## Engage NY Eureka Math 5th Grade Module 4 Lesson 22 Answer Key

### Eureka Math Grade 5 Module 4 Lesson 22 Problem Set Answer Key

Question 1.

Solve for the unknown. Rewrite each phrase as a multiplication sentence. Circle the scaling factor and put a box around the number of meters.

a. \(\frac{1}{2}\) as long as 8 meters = ______ meter(s)

Answer:

4 meters.

Explanation:

Given that \(\frac{1}{2}\) as long as 8 meters which is \(\frac{1}{2}\) Ã— 8 = 4 meters.

b. 8 times as long as \(\frac{1}{2}\) meter = _______ meter(s)

Answer:

4 meters.

Explanation:

Given that \(\frac{1}{2}\) meter is 8 times as long, so 8 Ã— \(\frac{1}{2}\) which is 4 meters.

Question 2.

Draw a tape diagram to model each situation in Problem 1, and describe what happened to the number of meters when it was multiplied by the scaling factor.

a.

Answer:

The scaling factor is less than 1, so the number of meters decreases.

Explanation:

The scaling factor is less than 1, so the number of meters decreases.

b.

Answer:

The scaling factor is greater than 1, so the number of meters increased.

Explanation:

The scaling factor is greater than 1, so the number of meters increased.

Question 3.

Fill in the blank with a numerator or denominator to make the number sentence true.

a. 7 Ã— \(\frac{}{4}\) < 7

Answer:

7 Ã— \(\frac{}{4}\) < 7.

Explanation:

Given that 7 Ã— \(\frac{}{4}\) < 7, so here in the numerator we will place a number that is less than 4. So we will place 3 in the numerator which will be 7 Ã— \(\frac{3}{4}\) < 7.

b. \(\frac{7}{}\) Ã— 15 > 15

Answer:

\(\frac{7}{2}\) Ã— 15 > 15

Explanation:

Given that \(\frac{7}{2}\) Ã— 15 > 15, so here in the denominator we will place a number that is less than 7. So we will place 2 in the denominator which will be \(\frac{7}{2}\) Ã— 15 > 15.

c. 3 Ã— \(\frac{}{5}\) = 3

Answer:

3 Ã— \(\frac{5}{5}\) = 3

Explanation:

Given that 3 Ã— \(\frac{}{5}\) = 3, so to justify the answer we will place 5 in the numerator which is 3 Ã— \(\frac{5}{5}\) = 3.

Question 4.

Look at the inequalities in each box. Choose a single fraction to write in all three blanks that would make all three number sentences true. Explain how you know.

a.

Answer:

\(\frac{5}{2}\).

Explanation:

Multiplying by a fraction greater than 1 will make the product larger than the other factor.

b.

Answer:

\(\frac{1}{2}\).

Explanation:

Multiplying by a fraction less than 1 will make the product less than the other factor.

Question 5.

Johnny says multiplication always makes numbers bigger. Explain to Johnny why this isnâ€™t true. Give more than one example to help him understand.

Answer:

4 times 0.5 equals 2.

Explanation:

Given that Johnny says multiplication always makes numbers bigger which is not true because if we multiply any number by a decimal number, we will make it smaller. Because if we multiply a number by something less than one, we will get something less than itself. This also works if you multiply a number by a fraction. For example, 4 times 0.5 equals 2 because you are getting half of the original number which is 4.

Question 6.

A company uses a sketch to plan an advertisement on the side of a building. The lettering on the sketch is \(\frac{3}{4}\) inch tall. In the actual advertisement, the letters must be 34 times as tall. How tall will the letters be on the building?

Answer:

The letters on the building would be 25 \(\frac{1}{2}\) inch.

Explanation:

Given that a company uses a sketch to plan an advertisement on the side of a building and lettering on the sketch is \(\frac{3}{4}\) inch tall and the letters must be 34 times as tall. So to find the height of the building, we will multiply 34 Ã— \(\frac{3}{4}\) inch and the height of the letters on the building which is 34 Ã— \(\frac{3}{4}\) inch

= \(\frac{104}{4}\) inch

= \(\frac{51}{2}\) inch

= 25 \(\frac{1}{2}\) inch.

Therefore the letters on the building would be 25 \(\frac{1}{2}\) inch.

Question 7.

