frac{1}{4}$$ $$\frac{3}{8}$$

Question 25.
$$\frac{1}{4}$$ $$\frac{7}{12}$$

Question 26.
$$\frac{1}{4}$$ $$\frac{11}{12}$$

Question 27.
$$\frac{1}{6}$$ $$\frac{7}{12}$$

Question 28.
$$\frac{1}{6}$$ $$\frac{11}{12}$$

Question 29.
$$\frac{2}{3}$$ $$\frac{1}{6}$$

Question 30.
$$\frac{2}{3}$$ $$\frac{5}{6}$$

Question 31.
$$\frac{2}{3}$$ $$\frac{2}{9}$$

Question 32.
$$\frac{2}{3}$$ $$\frac{4}{9}$$

Question 33.
$$\frac{2}{3}$$ $$\frac{1}{12}$$

Question 34.
$$\frac{2}{3}$$ $$\frac{5}{12}$$

Question 35.
$$\frac{2}{3}$$ $$\frac{11}{12}$$

Question 36.
$$\frac{2}{3}$$ $$\frac{7}{12}$$

Question 37.
$$\frac{3}{4}$$ $$\frac{1}{8}$$

Question 38.
$$\frac{3}{4}$$ $$\frac{1}{8}$$

Question 39.
$$\frac{5}{6}$$ $$\frac{7}{12}$$

Question 40.
$$\frac{5}{6}$$ $$\frac{5}{12}$$

Question 41.
$$\frac{6}{7}$$ $$\frac{38}{42}$$

Question 42.
$$\frac{7}{8}$$ $$\frac{62}{72}$$

Question 43.
$$\frac{49}{54}$$ $$\frac{8}{9}$$

Question 44.
$$\frac{67}{72}$$ $$\frac{11}{12}$$

B
Circle the Smaller Fraction

Question 1.
$$\frac{1}{2}$$ $$\frac{1}{6}$$

Question 2.
$$\frac{1}{2}$$ $$\frac{5}{6}$$

Question 3.
$$\frac{1}{2}$$ $$\frac{1}{8}$$

Question 4.
$$\frac{1}{2}$$ $$\frac{3}{8}$$

Question 5.
$$\frac{1}{2}$$ $$\frac{7}{10}$$

Question 6.
$$\frac{1}{2}$$ $$\frac{9}{10}$$

Question 7.
$$\frac{1}{2}$$ $$\frac{1}{12}$$

Question 8.
$$\frac{1}{2}$$ $$\frac{7}{12}$$

Question 9.
$$\frac{1}{5}$$ $$\frac{1}{10}$$

Question 10.
$$\frac{1}{5}$$ $$\frac{3}{10}$$

Question 11.
$$\frac{2}{5}$$ $$\frac{1}{10}$$

Question 12.
$$\frac{2}{5}$$ $$\frac{9}{10}$$

Question 13.
$$\frac{3}{5}$$ $$\frac{1}{10}$$

Question 14.
$$\frac{3}{5}$$ $$\frac{9}{10}$$

Question 15.
$$\frac{4}{5}$$ $$\frac{3}{10}$$

Question 16.
$$\frac{4}{5}$$ $$\frac{7}{10}$$

Question 17.
$$\frac{1}{3}$$ $$\frac{1}{6}$$

Question 18.
$$\frac{1}{3}$$ $$\frac{5}{6}$$

Question 19.
$$\frac{1}{3}$$ $$\frac{5}{9}$$

Question 20.
$$\frac{1}{3}$$ $$\frac{7}{9}$$

Question 21.
$$\frac{1}{3}$$ $$\frac{7}{12}$$

Question 22.
$$\frac{1}{3}$$ $$\frac{11}{12}$$

Question 23.
$$\frac{1}{4}$$ $$\frac{5}{8}$$

Question 24.
$$\frac{1}{4}$$ $$\frac{7}{8}$$

Question 25.
$$\frac{1}{4}$$ $$\frac{1}{12}$$

Question 26.
$$\frac{1}{4}$$ $$\frac{5}{12}$$

Question 27.
$$\frac{1}{6}$$ $$\frac{1}{12}$$

Question 28.
$$\frac{1}{6}$$ $$\frac{5}{12}$$

Question 29.
$$\frac{2}{3}$$ $$\frac{1}{9}$$

Question 30.
$$\frac{2}{3}$$ $$\frac{7}{9}$$

Question 31.
$$\frac{2}{3}$$ $$\frac{5}{9}$$

Question 32.
$$\frac{2}{3}$$ $$\frac{8}{9}$$

Question 33.
$$\frac{2}{3}$$ $$\frac{1}{12}$$

Question 34.
$$\frac{3}{4}$$ $$\frac{1}{2}$$

Question 35.
$$\frac{3}{4}$$ $$\frac{5}{12}$$

Question 36.
$$\frac{3}{4}$$ $$\frac{7}{12}$$

Question 37.
$$\frac{5}{6}$$ $$\frac{1}{12}$$

Question 38.
$$\frac{5}{6}$$ $$\frac{11}{12}$$

Question 39.
$$\frac{3}{4}$$ $$\frac{5}{8}$$

Question 40.
$$\frac{3}{4}$$ $$\frac{3}{8}$$

Question 41.
