## 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. Smithâ€™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 2Â $$\frac{1}{2}$$ 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 Â $$\frac{5}{8}$$ 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. Oâ€™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 timeÂ  (in hours) Robin $$\frac{1}{2}$$ Bill 1 Katrina $$\frac{3}{4}$$ Kelly 1Â $$\frac{3}{4}$$ 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 Â 7$$\frac{1}{2}$$ Martha 7$$\frac{3}{4}$$ Lilias 8 Susan 8$$\frac{1}{2}$$ Frances Â 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 Dickonâ€™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 Susanâ€™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 Marthaâ€™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 Liliasâ€™s and Marthaâ€™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. Jonesâ€™s shoe length was $$\frac{25}{2}$$ inches. Use >, <, or = to compare the length of Mr. Jonesâ€™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.