Jason is drawing the floor plan of his bedroom. He is drawing everything with dimensions that are \(\frac{1}{12}\) of the actual size. His bed measures 6 ft by 3 ft, and the room measures 14 ft by 16 ft. What are the dimensions of his bed and room in his drawing?

Answer:

The dimensions of his room in his drawing are 1 \(\frac{1}{3}\) by1 \(\frac{1}{6}\) ft,

The dimensions of his bed in his drawing are \(\frac{1}{2}\) ft by \(\frac{1}{4}\) ft.

Explanation:

Given that Jason is drawing the floor plan of his bedroom and he is drawing everything with dimensions that are \(\frac{1}{12}\) of the actual size and his bed measures 6 ft by 3 ft, and the room measures 14 ft by 16 ft. So the dimensions of his room in his drawing are \(\frac{1}{12}\) of 16 ft and \(\frac{1}{12}\) of 14 ft which is

= \(\frac{1}{12}\) Ã— 16

= \(\frac{4}{3}\)

= 1 \(\frac{1}{3}\)

\(\frac{1}{12}\) of 14 ft

= \(\frac{1}{12}\) Ã— 14 ft

= \(\frac{7}{6}\)

= 1 \(\frac{1}{6}\) ft

So the dimensions of his room in his drawing are 1 \(\frac{1}{3}\) by1 \(\frac{1}{6}\) ft.

For his bed in his drawing are \(\frac{1}{12}\) of 6 ft by \(\frac{1}{12}\) of 3 which is

= \(\frac{1}{12}\) Ã— 6

= \(\frac{1}{2}\) ft

\(\frac{1}{12}\) of 3

= \(\frac{1}{12}\) Ã— 3

= \(\frac{1}{4}\) ft.

So the dimensions of his bed in his drawing are \(\frac{1}{2}\) ft by \(\frac{1}{4}\) ft.

### Eureka Math Grade 5 Module 4 Lesson 22 Exit Ticket Answer Key

Fill in the blank to make the number sentences true. Explain how you know.

a. \(\frac{}{3}\) Ã— 11 Ëƒ 11

Answer:

\(\frac{4}{3}\) Ã— 11 Ëƒ 11.

Explanation:

Given that \(\frac{}{3}\) Ã— 11 Ëƒ 11, so here in the numerator we will place a number that is greater than 3. So we will place 4 in the numerator which will be \(\frac{4}{3}\) Ã— 11 Ëƒ 11.

b. 5 Ã— \(\frac{}{8}\) Ë‚ 5

Answer:

5 Ã— \(\frac{5}{8}\) Ë‚ 5.

Explanation:

Given that 5 Ã— \(\frac{}{8}\) Ë‚ 5, so here in the numerator we will place a number that is less than 8. So we will place 5 in the numerator which will be 5 Ã— \(\frac{5}{8}\) Ë‚ 5.

c. 6 Ã— \(\frac{2}{}\) = 6

Answer:

6 Ã— \(\frac{2}{2}\) = 6

Explanation:

Given that 6 Ã— \(\frac{2}{2}\) = 6, so to justify the answer we will place 2 in the numerator which is 6 Ã— \(\frac{2}{2}\) = 6

### Eureka Math Grade 5 Module 4 Lesson 22 Homework Answer Key

Question 1.

Solve for the unknown. Rewrite each phrase as a multiplication sentence. Circle the scaling factor and put a box around the number of meters.

a. \(\frac{1}{3}\) as long as 6 meters = ______ meter(s)

Answer:

2 meters.

Explanation:

Given that \(\frac{1}{3}\) as long as 6 meters which is \(\frac{1}{3}\) Ã— 6 = 2 meters.

b. 6 times as long as \(\frac{1}{3}\) meter = ______ meter(s)

Answer:

2 meters.

Explanation:

Given that \(\frac{1}{3}\) meter is 6 times as long, so 6 Ã— \(\frac{1}{3}\) which is2 meters.

Question 2.

Draw a tape diagram to model each situation in Problem 1, and describe what happened to the number of meters when it was multiplied by the scaling factor.

a.

Answer:

The scaling factor is less than 1, so the number of meters decreases.

Explanation:

The scaling factor is less than 1, so the number of meters decreases.

b.

Answer:

The scaling factor is greater than 1, so the number of meters increased.

Explanation:

The scaling factor is greater than 1, so the number of meters increased.