$$\frac{6}{7}$$ $$\frac{34}{42}$$

Question 42.
$$\frac{7}{8}$$ $$\frac{64}{72}$$

Question 43.
$$\frac{47}{54}$$ $$\frac{8}{9}$$

Question 44.
$$\frac{65}{72}$$ $$\frac{11}{12}$$

### Eureka Math Grade 5 Module 3 Lesson 15 Problem Set Answer Key

Solve the word problems using the RDW strategy. Show all of your work.
Question 1.
In a race, the-second place finisher crossed the finish line 1$$\frac{1}{3}$$ minutes after the winner. The third-place finisher was 1$$\frac{3}{4}$$ minutes behind the second-place finisher. The third-place finisher took 34$$\frac{2}{3}$$ minutes. How long did the winner take?
Fraction of time of Second place finisher crossed the line after = 1$$\frac{1}{3}$$ minutes = $$\frac{4}{3}$$
Fraction of time of Third place finisher is behind the second placeÂ  = 1$$\frac{3}{4}$$ minutesÂ  = $$\frac{7}{4}$$
Fraction of time the third place finisher took = 34$$\frac{2}{3}$$ = $$\frac{105}{3}$$
Fraction of time the second place runner took = $$\frac{105}{3}$$ – $$\frac{7}{4}$$ = $$\frac{420}{12}$$ – $$\frac{21}{12}$$ = $$\frac{399}{12}$$ = $$\frac{133}{4}$$
Fraction of time the First place runner took = $$\frac{133}{4}$$ – $$\frac{4}{3}$$ = $$\frac{399}{12}$$ – $$\frac{16}{12}$$ = $$\frac{383}{12}$$ = 31 $$\frac{11}{12}$$ .
Therefore the First Runner took =Â 31 $$\frac{11}{12}$$ .minutes.

Question 2.
John used 1$$\frac{3}{4}$$ kg of salt to melt the ice on his sidewalk. He then used another 3$$\frac{4}{5}$$ kg on the driveway. If he originally bought 10 kg of salt, how much does he have left?
Fraction of Salt used by John =1$$\frac{3}{4}$$ kg = $$\frac{7}{4}$$ kg
Fraction of Salt used again =3$$\frac{4}{5}$$ kg = $$\frac{24}{5}$$ kg
Fraction of salt used = $$\frac{7}{4}$$Â  + $$\frac{24}{5}$$ = $$\frac{35}{20}$$Â  + $$\frac{96}{20}$$ = $$\frac{131}{20}$$Â  = 6 $$\frac{11}{20}$$ .
Total Salt = 10 kg.
Fraction of salt left = 10 – $$\frac{131}{20}$$Â  = $$\frac{200}{20}$$Â  – $$\frac{131}{20}$$Â  = $$\frac{69}{20}$$Â  = 3$$\frac{9}{20}$$Â  .
Therefore Fraction of salt left = 3$$\frac{9}{20}$$Â  .

Question 3.
Sinister Stan stole 3$$\frac{3}{4}$$ oz of slime from Messy Molly, but his evil plans require 6$$\frac{3}{8}$$ oz of slime. He stole another 2$$\frac{3}{5}$$ oz of slime from Rude Ralph. How much more slime does Sinister Stan need for his evil plan?
Fraction of slime stolen from Messy Molly = 3$$\frac{3}{4}$$ = $$\frac{15}{4}$$ oz
Fraction of slime stolen from Messy Molly again = 2$$\frac{3}{5}$$ = $$\frac{13}{5}$$ oz
Total Fraction Stolen = $$\frac{15}{4}$$Â  + $$\frac{13}{5}$$ = $$\frac{75}{20}$$ + $$\frac{52}{20}$$ = $$\frac{127}{20}$$ = 6$$\frac{7}{20}$$ .
Fraction of more slime required = 6$$\frac{3}{8}$$ – $$\frac{127}{20}$$ = $$\frac{51}{8}$$ – $$\frac{127}{20}$$ = $$\frac{255}{40}$$ – $$\frac{254}{40}$$ = $$\frac{1}{40}$$ .
Therefore, Fraction of more slime required = $$\frac{1}{40}$$ oz.

