## Engage NY Eureka Math 5th Grade Module 2 Lesson 4 Answer Key

### Eureka Math Grade 5 Module 2 Lesson 4 Problem Set Answer Key

Question 1.

Circle each expression that is not equivalent to the expression in bold.

a. 16 × 29

Answer:

16 x 29 = 464.

Explanation:

In the above-given question,

given that,

29 sixteens = 29 x 16.

16 x (30 – 1).

16 x 29.

(15 – 1) x 29.

(10 x 29) – (6 x 29)

290 – 174.

26.

b. 38 × 45

Answer:

38 x 45 = 1710.

Explanation:

In the above-given question,

given that,

(38 + 40) x ( 38 + 45) = 78 x 83 = 6474.

(38 x 40 ) + ( 38 x 5) = 1520 + 190 = 1710.

45 x (40 + 2) = 45 x 42 = 1890.

45 thirty-eights = 45 x 38 = 1710.

c. 74 × 59

Answer:

74 x 59 = 4366.

Explanation:

In the above-given question,

given that,

74 x (50 + 9) = 74 x 59 = 4366.

74 x (60-1) = 74 x 59 = 4366.

(74 x 5) + (74 x 9) = 370 + 666 = 1036.

59 seventy-fours = 59 x 74 = 4366.

Question 2.

Solve using mental math. Draw a tape diagram and fill in the blanks to show your thinking. The first one is partially done for you.

a. 19 × 25 = __nineteen________ twenty-fives

Think: 20 twenty-fives – 1 twenty-five.

= ( ____20______ × 25) – ( ____1______ × 25)

= ____500______ – ____25______

= ___475_______

Answer:

19 x 25 = 475.

Explanation:

In the above-given question,

given that,

20 twenty-fives – 1 twenty-five.

20 x 25 – 1 x 25.

500 – 25.

475

b. 24 × 11 = _____eleven_____ twenty-fours

Think: ___10__ twenty fours + __1___ twenty four

= ( ____10______ × 24) + ( ____1______ × 24)

= _____240_____ + _____24_____

= __264________

Answer:

10 x 24 = 264.

Explanation:

In the above-given question,

given that,

10 twenty-fours + 1 twenty-four.

10 x 24 + 1 x 24.

240 + 24.

264.

c. 79 × 14 = _____79_____ fourteens

Think: _____78_____ fourteens – 1 fourteen

= (_____78_____ × 14) – (_____1_____ × 14)

= ____1092______ – ___14_______

= ____1078______

Answer:

79 x 14 = 79 fourteens.

Explanation:

In the above-given question,

given that,

78 fourteens – 1 fourteen.

78 x 14 – 1 x 14.

1092 – 14.

1078.

d. 21 × 75 = ______21____ seventy-fives

Think: ___20__ seventy-fives + __1___ seventy-five

= (____20______ × 75) + (_____1_____ × 75)

= ___1500_______ + ____75______

= ___1625_______

Answer:

21 x 75 = 1625.

Explanation:

In the above-given question,

given that,

20 seventy-fives + 1 seventy-five.

20 x 75 + 1 x 75.

1500 + 25.

1625.

Question 3.

Define the unit in word form and complete the sequence of problems as was done in the lesson.

a. 19 × 15 = 19 ___15_______

Think: 20 _______15______ – 1 ____15_________

= (20 × _____15_____) – (1 × __15________)

= ___300_______ – _____15_____

= _____285_____

Answer:

19 x 15 = 285.

Explanation:

In the above-given question,

given that,

20 fifteens – 1 fifteen.

20 x 15 – 1 x 15.

500 – 15.

285.

b. 14 × 15 = 14 ____15______

Think: 10 _____5_______ + 4 ______10_____

= (10 × ____5______) + (4 × ____10______)

= _____50_____ + ____40______

= ___90_______

Answer:

14 x 15 = 210.

Explanation:

In the above-given question,

given that,

10 5 + 4 10.

50 + 40.

90

c. 25 × 12 = 12 _____25_____

Think: 10 ____15______ + 2 __25_______

= (10 × ___25_______) + (2 × _____25_____)

= ____250______ + _____50_____

= ____300______

Answer:

25 x 12 = 300.

Explanation:

In the above-given question,

given that,

10 fifteens + 2 twenty-five.

10 x 15 + 2 x 25.

250 + 50.

