## Engage NY Eureka Math 4th Grade Module 5 Lesson 28 Answer Key

### Eureka Math Grade 4 Module 5 Lesson 28 Problem Set Answer Key

Question 1.
The chart to the right shows the distance fourth graders in Ms. Smith’s class were able to run before stopping for a rest. Create a line plot to display the data in the table.

 Student Distance (in miles) Joe 2 $$\frac{1}{2}$$ Arianna 1 $$\frac{3}{4}$$ Bobbi 2 $$\frac{1}{8}$$ Morgan 1 $$\frac{5}{8}$$ Jack 2 $$\frac{5}{8}$$ Saisha 2 $$\frac{1}{4}$$ Tyler 2 $$\frac{2}{4}$$ Jenny $$\frac{5}{8}$$ Anson 2 $$\frac{2}{8}$$ Chandra 2 $$\frac{4}{8}$$

Joe : 2(1/2) = 5/2.

Explanation:
In the above-given question,
given that,
2(1/2).
2 x 2 = 4.
4 +1 = 5.
5/2 = 2.5.
2(1/2) = 2.5.

Arianna : 1(3/4) = 7/4.

Explanation:
In the above-given question,
given that,
1(3/4).
1 x 4 = 4.
4 +3 = 7.
7/4 = 1.75.
1(3/4) = 1.75.

Bobbi : 2(1/8) = 17/8.

Explanation:
In the above-given question,
given that,
2(1/8).
8 x 2 = 16.
16 +1 = 17.
17/8 = 2.125.
2(1/8) = 2.125.

Morgan : 1(5/8) = 13/8.

Explanation:
In the above-given question,
given that,
1(5/8).
1 x 8 = 8.
8 +5 = 13.
13/8 = 1.625.
1(5/8) = 1.625.

Jack : 2(5/8) = 21/8.

Explanation:
In the above-given question,
given that,
2(5/8).
8 x 2 = 16.
16 +5 = 21.
21/8 = 2.6.
2(5/8) = 2.6.

Saisha : 2(1/4) = 7/4.

Explanation:
In the above-given question,
given that,
2(1/4).
2 x 4 = 8.
8 + 1 = 9.
9/4 = 2.25.
2(1/4) = 2.25.

Tyler : 2(2/4) = 10/4.

Explanation:
In the above-given question,
given that,
2(2/4).
2 x 4 = 8.
8 +2 = 10.
10/4 = 2.5.
2(2/4) = 2.5.

Jenny : (5/8).

Explanation:
In the above-given question,
given that,
5/8.
5/8 = 0.625.

Anson : 2(2/8) = 18/8.

Explanation:
In the above-given question,
given that,
2(2/8).
8 x 2 = 16.
16 +2 = 18.
18/8 = 2.25.
2(2/8) = 2.25.

Chandra : 2(4/8) = 20/8.

Explanation:
In the above-given question,
given that,
2(4/8).
8 x 2 = 16.
16 +4 = 20.
20/8 = 2.5.
2(4/8) = 2.5. Question 2.
Solve each problem.
a. Who ran a mile farther than Jenny?

Morgan ran a mile farther than Jenny = 1.625.

Explanation:
In the above-given question,
given that,
5/8.
5/8 = 0.625.
0.625 + 1.
1.625.
so morgan ran a mile more than jenny.

b. Who ran a mile less than Jack?

Morgan ran a mile less than Jack.

Explanation:
In the above-given question,
given that,
Jack: 2(5/8).
16 + 5/8.
21/8 = 2.6.
2.6 – 1.6 = 1.6.
so morgan ran a mile less than jack.

c. Two students ran exactly 2$$\frac{1}{4}$$ miles. Identify the students. How many quarter miles did each student run?

Joe and Saisha exactly ran exactly.

Explanation:
In the above-given question,
given that,
2(1/4).
4 x 2 = 8.
8 + 1/4 = 9/4.
9/4 = 2.25.
Joe = 2.25.
Saisha = 2.25.

d. What is the difference, in miles, between the longest and shortest distance run?

The difference in miles between the longest and shortest distance run = 1.875 miles.

Explanation:
In the above-given question,
given that,
The longest distance run is Joe and Chandra.
the shortest distance run is Jenny.
Joe and Chandra = 2.5.
Jenny = 0.625.
2.5 – 0.625 = 1.875 miles.

e. Compare the distances run by Arianna and Morgan using >, <, or =.

