Engage NY Eureka Math 5th Grade Module 6 Lesson 19 Answer Key

A
Make Larger Units

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

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

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

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

Question 5.
$$\frac{5}{15}$$ =
$$\frac{5}{15}$$ = $$\frac{1}{3}$$

Question 6.
$$\frac{5}{20}$$ =
$$\frac{5}{20}$$ = $$\frac{1}{4}$$

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

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

Question 9.
$$\frac{4}{16}$$ =
$$\frac{4}{16}$$ = $$\frac{1}{4}$$

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

Question 11.
$$\frac{3}{9}$$ =
$$\frac{3}{9}$$ = $$\frac{1}{3}$$

Question 12.
$$\frac{3}{12}$$ =
$$\frac{3}{12}$$ = $$\frac{1}{4}$$

Question 13.
$$\frac{4}{6}$$ =
$$\frac{4}{6}$$ = $$\frac{2}{3}$$

Question 14.
$$\frac{6}{12}$$ =
$$\frac{6}{12}$$ = $$\frac{1}{2}$$

Question 15.
$$\frac{6}{18}$$ =
$$\frac{6}{18}$$ = $$\frac{1}{3}$$

Question 16.
$$\frac{6}{30}$$ =
$$\frac{6}{30}$$ = $$\frac{1}{5}$$

Question 17.
$$\frac{6}{9}$$ =
$$\frac{6}{9}$$ = $$\frac{2}{3}$$

Question 18.
$$\frac{7}{14}$$ =
$$\frac{7}{14}$$ = $$\frac{1}{2}$$

Question 19.
$$\frac{7}{21}$$ =
latex]\frac{7}{21}[/latex] = latex]\frac{1}{3}[/latex]