Question 4.
Gavin had 20 minutes to do a three-problem quiz. He spent 9$$\frac{3}{4}$$ minutes on Problem 1 and 3$$\frac{4}{5}$$ minutes on Problem 2. How much time did he have left for Problem 3? Write the answer in minutes and seconds.
Time given for 3 problems = 20 minutes
Fraction of time Spent on Problem 1 = 9$$\frac{3}{4}$$ minutes = $$\frac{39}{4}$$ .
Fraction of Time spent on Problem 2 = 3$$\frac{4}{5}$$ = $$\frac{19}{5}$$ .
Fraction of Time spent on Problem 3 = x
20 = $$\frac{39}{4}$$ + $$\frac{19}{5}$$ + x
x = 20 – $$\frac{39}{4}$$ – $$\frac{19}{5}$$
x = $$\frac{400}{20}$$ – $$\frac{195}{20}$$ – $$\frac{76}{20}$$
x = $$\frac{129}{20}$$ = 6$$\frac{9}{20}$$ .
Therefore, Fraction of Time spent on Problem 3 = 6$$\frac{9}{20}$$ .

Question 5.
Matt wants to shave 2$$\frac{1}{2}$$ minutes off his 5K race time. After a month of hard training, he managed to lower his overall time from 21$$\frac{1}{5}$$ minutes to 19$$\frac{1}{4}$$ minutes. By how many more minutes does Matt need to lower his race time?
Fraction of Time lowered = 21$$\frac{1}{5}$$ minutes to 19$$\frac{1}{4}$$ minutes. = $$\frac{106}{5}$$ – $$\frac{77}{4}$$ = $$\frac{424}{20}$$ – $$\frac{385}{20}$$ = $$\frac{39}{20}$$ =1$$\frac{19}{20}$$ .
Fraction of Time shaved = 2$$\frac{1}{2}$$ =$$\frac{5}{2}$$ .
Fraction of More Time Matt need to lower his race time = $$\frac{5}{2}$$ – $$\frac{39}{20}$$ = $$\frac{50}{20}$$ – $$\frac{39}{20}$$ = $$\frac{11}{20}$$ = $$\frac{33}{60}$$ = 33 minutes .

### Eureka Math Grade 5 Module 3 Lesson 15 Exit Ticket Answer Key

Solve the word problem using the RDW strategy. Show all of your work.
Cheryl bought a sandwich for 5$$\frac{1}{2}$$ dollars and a drink for $2.60. If she paid for her meal with a$10 bill, how much money did she have left? Write your answer as a fraction and in dollars and cents.
Fraction of Cost of sandwich = 5$$\frac{1}{2}$$ = $$\frac{11}{2}$$ dollar = 5.5 dollar
Fraction of Cost of Drink = $2.60. Total Cost = 5.5 +2.60 = 8.1$.
Amount paid = 10$. Money left = 10 – 8.1 = 1.9$ .

### Eureka Math Grade 5 Module 3 Lesson 15 Homework Answer Key

Solve the word problems using the RDW strategy. Show all of your work.
Question 1.
A baker buys a 5 lb bag of sugar. She uses 1$$\frac{2}{3}$$ lb to make some muffins and 2$$\frac{3}{4}$$ lb to make a cake. How much sugar does she have left?
Total Quantity of Sugar = 5 lb
Fraction of Quantity of Suagr used for muffins = 1$$\frac{2}{3}$$ lb = $$\frac{5}{3}$$
Fraction of Quantity of Suagr used cake = 2$$\frac{3}{4}$$ lb = $$\frac{11}{4}$$
Fraction of Quantity of Sugar used = $$\frac{5}{3}$$ + $$\frac{11}{4}$$ = $$\frac{20}{12}$$ + $$\frac{33}{12}$$ = $$\frac{53}{12}$$
Fraction of Quantity of Sugar left = 5 – $$\frac{53}{12}$$ = $$\frac{60}{12}$$ – $$\frac{53}{12}$$ =$$\frac{7}{12}$$ .
Therefore, Fraction of Quantity of sugar left = $$\frac{7}{12}$$ .