300.

d. 18 × 17 = 18 ___17_______

Think: 20 ____17______ – 2 ____17______

= (20 × _____17_____) – (2 × ___17_______)

= ______340____ – ____34______

= ____306______

Answer:

18 x 17 = 306.

Explanation:

In the above-given question,

given that,

20 seventeen – 2 seventeen.

20 x 17 – 2 x 17.

340 – 34.

306.

Question 4.

How can 14 × 50 help you find 14 × 49?

Answer:

14 x 50 = 14 x (50 – 1).

Explanation:

In the above-given question,

given that,

14 fifty – 14 fourty nine.

14 x 50 – 14 x 49.

700 – 686.

14

Question 5.

Solve mentally.

a. 101 × 15 = __1515________

Answer:

101 x 15 = 1515.

Explanation:

In the above-given question,

given that,

101 x 15

1515.

b. 18 × 99 = ____1782______

Answer:

18 x 99 = 1782.

Explanation:

In the above-given question,

given that,

18 x 99

1782.

Question 6.

Saleem says 45 × 32 is the same as (45 × 3) + (45 × 2). Explain Saleem’s error using words, numbers, and/or pictures.

Answer:

45 x 32 = 1440 and (45 x 3) + (45 x 2) = 135 + 90 = 225..

Explanation:

In the above-given question,

given that,

45 x 32

1440.

Question 7.

Juan delivers 174 newspapers every day. Edward delivers 126 more newspapers each day than Juan.

a. Write an expression to show how many newspapers Edward will deliver in 29 days.

Answer:

The newspapers Edward will deliver in 29 days =

Explanation:

In the above-given question,

given that,

Juan delivers 174 newspapers every day.

Edward delivers 126 more newspapers each day than Juan.

174 + 126 = 300.

Edward will deliver in 29 days = 300 x 29.

300 x 29 = 8700.

b. Use mental math to solve. Show your thinking.

### Eureka Math Grade 5 Module 2 Lesson 4 Exit Ticket Answer Key

Solve using mental math. Draw a tape diagram and fill in the blanks to show your thinking.

a. 49 × 11 = ____49______ elevens

Think: 50 elevens – 1 eleven

= (___50_______ × 11) – (_____1_____ × 11)

= ____550______ – _____11_____

= _____539_____

Answer:

49 x 11 = 539.

Explanation:

In the above-given question,

given that,

50 x 11 – 1 x 11.

550 – 11.

539.

b. 25 × 13 = ____13______ twenty-fives

Think: __10___ twenty-fives + __3___ twenty-fives

= (____10______ × 25) + (____3______ × 25)

= ____250______ + ____75______

= _____325_____

Answer:

25 x 13 = 325.

Explanation:

In the above-given question,

given that,

10 x 25 + 3 x 25.

250 + 75

325.

### Eureka Math Grade 5 Module 2 Lesson 4 Homework Answer Key

Question 1.

Circle each expression that is not equivalent to the expression in bold.

a. 37 × 19

Answer:

37 x 19 = 703.

Explanation:

In the above-given question,

given that,

37 nineteens = 37 x 19 = 703.

(30 x 19) – (7 x 29) = 570 – 203 = 367.

37 x (20 – 1) = 37 x 19 = 703.

(40 – 2) x 19 = 38 x 19 = 722.

b. 26 × 35

Answer:

26 x 35 = 910

Explanation:

In the above-given question,

given that,

35 x 26 = 910

(26 + 30) x (26 + 5) = 56 x 31 = 1736.

(26 x 30) + (26 x 5) = 780 + 130 = 910.

35 x (20 + 60) = 35 x 80 = 2800

c. 34 × 89

Answer:

34 x 89 = 3026

Explanation:

In the above-given question,

given that,

34 x (89) = 3026.

(34 x 8) + (34 x 9) = 272 + 306 = 578.

34 x 89 = 3026.

89 thirty-fours = 89 x 34 = 3026.

Question 2.

Solve using mental math. Draw a tape diagram and fill in the blanks to show your thinking. The first one is partially done for you.

a. 19 × 50 = _____19_____ fifties

Think: 20 fifties – 1 fifty

= ( _____20_____ × 50) – ( ____1______ × 50)

= _____1000_____ – ____50______

= ____950______

Answer:

19 x 50 = 950.

Explanation:

In the above-given question,

given that,

19 x 50

20 x 50 – 1 x 50.