Question 20.
$$\frac{7}{42}$$ =
$$\frac{7}{42}$$ = $$\frac{1}{6}$$

Question 21.
$$\frac{8}{12}$$ =
$$\frac{8}{12}$$ = $$\frac{2}{3}$$

Question 22.
$$\frac{9}{18}$$ =
$$\frac{9}{18}$$ = $$\frac{1}{2}$$

Question 23.
$$\frac{9}{27}$$ =
$$\frac{9}{27}$$ = $$\frac{1}{3}$$

Question 24.
$$\frac{9}{63}$$ =
$$\frac{9}{63}$$ = $$\frac{1}{7}$$

Question 25.
$$\frac{8}{12}$$ =
$$\frac{8}{12}$$ = $$\frac{2}{3}$$

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

Question 27.
$$\frac{8}{24}$$ =
$$\frac{8}{24}$$ = $$\frac{1}{3}$$

Question 28.
$$\frac{8}{64}$$ =
$$\frac{8}{64}$$ = $$\frac{1}{8}$$

Question 29.
$$\frac{12}{18}$$ =
$$\frac{12}{18}$$ = $$\frac{2}{3}$$

Question 30.
$$\frac{12}{16}$$ =
$$\frac{12}{16}$$ = $$\frac{3}{4}$$

Question 31.
$$\frac{9}{12}$$ =
$$\frac{9}{12}$$ = $$\frac{3}{4}$$

Question 32.
$$\frac{6}{8}$$ =
$$\frac{6}{8}$$ = $$\frac{3}{4}$$

Question 33.
$$\frac{10}{12}$$ =
$$\frac{10}{12}$$ = $$\frac{5}{6}$$

Question 34.
$$\frac{15}{18}$$ =
$$\frac{15}{18}$$ = $$\frac{5}{6}$$

Question 35.
$$\frac{8}{10}$$ =
$$\frac{8}{10}$$ = $$\frac{4}{5}$$

Question 36.
$$\frac{16}{20}$$ =
$$\frac{16}{20}$$ = $$\frac{4}{5}$$

Question 37.
$$\frac{12}{15}$$ =
$$\frac{12}{15}$$ = $$\frac{4}{5}$$

Question 38.
$$\frac{18}{27}$$ =
$$\frac{18}{27}$$ = $$\frac{6}{9}$$

Question 39.
$$\frac{27}{36}$$ =
$$\frac{27}{36}$$ = $$\frac{3}{4}$$

Question 40.
$$\frac{32}{40}$$ =
$$\frac{32}{40}$$ = $$\frac{4}{5}$$

Question 41.
$$\frac{45}{54}$$ =
$$\frac{45}{54}$$ = $$\frac{5}{6}$$

Question 42.
$$\frac{24}{36}$$ =
$$\frac{24}{36}$$ = $$\frac{6}{9}$$

Question 43.
$$\frac{60}{72}$$ =
$$\frac{60}{72}$$ = $$\frac{5}{6}$$

Question 44.
$$\frac{48}{60}$$ =
$$\frac{48}{60}$$ = $$\frac{4}{5}$$

B
Make Larger Units

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

Question 2.
$$\frac{5}{15}$$ =
$$\frac{5}{15}$$ = $$\frac{1}{3}$$

Question 3.
$$\frac{5}{20}$$ =
$$\frac{5}{20}$$ = $$\frac{1}{4}$$

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

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

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

Question 7.
$$\frac{3}{6}$$ =
$$\frac{3}{6}$$ = $$\frac{1}{2}$$

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

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

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

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

Question 12.
$$\frac{4}{16}$$ =
$$\frac{4}{16}$$ = $$\frac{1}{4}$$

Question 13.
$$\frac{4}{6}$$ =
$$\frac{4}{6}$$ = $$\frac{2}{3}$$

Question 14.
$$\frac{7}{14}$$ =
$$\frac{7}{14}$$ = $$\frac{1}{2}$$

Question 15.
$$\frac{7}{21}$$ =
$$\frac{7}{21}$$ = $$\frac{1}{3}$$

Question 16.
$$\frac{7}{35}$$ =
$$\frac{7}{35}$$ = $$\frac{1}{5}$$

Question 17.
$$\frac{6}{9}$$ =
$$\frac{6}{9}$$ = $$\frac{2}{3}$$

Question 18.
$$\frac{6}{12}$$ =
$$\frac{6}{12}$$ = $$\frac{1}{2}$$

Question 19.
$$\frac{6}{18}$$ =
$$\frac{6}{18}$$ = $$\frac{1}{3}$$

Question 20.
$$\frac{6}{36}$$ =
$$\frac{6}{36}$$ = $$\frac{1}{6}$$

Question 21.
$$\frac{8}{12}$$ =
$$\frac{8}{12}$$ = $$\frac{2}{3}$$

Question 22.
$$\frac{8}{16}$$ =
$$\frac{8}{16}$$ = $$\frac{1}{2}$$

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

Question 24.
