## 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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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

Answer:

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.Â Â Â Â Â Â 12Â Ã—Â (5Â +Â 25) | 12 times the sum of 5 and 25 | 12 x ( 30) = 360 |

b.Â Â Â Â Â (62Â â€“Â 12)Â Ã—Â 11 | 11 times the difference of 62 and 12 | (50) x 11 = 550 |

c.Â Â Â Â Â Â (45Â +Â 55)Â Ã—Â 23 | 23 times the sum of 45 and 55 | (100) x 23 = 2300 |

d.Â Â Â Â Â (30Â Ã—Â 2)Â +Â (8Â Ã—Â 2) | product of 30,2 and product of 8,2 | (60) + (16) = 76 |

Answer:

360.

Explanation:

In the above-given question,

given that,

12 x ( 5 + 25).

12 x (30).

360.

Answer:

550.

Explanation:

In the above-given question,

given that,

(62 â€“ 12) Ã— 11

50 x 11 = 550.

Answer:

2300.

Explanation:

In the above-given question,

given that,

(45 + 55) Ã— 23.

100 x 23.

2300.

Answer:

76.

Explanation:

In the above-given question,

given that,

(30Â Ã—Â 2)Â +Â (8Â Ã—Â 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.

Answer:

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.

Answer:

487 > 513.

Explanation:

In the above-given question,

given that,

18 x 27.

487.

20 twenty-seven – 1 27.

540 – 27.

513.

487 < 513.

Answer:

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.

Answer:

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) Ã— (38 + 15)

MeiLing: 15 Ã— (7 + 38)Â

Are the studentsâ€™ expressions equivalent to your answer in Problem 4? Explain your answer.

Answer:

Yes, the student’s expressions equivalent.

Explanation:

In the above-given question,

given that,

Angeline: (7 + 15) Ã— (38 + 15)

Meiling: 15 Ã— (7 + 38)Â

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.

Answer:

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 weekâ€™s order.

Answer:

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.

Answer:

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

Answer:

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

Answer:

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 =.

Answer:

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

Answer:

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.

Answer:

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.

Answer:

2 times the difference between 49.5 and 37.5Â = 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.

Answer:

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.

Answer:

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.

Answer:

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 Ã— (2.5 + 13.5) | one hundred and sixty | 10 x (16) = 160 |

b.Â (98 â€“ 78) Ã— 11 | two hundred and twenty | (20) x 11 = 220 |

c. (71 + 29) Ã— 26 | two thousand six hundred | (100) x 26 = 2600 |

d.Â (50 Ã— 2) + (15 Ã— 2) | one hundred and thirty | (100) + 30 = 130 |

Answer:

160.

Explanation:

In the above-given question,

given that,

10 x ( 2.5 + 13.5).

10 x (16).

160.

Answer:

220.

Explanation:

In the above-given question,

given that,

11 x ( 98 – 78).

11 x (20).

220.

Answer:

2600.

Explanation:

In the above-given question,

given that,

26 x ( 71 + 29).

26 x (30).

2600.

Answer:

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.

Answer:

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.

Answer:

1525 > 1475.

Explanation:

In the above-given question,

given that,

61 x ( 25).

1525.

60 twenty fives minus one twenty-five.

60Â x 25 – 25.

1500 – 25.

1475.

1525 > 1475.

Question 4.

Larry claims that (14 + 12) Ã— (8 + 12) and (14 Ã— 12) + (8 Ã— 12) are equivalent because they have the same digits and the same operations.

a. Is Larry correct? Explain your thinking.

Answer:

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?

Answer:

(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.