## Engage NY Eureka Math 5th Grade Module 2 Lesson 3 Answer Key

### Eureka Math Grade 5 Module 2 Lesson 3 Problem Set Answer Key

Question 1.
Draw a model. Then, write the numerical expressions.
a. The sum of 8 and 7, doubled

The sum of 8 and 7, doubled = 30.

Explanation:
In the above-given question,
given that,
the sum of 8 and 7 is 15.
8 + 7 = 15.
15 + 15 = 30. b. 4 times the sum of 14 and 26

The sum of 14 and 26, 4 times = 160.

Explanation:
In the above-given question,
given that,
the sum of 14 and 26 is 40.
40 + 40 + 40 + 40 = 160.
14 + 26 = 40. c. 3 times the difference between 37.5 and 24.5

The difference of 37.5 and 24.5, 3 times = 13.0.

Explanation:
In the above-given question,
given that,
the difference of 37.5 and 24.5 is 13.0.
37.5 – 24.5 = 13.0.
13.0 + 13.0 + 13.0 = 39. d. The sum of 3 sixteens and 2 nines

The sum of 3 sixteens and 2 nines = 30.

Explanation:
In the above-given question,
given that,
the sum of 3 sixteens and 2 nines is 66.
48 + 18 = 66.
16 + 16 + 16 + 9 + 9 = 66. e. The difference between 4 twenty-fives and 3 twenty-fives

The difference between 4 25 and 3 25 = 25.

Explanation:
In the above-given question,
given that,
the difference between 4 25 and 3 25 = 25.
100 – 75 = 25.
4 x 25 = 100.
3 x 25 = 75.
100 – 75 = 25. f. Triple the sum of 33 and 27

The sum of 33 and 27, 3 times = 180.

Explanation:
In the above-given question,
given that,
the sum of 33 and 27 is 180.
60 + 60 + 60 = 180.
33 + 27 = 60. Question 2.
Write the numerical expressions in words. Then, solve.

 Expression Words The Value of the Expression a.       12 × (5 + 25) 12 times the sum of 5 and 25 12 x ( 30) = 360 b.      (62 – 12) × 11 11 times the difference of 62 and 12 (50) x 11 = 550 c.       (45 + 55) × 23 23 times the sum of 45 and 55 (100) x 23 = 2300 d.      (30 × 2) + (8 × 2) product of 30,2 and product of 8,2 (60) + (16) = 76

360.

Explanation:
In the above-given question,
given that,
12 x ( 5 + 25).
12 x (30).
360.

550.

Explanation:
In the above-given question,
given that,
(62 – 12) × 11
50 x 11 = 550.

2300.

Explanation:
In the above-given question,
given that,
(45 + 55) × 23.
100 x 23.
2300.

76.

Explanation:
In the above-given question,
given that,
(30 × 2) + (8 × 2)
60 + 16.
76.

Question 3.
Compare the two expressions using > , < , or = . In the space beneath each pair of expressions, explain how you can compare without calculating. Draw a model if it helps you. 600 > 360.

Explanation:
In the above-given question,
given that,
24 x (20 + 5).
24 x 25.
600.
(20 + 5) x 12.
30 x 12.
360.
600 > 360.

487 > 513.

Explanation:
In the above-given question,
given that,
18 x 27.
487.
20 twenty-seven – 1 27.
540 – 27.
513.
487 < 513.

171 = 171.

Explanation:
In the above-given question,
given that,
19 x 9.
171.
3 nineteens tripled.
57 x 3.
171.
171 = 171. Question 4.
Mr. Huynh wrote the sum of 7 fifteens and 38 fifteens on the board.
Draw a model, and write the correct expression.

The sum of 7 fifteens and 38 fifteens = 675.

Explanation:
In the above-given question,
given that,
the sum of 7 fifteens and 38 fifteens
105 + 570 = 675. Question 5.
Two students wrote the following numerical expressions.
Angeline: (7 + 15) × (38 + 15)
MeiLing: 15 × (7 + 38)

Yes, the student’s expressions equivalent.

Explanation:
In the above-given question,
given that,
Angeline: (7 + 15) × (38 + 15)
Meiling: 15 × (7 + 38)
105 + 570 = 675.

Question 6.
A box contains 24 oranges. Mr. Lee ordered 8 boxes for his store and 12 boxes for his restaurant.
a. Write an expression to show how to find the total number of oranges ordered.

The total number of oranges ordered= 480.

Explanation:
In the above-given question,
given that,
A box contains 24 oranges. Mr. Lee ordered 8 boxes for his store and 12 boxes for his restaurant.
( 24 x 8 ) + ( 24 x 12)
192 + 288
480

b. Next week, Mr. Lee will double the number of boxes he orders. Write a new expression to represent the number of oranges in next week’s order.

The total number of oranges ordered= 960.

Explanation:
In the above-given question,
given that,
A box contains 24 oranges. Mr. Lee ordered 8 boxes for his store and 12 boxes for his restaurant.
( 24 x 8 ) + ( 24 x 12)
192 + 288
480 + 480 = 960

c. Evaluate your expression from Part (b) to find the total number of oranges ordered in both weeks.