$$\frac{8}{56}$$ =
$$\frac{8}{56}$$ = $$\frac{1}{7}$$

Question 25.
$$\frac{8}{12}$$ =
$$\frac{8}{12}$$ = $$\frac{2}{3}$$

Question 26.
$$\frac{9}{18}$$ =
$$\frac{9}{18}$$ = $$\frac{1}{2}$$

Question 27.
$$\frac{9}{27}$$ =
$$\frac{9}{27}$$ = $$\frac{1}{3}$$ =

Question 28.
$$\frac{9}{72}$$ =
$$\frac{9}{72}$$ = $$\frac{1}{8}$$

Question 29.
$$\frac{12}{18}$$ =
$$\frac{12}{18}$$ = $$\frac{4}{6}$$

Question 30.
$$\frac{6}{8}$$ =
$$\frac{6}{8}$$ = $$\frac{3}{4}$$

Question 31.
$$\frac{9}{12}$$ =
$$\frac{9}{12}$$ = $$\frac{3}{4}$$

Question 32.
$$\frac{12}{16}$$ =
$$\frac{12}{16}$$ = $$\frac{3}{4}$$

Question 33.
$$\frac{8}{10}$$ =
$$\frac{8}{10}$$ = $$\frac{4}{5}$$

Question 34.
$$\frac{16}{20}$$ =
$$\frac{16}{20}$$ = $$\frac{4}{5}$$

Question 35.
$$\frac{12}{15}$$ =
$$\frac{12}{15}$$ = $$\frac{4}{5}$$

Question 36.
$$\frac{10}{12}$$ =
$$\frac{10}{12}$$ = $$\frac{5}{6}$$

Question 37.
$$\frac{15}{18}$$ =
$$\frac{15}{18}$$ = $$\frac{5}{6}$$

Question 38.
$$\frac{16}{24}$$ =
$$\frac{16}{24}$$ = $$\frac{2}{3}$$

Question 39.
$$\frac{24}{32}$$ =
$$\frac{24}{32}$$ = $$\frac{3}{4}$$

Question 40.
$$\frac{36}{45}$$ =
$$\frac{36}{45}$$ = $$\frac{4}{5}$$

Question 41.
$$\frac{40}{48}$$ =
$$\frac{40}{48}$$ = $$\frac{5}{6}$$

Question 42.
$$\frac{24}{36}$$ =
$$\frac{24}{36}$$ = $$\frac{2}{3}$$

Question 43.
$$\frac{48}{60}$$ =
$$\frac{48}{60}$$ = $$\frac{4}{5}$$

Question 44.
$$\frac{60}{72}$$ =
$$\frac{60}{72}$$ = $$\frac{5}{6}$$

Eureka Math Grade 5 Module 6 Lesson 19 Problem Set Answer Key

Question 1.
The line graph below tracks the rain accumulation, measured every half hour, during a rainstorm that began at 2:00 p.m. and ended at 7:00 p.m. Use the information in the graph to answer the questions that follow.

a. How many inches of rain fell during this five-hour period?
b. During which half-hour period did $$\frac{1}{2}$$ inch of rain fall? Explain how you know.
c. During which half-hour period did rain fall most rapidly? Explain how you know.
d. Why do you think the line is horizontal between 3:30 p.m. and 4:30 p.m.?
e. For every inch of rain that fell here, a nearby community in the mountains received a foot and a half of snow. How many inches of snow fell in the mountain community between 5:00 p.m. and 7:00 p.m.?
a.  The Rain fell During this Five-hour period is 1$$\frac{3}{4}$$ inches .
b. The $$\frac{1}{2}$$ inch of rain fall during 2:30 to 3:00 p.m
Explanation :
The line went up $$\frac{1}{2}$$ inch as time went 2:30 to 3:00 p.m
c. The rain fall most rapidly took place during 4:30 to 5:00 p.m because the line steepest .
d. The line is horizontal between 3:30 p.m. and 4:30 p.m because they is a constant rainfall .
e. The rainfall from 5:00 p.m. to 7:00 p.m is $$\frac{1}{2}$$. That means The community got a foot and a half of snow.
12 inches = 1 foot .
For 1 inch we receive foot and a half of snow = 1$$\frac{1}{2}$$.
For $$\frac{1}{2}$$ we receive $$\frac{3}{4}$$ foot of snow .( $$\frac{1}{2}$$ of foot and a half of snow ) .
=$$\frac{3}{4}$$  (12 inches)  = 9 inches .

Question 2.
Mr. Boyd checks the gauge on his home’s fuel tank on the first day of every month. The line graph to the right was created using the data he collected.