Arianna > Morgan.

Explanation:
In the above-given question,
given that,
the distances run by Arianna and Morgan is
Arianna = 1.75 miles.
Morgan = 1.625.
1.75 > 1.625.
Arianna is greater than Morgan.

f. Ms. Smith ran twice as far as Jenny. How far did Ms. Smith run? Write her distance as a mixed number.

Ms. smith ran as far as Jenny = 1.25 miles.

Explanation:
In the above-given question,
given that,
Ms. Smith ran twice as far as Jenny.
Jenny run = 0.625.
smith = 1.25 miles.
0.625 + 0.625 = 1.25.

g. Mr. Reynolds ran 1$$\frac{3}{10}$$ miles. Use >, <, or = to compare the distance Mr. Reynolds ran to the distance that Ms. Smith ran. Who ran farther?

Mr. Reynold > Ms. Smith.

Explanation:
In the above-given question,
given that,
Mr. Reynolds ran 1(3/10) miles.
1(3/10) = 10 x 1.
10 x 1 = 10.
10 + 3/10.
13/10 = 1.3.
1.3 > 1.25.

Question 3.
Using the information in the table and on the line plot, develop and write a question similar to those above. Solve, and then ask your partner to solve. Did you solve in the same way? Did you get the same answer?

Yes, I get the same answer.

Explanation:
In the above-given question,
given that,
my partner also draws the same.
so we both solved in the same way.
so I get the same answer.

### Eureka Math Grade 4 Module 5 Lesson 28 Exit Ticket Answer Key

Mr. O’Neil asked his students to record the length of time they read over the weekend. The times are listed in the table.

 Student Length of time  (in hours) Robin $$\frac{1}{2}$$ Bill 1 Katrina $$\frac{3}{4}$$ Kelly 1 $$\frac{3}{4}$$ Mary 1 $$\frac{1}{2}$$ Gail 2$$\frac{1}{4}$$ Scott 1$$\frac{3}{4}$$ Ben 2$$\frac{2}{4}$$

Question 1.
At the bottom of the page, make a line plot of the data.
Robin: 1/2 = 0.5.

Explanation:
In the above-given question,
given that,
Robin = 1/2.
1/2 = 0.5.

Bill: 1.

Explanation:
In the above-given question,
given that,
1.

Katrina: 3/4.

Explanation:
In the above-given question,
given that,
3/4 = 0.75.

Kelly: 1(3/4).

Explanation:
In the above-given question,
given that,
1(3/4) = 4 x 1.
4 + 3/4 = 7/4.
7/4 = 1.75.

Mary: 1(1/2).

Explanation:
In the above-given question,
given that,
1(1/2) = 2 x 1.
2 + 1/2 = 3/2.
3/2 = 1.5.

Gail: 2(1/4).

Explanation:
In the above-given question,
given that,
2(1/4) = 2 x 4.
8 + 1/4 = 9/4.
9/4 = 2.25.

Scott: 1(3/4).

Explanation:
In the above-given question,
given that,
1(3/4) = 4 x 1.
4 + 3/4 = 7/4.
7/4 = 1.75.

Ben: 2(2/4).

Explanation:
In the above-given question,
given that,
2(2/4) = 2 x 4.
8 + 2/4 = 10/4.
10/4 = 2.5.

Question 2.
One of the students read $$\frac{3}{4}$$ hour on Friday, $$\frac{3}{4}$$ hour on Saturday, and $$\frac{3}{4}$$ hour on Sunday. How many hours did that student read over the weekend? Name that student.

Katrina, Scott, and Kelly.

Explanation:
In the above-given question,
given that,
Katrina read 3/4 hours on Friday.
3/4 = 0.75.
Kelly read 3/4 hours on Saturday.
Scott read 3/4 hours on Sunday.

### Eureka Math Grade 4 Module 5 Lesson 28 Homework Answer Key

Question 1.
A group of students measured the lengths of their shoes. The measurements are shown in the table. Make a line plot to display the data.

 Students Length of shoe (in inches) Collin 8$$\frac{1}{2}$$ Dickon 7$$\frac{3}{4}$$ Ben 7$$\frac{1}{2}$$ Martha 7$$\frac{3}{4}$$ Lilias 8 Susan 8$$\frac{1}{2}$$ Frances 7$$\frac{3}{4}$$ Mary 8$$\frac{3}{4}$$

Collin: 8(1/2).