Question 2.
A boxer needs to lose 3$$\frac{1}{2}$$ kg in a month to be able to compete as a flyweight. In three weeks, he lowers his weight from 55.5 kg to 53.8 kg. How many kilograms must the boxer lose in the final week to be able to compete as a flyweight?
Fraction of weight need to lose in month = 3$$\frac{1}{2}$$ = $$\frac{7}{2}$$ = 3.5 kg
Weight lost in 3 weeks = 55.5 –Â  53.8 = 1.7 kg
Weight need to lose in final week = 3.5 – 1.7 = 1.8 kg.

Question 3.
A construction company builds a new rail line from Town A to Town B. They complete 1$$\frac{1}{4}$$ miles in their first week of work and 1$$\frac{2}{3}$$ miles in the second week. If they still have 25$$\frac{3}{4}$$ miles left to build, what is the distance from Town A to Town B?
Fraction of work completed in first week = 1$$\frac{1}{4}$$ miles = $$\frac{5}{4}$$
Fraction of work completed in second week = 1$$\frac{2}{3}$$ miles = $$\frac{5}{3}$$
Fraction of work left to built = 25$$\frac{3}{4}$$ miles = $$\frac{103}{4}$$
Fraction of Distance from Town A to Town B = $$\frac{103}{4}$$ + $$\frac{5}{4}$$Â  + $$\frac{5}{3}$$ = $$\frac{108}{4}$$ + $$\frac{5}{3}$$ = $$\frac{324}{12}$$ + $$\frac{20}{12}$$ = $$\frac{344}{12}$$= 28$$\frac{2}{3}$$ .
Therefore, Fraction of Distance from Town A to Town B = 28$$\frac{2}{3}$$ miles.

Question 4.
A catering company needs 8.75 lb of shrimp for a small party. They buy 3$$\frac{2}{3}$$ lb of jumbo shrimp, 2$$\frac{5}{8}$$ lb of medium-sized shrimp, and some mini-shrimp. How many pounds of mini-shrimp do they buy?
Quantity of shrimp needed = 8.75 lb =8$$\frac{3}{4}$$ = $$\frac{27}{4}$$
Quantity of jumbo shrimp = 3$$\frac{2}{3}$$ lb = $$\frac{11}{3}$$
Quantity ofÂ  medium – sized shrimp = 2$$\frac{5}{8}$$ lb = $$\frac{21}{8}$$
Quantity of mini shrimp = x
$$\frac{35}{4}$$Â Â = $$\frac{11}{3}$$ + $$\frac{21}{8}$$ + x
x = $$\frac{210}{24}$$Â  – $$\frac{88}{24}$$ – $$\frac{63}{24}$$
x =Â  $$\frac{59}{24}$$ = 2 $$\frac{11}{24}$$
Therefore, Quantity of mini shrimp = x = 2 $$\frac{11}{24}$$ lb .

Question 5.
Mark breaks up a 9-hour drive into 3 segments. He drives 2$$\frac{1}{2}$$ hours before stopping for lunch. After driving some more, he stops for gas. If the second segment of his drive was 1$$\frac{2}{3}$$ hours longer than the first segment, how long did he drive after stopping for gas?
Fraction of Time drived for first segment = 2$$\frac{1}{2}$$ hoursÂ  = $$\frac{5}{2}$$
Fraction of Time of second segment = 1$$\frac{2}{3}$$ hours longer than the first segment = $$\frac{5}{3}$$ + $$\frac{5}{2}$$ = $$\frac{10}{6}$$ + $$\frac{15}{6}$$ = $$\frac{25}{6}$$ =4$$\frac{1}{6}$$
Fraction of Time of first and second segment= $$\frac{5}{2}$$ + $$\frac{25}{6}$$ = $$\frac{15}{6}$$ + $$\frac{25}{6}$$ = $$\frac{40}{6}$$ = 6$$\frac{4}{6}$$
Fraction of Time he drive after stopping gas = 9 – $$\frac{40}{6}$$ = $$\frac{54}{6}$$ –Â  $$\frac{40}{6}$$ = $$\frac{14}{6}$$ = 2$$\frac{2}{6}$$ .
Therefore, Fraction of Time he drive after stopping gas = third segment = 2$$\frac{2}{6}$$ hours .