## 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
=

4 inches

Explanation:
1/3 foot = 1/3 * 1 foot
= 1/3 * 12 inches
= 12/3
= 4 inches

c. $$\frac{5}{6}$$ year = ________ months
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
80 centimeters

Explanation:
4/5 m = 4/5 *1m
= 4/5 * 100 cm
= 400/5
= 80 cm

e. $$\frac{2}{3}$$ hour = ________ minutes
40 minutes

Explanation:
2/3 hr = 2/3 * 1 hr
= 2/3 * 60
= 120/3 min
= 40 min

f. $$\frac{3}{4}$$ yard = ________ inches
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?
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?
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?
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?
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?
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?
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
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
2 inches

Explanation:
2/3 feet = 2/3 * 12 inches
= (2*12)/12
= 24/12
= 2 inches

b. $$\frac{2}{5}$$ m = _______ cm
40 cm

Explanation:
2/5 m = 2/5 * 100 cm
= (2*100)/5
= 40 cm

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

2 inches

Explanation:
1/6 * 12 =2 inches

c. $$\frac{3}{4}$$ year = ________ months
9 inches

Explanation:
3/4 year = 3/4 * 12 months
= (3*12)/4
= 9 inches

d. $$\frac{3}{5}$$ meter = ________ centimeters
60 centimeters

Explanation:
3/5 m = 3/5 * 100
= (3*100)/5
= 60 centimeters

e. $$\frac{5}{12}$$ hour = ________ minutes
25 minutes

Explanation:
5/12 hr = 5/12 * 60 minutes
= (5*60)/12
= 25 minutes

f. $$\frac{2}{3}$$ yard = ________ inches
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?
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?
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?
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?
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?
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?