1000 – 50.

950.

b. 11 × 26 = ____11______ twenty-sixes

Think: __10___ twenty-sixes + __1___ twenty-six

= ( _____10_____ × 26) + ( ___1_______ × 26)

= _____260_____ + _____26_____

= _____234_____

Answer:

11 x 26 = 234.

Explanation:

In the above-given question,

given that,

11 x 26

10 x 26 + 1 x 26.

260 + 26.

234.

c. 49 × 12 = ______49____ twelves

Think: ___50__ twelves – 1 twelve

= ( ____50______ × 12) – ( ____1______ × 12)

= ____600______ – _____12_____

= ____588______

Answer:

49 x 12 = 588.

Explanation:

In the above-given question,

given that,

49 x 12

50 x 12 – 1 x 12.

600 – 12.

588.

d. 12 × 25 = ______12____ twenty-fives

Think: ___10__ twenty-fives + __2___ twenty-fives

= ( ____10______ × 25) + ( ____2______ × 25)

= _____250_____ + ____50______

= ____300______

Answer:

12 x 25 = 300.

Explanation:

In the above-given question,

given that,

12 x 25

10 x 25 + 2 x 25.

250 – 50.

300.

Question 3.

Define the unit in word form and complete the sequence of problems as was done in the lesson.

a. 29 × 12 = 29 ____12______

Think: 30 _____12_____ – 1 ____12______

= (30 × ______12____ ) – (1 × _____12_____ )

= ____360______ – ___12_______

= ____348______

Answer:

29 x 12 = 348.

Explanation:

In the above-given question,

given that,

29 x 12

30 x 12 – 1 x 12.

360 – 12.

348.

b. 11 × 31 = 31 __11________

Think: 30 _____11_____ + 1 _____11_____

= (30 × ___11_______ ) + (1 × ___11_______ )

= _______330___ + ____11______

= _____341_____

Answer:

11 x 31 = 341.

Explanation:

In the above-given question,

given that,

11 x 31

30 x 11 + 1 x 11.

330 + 11.

341.

c. 19 × 11 = 19 _____11_____

Think: 20 ____11______ – 1 ______11____

= (20 × ___11_______ ) – (1 × ____11______ )

= ____220______ – ___11_______

= ____209______

Answer:

19 x 50 = 950.

Explanation:

In the above-given question,

given that,

19 x 50

20 x 50 – 1 x 50.

1000 – 50.

950.

d. 50 × 13 = 13 ____50______

Think: 10 _____50_____ + 3 _____50_____

= (10 × ____50______ ) + (3 × ____50______ )

= ___500_______ + ____150______

= ____650______

Answer:

13 x 50 = 650.

Explanation:

In the above-given question,

given that,

13 x 50

10 x 50 + 3 x 50.

500 + 150.

650.

Question 4.

How can 12 × 50 help you find 12 × 49?

Answer:

12 x 50 = 600.

Explanation:

In the above-given question,

given that,

12 x 49 = 12 x (50 – 1).

12 x 49 = 588.

12 x 50 = 600.

Question 5.

Solve mentally.

a. 16 × 99 = ___1584_______

Answer:

16 x 99 = 1584.

Explanation:

In the above-given question,

given that,

16 x 99.

1584.

b. 20 × 101 = ___2020_______

Answer:

20 x 101 = 2020.

Explanation:

In the above-given question,

given that,

20 x 101

20 x 102 – 1.

20 x 101.

2020.

Question 6.

Joy is helping her father to build a rectangular deck that measures 14 ft by 19 ft. Find the area of the deck using a mental strategy. Explain your thinking.

Answer:

The area of the deck = 266 sq ft.

Explanation:

In the above-given question,

given that,

Joy is helping her father to build a rectangular deck that measures 14 ft by 19 ft.

area = l x b.

area = 14 x 19.

area = 266 sq ft.

Question 7.

The Lason School turns 101 years old in June. In order to celebrate, they ask each of the 23 classes to collect 101 items and make a collage. How many total items will be in the collage? Use mental math to solve. Explain your thinking.

Answer:

The total items will be in the college = 2323.

Explanation:

In the above-given question,

given that,

The Lason School turns 101 years old in june.

In order to celebrate, they ask each of the 23 classes to collect 101 items and make a collage.

23 x 101 = 2323.