## Engage NY Eureka Math 5th Grade Module 4 Lesson 9 Answer Key

### Eureka Math Grade 5 Module 4 Lesson 9 Problem Set Answer Key

Question 1.

Convert. Show your work using a tape diagram or an equation. The first one is done for you.

a. \(\frac{1}{2}\) yard = __1\(\frac{1}{2}\)__ feet

\(\frac{1}{2}\) yard = \(\frac{1}{2}\) × 1 yard

= \(\frac{1}{2}\) × 3 feet

= \(\frac{3}{2}\) feet

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

b. \(\frac{1}{3}\) foot = ________ inches

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

= \(\frac{1}{3}\) × 12 inches

=

Answer:

4 inches

Explanation:

1/3 foot = 1/3 * 1 foot

= 1/3 * 12 inches

= 12/3

= 4 inches

c. \(\frac{5}{6}\) year = ________ months

Answer:

10 months

Explanation:

5/6 year = 5/6 * 1 year

= 5/6 * 12 months

= 60/6 months

= 10 months

d. \(\frac{4}{5}\) meter = ________ centimeters

Answer:

80 centimeters

Explanation:

4/5 m = 4/5 *1m

= 4/5 * 100 cm

= 400/5

= 80 cm

e. \(\frac{2}{3}\) hour = ________ minutes

Answer:

40 minutes

Explanation:

2/3 hr = 2/3 * 1 hr

= 2/3 * 60

= 120/3 min

= 40 min

f. \(\frac{3}{4}\) yard = ________ inches

Answer:

27 inches

Explanation:

3/4 yard = 3/4 * 1 yd

= 3/4 * 36 inches

= 108/4 inches

= 27 inches

Question 2.

Mrs. Lang told her class that the class’s pet hamster is \(\frac{1}{4}\) ft in length. How long is the hamster in inches?

Answer:

The hamster is 3 inches long

Explanation:

1/4 ft = 1/4 * 1 ft

= 1/4 *12 inc

= 3 inc

Question 3.

At the market, Mr. Paul bought \(\frac{7}{8}\) lb of cashews and \(\frac{3}{4}\) lb of walnuts. How many ounces of cashews did Mr. Paul buy?

Answer:

14 ounces of cashews.

Explanation:

7/8 lb = 7/8 *1 lb

= 7/8 * 16 oz

= 112 oz/8

= 14 oz

Hence Mr paul bought 14 ounces of cashews.

b. How many ounces of walnuts did Mr. Paul buy?

Answer:

12 ounces of walnuts.

Explanation:

3/4 lb = 3/4 * 1 lb

= 3/4 * 16 oz

= 48/4 oz

= 12 oz.

Hence Mr paul bought 12 ounces of walnuts.

c. How many more ounces of cashews than walnuts did Mr. Paul buy?

Answer:

2 ounces.

Explanation:

14 oz – 12 oz = 2 oz

Mr.paul bought 2 ounces more cashews than walnuts.

d. If Mrs. Toombs bought 1\(\frac{1}{2}\) pounds of pistachios, who bought more nuts, Mr. Paul or Mrs. Toombs? How many ounces more?

Answer:

2 ounces more

Explanation:

Mr paul = 14 oz + 12 oz = 26 oz

Mrs. Toombs = 1 1/2 lb = 3/2 lb = 3/2 * 1 lb

= 3/2 * 16 oz

= 48/2

= 24 oz

So 26 oz – 24 oz = 2oz.

Hence Mr. paul bought more nuts than Mrs. Toombs. He bought 2 ounces more than she did.

Question 4.

A jewelry maker purchased 20 inches of gold chain. She used \(\frac{3}{8}\) of the chain for a bracelet. How many inches of gold chain did she have left?

Answer:

She had 12 1/2 inches left.

Explanation:

8 units = 20

1 unit = 20/8

= 2 4/8

5 units = 2 4/8 + 2 4/8 + 2 4/8 + 2 4/8 + 2 4/8

= 10 20/8

= 12 4/8

= 12 1/2

### Eureka Math Grade 5 Module 4 Lesson 9 Exit Ticket Answer Key

Question 1.

Express 36 minutes as a fraction of an hour: 36 minutes = _______ hour

Answer:

3/5

Explanation:

1 hr =60minutes

take 36min /60 min=18/30

=9/15=3/5

Question 2.