The total number of oranges ordered in both weeks = 1440.

Explanation:
In the above-given question,
given that,
960 + 480 = 1440.

### Eureka Math Grade 5 Module 2 Lesson 3 Exit Ticket Answer Key

Question 1.
Draw a model. Then, write the numerical expressions.
a. The difference between 8 forty-sevens and 7 forty-sevens

The difference of 8 forty-sevens and 7 forty-sevens = 47.

Explanation:
In the above-given question,
given that,
the difference of 8 forty sevens and 7 forty-sevens.
8 x 47 – 7 x 47.
376 – 329.
47

b. 6 times the sum of 12 and 8

The sum of 12 and 8, 6 times = 120.

Explanation:
In the above-given question,
given that,
the sum of 12 and 8 is 120.
20 + 20 + 20 + 20 + 20 + 20 = 120.
12 + 8 = 20.

Question 2.
Compare the two expressions using >, <, or =. 4836 > 2028.

Explanation:
In the above-given question,
given that,
62 x ( 70 + 8).
62 x 78 = 4836.
(70 + 8) x 26.
78 x 26 = 2,028. ### Eureka Math Grade 5 Module 2 Lesson 3 Homework Answer Key

Question 1.
Draw a model. Then, write the numerical expressions.
a. The sum of 21 and 4, doubled
b. 5 times the sum of 7 and 23
c. 2 times the difference between 49.5 and 37.5
d. The sum of 3 fifteens and 4 twos
e. The difference between 9 thirty-sevens and 8 thirty-sevens
f. Triple the sum of 45 and 55

The sum of 21 and 4, 2 times = 50.

Explanation:
In the above-given question,
given that,
the sum of 21 and 4 is 25.
25 + 25 = 50.
21 + 4 = 25. The sum of 7 and 23, 5 times = 150.

Explanation:
In the above-given question,
given that,
the sum of 7 and 23 is 30.
30 + 30 + 30 + 30 + 30 = 150.
7 + 23 = 30. 2 times the difference between 49.5 and 37.5 = 24.

Explanation:
In the above-given question,
given that,
2 times the difference between 49.5 and 37.5
49.5 – 37.5 = 12.0.
12 + 12 = 24. The sum of 3 fifteens and 4 twos = 53.

Explanation:
In the above-given question,
given that,
The sum of 3 fifteens and 4 twos
45 + 8.
53. The difference between 9 thirty-sevens and 8 thirty-sevens = 37.

Explanation:
In the above-given question,
given that,
The difference between 9 thirty-sevens and 8 thirty-sevens
9 x 37 – 8 x 37.
333 – 296.
37.

Triple the sum of 45 and 55 = 300.

Explanation:
In the above-given question,
given that,
Triple the sum of 45 and 55
45 + 55 = 100.
100 + 100 + 100 = 300.

Question 2.
Write the numerical expressions in words. Then, solve.

 Expression Words The Value of the Expression a. 10 × (2.5 + 13.5) one hundred and sixty 10 x (16) = 160 b.  (98 – 78) × 11 two hundred and twenty (20) x 11 = 220 c. (71 + 29) × 26 two thousand six hundred (100) x 26 = 2600 d.  (50 × 2) + (15 × 2) one hundred and thirty (100) + 30 = 130

160.

Explanation:
In the above-given question,
given that,
10 x ( 2.5 + 13.5).
10 x (16).
160.

220.

Explanation:
In the above-given question,
given that,
11 x ( 98 – 78).
11 x (20).
220.

2600.

Explanation:
In the above-given question,
given that,
26 x ( 71 + 29).
26 x (30).
2600.

3000.

Explanation:
In the above-given question,
given that,
(50 x 2) + ( 15 + 2).
100 x (30).
3000.

Question 3.
Compare the two expressions using > , < , or = . In the space beneath each pair of expressions, explain how you can compare without calculating. Draw a model if it helps you. 3906 > 1438.

Explanation:
In the above-given question,
given that,
93 x ( 40 + 2).
93 x (42).
3906.
(40 + 2) x 36
42 x 36.
1438.
3906 > 1438.

1525 > 1475.

Explanation:
In the above-given question,
given that,
61 x ( 25).
1525.
60 twenty fives minus one twenty-five.
60  x 25 – 25.
1500 – 25.
1475.
1525 > 1475.

Question 4.
Larry claims that (14 + 12) × (8 + 12) and (14 × 12) + (8 × 12) are equivalent because they have the same digits and the same operations.
a. Is Larry correct? Explain your thinking.

Yes, Larry was not correct.

Explanation:
In the above-given question,
given that,
Larry claims that (14 + 12) x (8 + 12) and (14 x 12) + (8 x 12).
42 + 12 = 26.
8 + 12 = 20.
26 x 20 = 520.
(14 x 12) + (8 x 12).
168 + 96.
264.
520 is not equal to 264.

b. Which expression is greater? How much greater?

(14 + 12) x (8 + 12) is greater.
256 is greater.

Explanation:
In the above-given question,
given that,
42 + 12 = 26.
8 + 12 = 20.
26 x 20 = 520.
(14 x 12) + (8 x 12).
168 + 96.
264.
520 is not equal to 264.

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