a. According to the graph, during which month(s) does the amount of fuel decrease most rapidly?
b. The Boyds took a month-long vacation. During which month did this most likely occur? Explain how you know using the data in the graph.
c. Mr. Boyd’s fuel company filled his tank once this year. During which month did this most likely occur? Explain how you know.
d. The Boyd family’s fuel tank holds 284 gallons of fuel when full. How many gallons of fuel did the Boyds use in February?
e. Mr. Boyd pays $3.54 per gallon of fuel. What is the cost of the fuel used in February and March? Answer: a. The amount of fuel decrease most rapidly From January . b. In the Month of july no fuel is used .because the line is flat . c. In the may month the tank is filled because the line went up that means the fuel is filled . d. Amount of fuel used to fill = 284 gallons . Total Number of lines = 16 Each line represent how much of fuel = 284 /16 = 17.75 gallons. In febuary 2 units went down that means 17.75 × 2 = 35.5 gallons . that means 35.5 gallons of fuel is used . e. In febuary 2 units went down that means 17.75 × 2 = 35.5 gallons that means 35.5 gallons of fuel is used . In March 1 unit went down that means 17.75 × 1 = 17.75 gallons . Total Fuel used in febuary and march = 35.5 +17.75 = 53.25. Cost of Each galloon of fuel =$3.54 per gallons.
Cost of 53.25 gallon of fuel = $3.54 × 53.25 per gallons. = 188.505$ .

Eureka Math Grade 5 Module 6 Lesson 19 Exit Ticket Answer Key

The line graph below tracks the water level of Plainsview Creek, measured each Sunday, for 8 weeks. Use the information in the graph to answer the questions that follow.

a. About how many feet deep was the creek in Week 1? ________
b. According to the graph, which week had the greatest change in water depth? __________
c. It rained hard throughout the sixth week. During what other weeks might it have rained? Explain why you think so.
d. What might have been another cause leading to an increase in the depth of the creek?
a. The depth of the creek in Week 1 was 4 feet.
b. The greatest change in water depth Occurred in Week 2 that is 1$$\frac{1}{2}$$.
c. In week 6 the water level is increased t 1 unit that means it have rained . In week 1 and week 2 the water level is increased     $$\frac{1}{2}$$ and 1$$\frac{1}{2}$$ units respectively .
d. Riffles and glides leading to an increase in the depth of the creek .

Question 1.
The line graph below tracks the balance of Howard’s checking account, at the end of each day, between May 12 and May 26. Use the information in the graph to answer the questions that follow.

a. About how much money does Howard have in his checking account on May 21?
b. If Howard spends $250 from his checking account on May 26, about how much money will he have left in his account? c. Explain what happened with Howard’s money between May 21 and May 23 d. Howard received a payment from his job that went directly into his checking account. On which day did this most likely occur? Explain how you know. e. Howard bought a new television during the time shown in the graph. On which day did this most likely occur? Explain how you know. Answer: a. The Money in the account on 21st may = it is marked on 1$$\frac{1}{4}$$ . It represents in1000$.
So, 1$$\frac{1}{2}$$ = 1.25$in thousands =1.25 × 1000 =1250$ .
b. The point is marked between 1 and 1$$\frac{1}{4}$$ so take 1.1$approximately . So, 1.1$= 1.1$in thousands =1.1 × 1000 =1100$ .
Amount spent = $250 . Remaining amount =$1100 – 250 = 850\$ approximately .
c. The Money in the Howard’s account between May 21 and May 23 is same ,No transaction have taken place .
d. On 16 may we can see the line went up that means account is credited with the money . so, On 16th may the salary has been                 credited to his account .
e. On 18th may we see a decline in the account balance  that means how much has been debited from the account . so, on 18 th may       he might have bought new tv .

Question 2.
The line graph below tracks Santino’s time at the beginning and end of each part of a triathlon. Use the information in the graph to answer the questions that follow.

a. How long does it take Santino to finish the triathlon?
b. To complete the triathlon, Santino first swims across a lake, then bikes through the city, and finishes by running around the lake. According to the graph, what was the distance of the running portion of the race?
c. During the race, Santino pauses to put on his biking shoes and helmet and then later to change into his running shoes. At what times did this most likely occur? Explain how you know.
d. Which part of the race does Santino finish most quickly? How do you know?
e. During which part of the triathlon is Santino racing most quickly? Explain how you know.