Question 3.

Fill in the blank with a numerator or denominator to make the number sentence true.

a. 5 Ã— \(\frac{}{3}\) Ëƒ 5

Answer:

5 Ã— \(\frac{2}{3}\) Ëƒ 5.

Explanation:

Given that 5 Ã— \(\frac{4}{3}\) Ëƒ 5, so here in the numerator, we will place a number that is greater than 3. So we will place 4 in the numerator which will be 5 Ã— \(\frac{4}{3}\) Ëƒ 5.

b. \(\frac{6}{}\) Ã— 12 Ë‚ 12

Answer:

\(\frac{6}{}\) Ã— 12 Ë‚ 12.

Explanation:

Given that \(\frac{6}{7}\) Ã— 12 Ë‚ 12, so here in the numerator, we will place a number that is greater than 6. So we will place 7 in the numerator which will be \(\frac{6}{7}\) Ã— 12 Ë‚ 12.

c. 4 Ã— \(\frac{}{5}\) = 4

Answer:

4 Ã— \(\frac{5}{5}\) = 4

Explanation:

Given that 4 Ã— \(\frac{5}{5}\) = 4, so to justify the answer we will place 5 in the numerator which is 4 Ã— \(\frac{5}{5}\) = 4.

Question 4.

Look at the inequalities in each box. Choose a single fraction to write in all three blanks that would make all three number sentences true. Explain how you know.

a.

Answer:

\(\frac{5}{4}\).

Explanation:

Multiplying by a fraction greater than 1 will make the product larger than the other factor.

b.

Answer:

\(\frac{1}{2}\).

Explanation:

Multiplying by a fraction less than 1 will make the product less than the other factor.

Question 5.

Write a number in the blank that will make the number sentence true.

a. 3 Ã— _____ Ë‚ 1

Answer:

3 Ã— \(\frac{1}{4}\) < 1.

Explanation:

To make the number sentence true we will place the number which is less than \(\frac{1}{3}\), so we will place \(\frac{1}{4}\) which will be less than 1. So the expression will be 3 Ã— \(\frac{1}{4}\) < 1.

b. Explain how multiplying by a whole number can result in a product less than 1.

Answer:

When a positive whole number is multiplied by a fraction between 0 and 1, the product is less than the whole number. When a number greater than 1 is multiplied by a number greater than 1, the product is greater than both numbers.

Question 6.

In a sketch, a fountain is drawn \(\frac{1}{4}\) yard tall. The actual fountain will be 68 times as tall. How tall will the

fountain be?

Answer:

The actual height of the fountain is 17 yards.

Explanation:

Given that a fountain is drawn \(\frac{1}{4}\) yard tall and the actual fountain will be 68 times as tall. So the actual height of the fountain is \(\frac{1}{4}\) Ã— 68 which is 17 yards.

Question 7.

In blueprints, an architectâ€™s firm drew everything \(\frac{1}{24}\) of the actual size. The windows will actually measure 4 ft by 6 ft and doors measure 12 ft by 8 ft. What are the dimensions of the windows and the doors in the drawing?

Answer:

The dimensions of the windows are 2 in by 3 in.

The dimensions of the windows are 6 in by 4 in.

Explanation:

Given that an architectâ€™s firm drew everything \(\frac{1}{24}\) of the actual size and the windows will actually measure 4 ft by 6 ft, so the dimensions of the length of the windows are \(\frac{1}{24}\) Ã— 4 which is \(\frac{1}{6}\) ft, so in inch, it will be \(\frac{1}{6}\) Ã— 12 which is 2 in. And the width of the windows is \(\frac{1}{24}\) Ã— 6 which is \(\frac{1}{4}\), so in inch, it will be \(\frac{1}{4}\) Ã— 12 which is 3 in. So the dimensions of the windows are 2 in by 3 in. Given that the measures of the door are 12 ft by 8 ft, so the dimensions of the length of the doors are \(\frac{1}{24}\) Ã— 12 which is \(\frac{1}{2}\) ft, so in inch, it will be \(\frac{1}{2}\) Ã— 12 which is 6 in. And the width of the windows is \(\frac{1}{24}\) Ã— 8 which is \(\frac{1}{3}\), so in inch, it will be \(\frac{1}{3}\) Ã— 12 which is 4 in.