Solve.

a. \(\frac{2}{3}\) feet = _______ inches

Answer:

2 inches

Explanation:

2/3 feet = 2/3 * 12 inches

= (2*12)/12

= 24/12

= 2 inches

b. \(\frac{2}{5}\) m = _______ cm

Answer:

40 cm

Explanation:

2/5 m = 2/5 * 100 cm

= (2*100)/5

= 40 cm

c. \(\frac{5}{6}\) year = _______ months

Answer:

10 months

Explanation:

1 year = 12 months

5/6 year = 5/6 * 12

= (5*12)/6

= 10

### Eureka Math Grade 5 Module 4 Lesson 9 Homework Answer Key

Question 1.

Convert. Show your work using a tape diagram or an equation. The first one is done for you.

a. \(\frac{1}{4}\) yard = __9__ inches

\(\frac{1}{4}\) yard = \(\frac{1}{4}\) × 1 yard

= \(\frac{1}{4}\) × 36 inches

= \(\frac{36}{4}\) inches

= 9 inches

b. \(\frac{1}{6}\) foot = ________ inches

\(\frac{1}{6}\) foot = \(\frac{1}{6}\) × 1 foot

= \(\frac{1}{6}\) × 12 inches

Answer:

2 inches

Explanation:

1/6 * 12 =2 inches

c. \(\frac{3}{4}\) year = ________ months

Answer:

9 inches

Explanation:

3/4 year = 3/4 * 12 months

= (3*12)/4

= 9 inches

d. \(\frac{3}{5}\) meter = ________ centimeters

Answer:

60 centimeters

Explanation:

3/5 m = 3/5 * 100

= (3*100)/5

= 60 centimeters

e. \(\frac{5}{12}\) hour = ________ minutes

Answer:

25 minutes

Explanation:

5/12 hr = 5/12 * 60 minutes

= (5*60)/12

= 25 minutes

f. \(\frac{2}{3}\) yard = ________ inches

Answer:

24 inches

Explanation:

1 yard = 36 inches

2/3 yard = 2/3 * 36 inches

= (2*36)/3

= 24 inches

Question 2.

Michelle measured the length of her forearm. It was \(\frac{3}{4}\) of a foot. How long is her forearm in inches?

Answer:

The length of Michelle’s forearm is 9 inches

Explanation:

1 ft = 12 in

length of Michelle’s forearm was 3/4 of a foot

Now convert to inches

3/4 ft = 3/4 * 12

= 9 inc

Therefore the length of Michelle’s forearm is 9 inches.

Question 3.

At the market, Ms. Winn bought \(\frac{3}{4}\) lb of grapes and \(\frac{5}{8}\) lb of cherries.

a. How many ounces of grapes did Ms. Winn buy?

Answer:

12 ounces of grapes

Explanation:

3/4 lb = 3/4 * ounces

= 3/4 * 1 lb

= 3/4 * 16 ounces

= 12 ounces

b. How many ounces of cherries did Ms. Winn buy?

Answer:

10 ounces of cherries

Explanation:

5/8 lb = 5/8 * 1 lb

= 5/8 * 16 ounces

= 10 ounces

c. How many more ounces of grapes than cherries did Ms. Winn buy?

Answer:

There are 12 ounces of grapes and 10 ounces of cherries. Hence by doing the difference for both we can get more ounces of grapes than cherries.

So 12 -10 = 2 ounces. Hence 2 more ounces of grapes than cherries.

d. If Mr. Phillips bought 1\(\frac{3}{4}\) pounds of raspberries, who bought more fruit, Ms. Winn or Mr. Phillips? How many ounces more?

Answer:

Explanation:

1 3/4 pounds = 7/4 pounds

1 pound = 16 oz

7/4 pounds = 7/4 * 16

= 21

Ms.Winn bought 22 ounces of fruits and Mr. Phillips bought 21 ounces of fruit. Therefore, 1 ounce more fruits are there.

Question 4.

A gardener has 10 pounds of soil. He used \(\frac{5}{8}\) of the soil for his garden. How many pounds of soil did he use in the garden? How many pounds did he have left?

Answer:

3 3/4

Explanation:

5/8 *10

50/8

6 2/8

6 1/4

10 -6 1/4

Hence 3 3/4 pounds have left.