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.