Explanation:
In the above-given question,
given that,
The length of the Collin shoes.
8(1/2) = 2 x 8.
16 + 1/2.
17/2 = 8.5.

Dickon: 7(3/4).

Explanation:
In the above-given question,
given that,
The length of the Dickon shoes.
7(3/4) = 7 x 4.
28 + 3/4.
31/4 = 7.75.

Ben: 7(1/2).

Explanation:
In the above-given question,
given that,
The length of the Ben shoes.
7(1/2) = 2 x 7.
14 + 1/2.
15/2 = 7.5.

Martha: 7(3/4).

Explanation:
In the above-given question,
given that,
The length of the Martha shoes.
7(3/4) = 7 x 4.
28 + 3/4.
31/4 = 7.75.

Lilias: 8.

Explanation:
In the above-given question,
given that,
The length of the Lilias shoes.
8.

Susan: 8(1/2).

Explanation:
In the above-given question,
given that,
The length of the Susan shoes.
8(1/2) = 2 x 8.
16 + 1/2.
17/2 = 8.5.

Frances: 7(3/4).

Explanation:
In the above-given question,
given that,
The length of the Frances shoes.
7(3/4) = 7 x 4.
28 + 3/4.
31/4 = 7.75.

Mary: 8(3/4).

Explanation:
In the above-given question,
given that,
The length of the Mary shoes.
8(3/4) = 4 x 8.
32 + 3/4.
35/4 = 8.75. Question 2.
Solve each problem.
a. Who has a shoe length 1 inch longer than Dickon’s?

The shoe length 1-inch longer than Dickon’s is Mary.

Explanation:
In the above-given question,
given that,
The shoe length of Mary = 8(3/4).
8 x 4 = 32.
32 + 3/4 = 35/4.
35/4 = 8.75.
8.75 – 1 = 7.75.

b. Who has a shoe length 1 inch shorter than Susan’s?

The shoe length 1-inch is shorter than Susan’s is Ben.

Explanation:
In the above-given question,
given that,
The shoe length of Ben = 7(1/2).
7 x 2 = 14.
14 + 1/2 = 15/2.
15/2 = 7.5.
7.5 + 1 = 8.5.

c. How many quarter inches long is Martha’s shoe length?

The length of Martha’s Shoe length = 7 quarter inches.

Explanation:
In the above-given question,
given that,
The length of Martha’s Shoe = 7(3/4).
1 quarter-inch = 3/4.
7(3/4) = 7 quarter inches.

d. What is the difference, in inches, between Lilias’s and Martha’s shoe lengths?

The difference in inches between the Lilias’s and Martha’s shoe lengths = 0.25 inches.

Explanation:
In the above-given question,
given that,
Lilias’s shoe length = 8.
Martha’s shoe length = 7.75.
8 – 7.75 = 0.25 inches.

e. Compare the shoe length of Ben and Frances using >, <, or =.

France > Ben.

Explanation:
In the above-given question,
given that,
Shoe length of Ben = 7.5.
Shoe length of France = 7.75.
7.7 > 7.5.
so Ben is greater than France.

f. How many students had shoes that measured less than 8 inches?

The students who measured less than 8 inches = 4.

Explanation:
In the above-given question,
given that,
The students who measured less than 8 inches is 4.
they are Dickon = 7.75.
Ben = 7.5.
Martha = 7.75.
Frances = 7.75.

g. How many students measured the length of their shoes?

The number of students measured the length of their shoes = 8.

Explanation:
In the above-given question,
given that,
the 8 students measured their shoes.
the students are Collin, Dickon, Ben, Martha, Lilias, Susan, Frances, and Mary.

h. Mr. Jones’s shoe length was $$\frac{25}{2}$$ inches. Use >, <, or = to compare the length of Mr. Jones’s shoe to the length of the longest student shoe length. Who had the longer shoe?

Mary < Mr. Jones’s.

Explanation:
In the above-given question,
given that,
Mr. Jone’s shoe length was 25/2 inches.
25/2 = 12.5.
Mary shoe length = 8.75.
8.75 < 12.5.

Question 3.
Using the information in the table and on the line plot, write a question you could solve by using the line plot. Solve.