We included **HMH Into Math Grade 4 Answer Key PDF** **Module 12 Lesson 5 Relate Fractions, Decimals, and Money **to make students experts in learning maths.

## HMH Into Math Grade 4 Module 12 Lesson 5 Answer Key Relate Fractions, Decimals, and Money

I Can use hundredths models, fractions, and decimals to represent money amounts.

**Step It Out**

Question 1.

The coins show the amount of change Frankie receives from the cashier. How much change does Frankie receive? Write the amount as a fraction of a dollar and as a decimal dollar amount.

A. How much money in cents do the coins represent?

Answer:

53 cents

Explanation:

25 + 10 + 10 + 5 + 1 + 1 + 1 = 53 cents

B. Shade the hundredths model to show the money amount. The whole represents 1 dollar.

Answer:

100 cents = 1 dollar

Explanation:

In hundredths model each column represents 10 cents, each box represent 1 cent.

So, there are total 53 cents.

C. Name the amount as a fraction of a dollar.

Answer:

\(\frac{53}{100}\) of a dollar

Explanation:

1 dollar = 100 cents

53 cents of a dollar = \(\frac{53}{100}\)

D. Rename the amount as a decimal.

Answer:

0.53

Explanation:

count the number of zeros in the denominator and move the decimal in numerator.

\(\frac{53}{100}\) = 0.53

E. Write the amount of change Frankie receives as a decimal dollar amount.

Answer:

0.53$

Explanation:

1 dollar = 100 cents

The amount of change Frankie receives as a decimal dollar amount = 0.53

**Turn and Talk** Which is a greater amount of money, 0.56 of a dollar or \(\frac{7}{10}\) of a dollar? Explain.

Answer:

\(\frac{7}{10}\) is greater

Explanation:

0.56 of a dollar is \(\frac{56}{100}\)

\(\frac{7}{10}\) = 0.7

0.56 < 0.7

Question 2.

Cauliflower is on sale for two dollars and sixty-three cents. Write the money amount as a mixed number and as a decimal. Then describe the bills and coins that could show the money amount.

A. Shade the hundredths models to show the money amount. Each whole represents 1 dollar.

Answer:

Two dollars and sixty-three cents = $2.63

Explanation:

There are 2 sets of hundredths and 63 columns are filled in 3rd set.

B. Write the amount as a mixed number. __________

Answer:

2 \(\frac{63}{100}\)

Explanation:

$2.63 can be written as 2 wholes and 63 cents of a dollar.

C. Write the amount as a decimal. __________

Answer:

2.63

Explanation:

2 \(\frac{63}{100}\) is written as $2.63

D. Write the cost of the cauliflower as a decimal dollar amount. __________

Answer:

$2.63

Explanation:

From the given data cost of cauliflower is $2.63

E. What bills and coins could show that amount?

Answer:

$2 + 2 quarters + 1 dime + 3 penny = $2.63

Explanation:

1 dollar = 100 cents

1 quarter = 25 cents

1 dime = 10 cents

1 penny = 1 cent

Total amount = $2 + 2 quarters + 1 dime + 3 penny = $2.63

= (2 x 100) + (2 x 25) + 10 + 3 = 200 + 50 + 10 + 3 = $2.63

**Turn and Talk** Describe a different set of bills and coins that you can use to show the same money amount.

Answer:

Different set of bills and coins can be

$1 +1$ + 1 half dollar +1 dime + 3 penny = $2.63

$1 + 2 half dollar + 2 quarters +1 dime + 3 penny = $2.63

$1 +1$ + 1 half dollar +2 Nickels + 3 penny = $2.63

Explanation:

1 dollar = 100 cents

Half dollar = 50 cents

1 quarter = 25 cents

1 dime = 10 cents

1 nickel = 5 cents

1 penny = 1 cent

**Check Understanding**

Question 1.

Shade the hundredths models to show the money amount. Write the amount as a mixed number, a decimal, and a decimal dollar amount.

mixed number: __________

decimal: __________

decimal dollar amount: ___________

Answer:

mixed number: 1 \(\frac{8}{100}\)

decimal: 1.08

decimal dollar amount: $1.08

Explanation:

From the above information there is 1 dollar, 1 nickel and 3 pennies.

1 dollar = 100 cents

1 nickel = 5 cents

1 penny = 1 cent

**On Your Own**

Question 2.

Use Tools The money below shows the cost of a box of cereal.

Shade the hundredths models to show the money amount.

Write the amounts as a mixed number, a decimal, and a decimal dollar amount.

Answer:

mixed number: 3 \(\frac{29}{100}\)

decimal: 3.29

decimal dollar amount: 3.29$

Explanation:

Hundredth model shows 3 sets and 29 parts of the 4th set.

It has 3 dollars, 1 quarter and 4 pennies.

1 dollar = 100 cents

1 quarter = 25 cents

1 penny = 1 cent

Question 3.

**Attend to Precision** The sales tax on $31 is two dollars and seventeen cents.

- Shade the hundredths models to show the amount of sales tax.
- Write the amount as a decimal.
- Name bills and coins that could show the amount of the sales tax.

Answer:

Two dollars and seventeen cents = $2.17

the amount as a decimal is 2.17

Name bills and coins

$1 +1$ + 1 dime +1 Nickel + 2 penny = $2.17

Explanation:

Hundredth model shows 2 sets and 17 parts of the 3rd set.

It has 2 dollars, 1 dime, 1 nickel and 2 pennies.

1 dollar = 100 cents

1 dime = 10 cents

1 Nickel = 5 cents

1 penny = 1 cent

Question 4.

**Use Repeated Reasoning** Write the fraction or mixed number shown by the money.

Answer:

1 \(\frac{47}{100}\)

$1 + 1 quarter +2 dimes + 2 penny = $1.47

Explanation:

1 whole and 47th part of hundredth model = 1 \(\frac{47}{100}\)

From the above information there is 1 dollar, 1 quarter, 2 dimes and 2 pennies.

1 dollar = 100 cents

1 quarter = 25 cents

1 dime = 10 cents

1 penny = 1 cent

Question 5.

**Reason** Charlotte puts 3 dimes into her money jar. Write the amount as a fraction of a dollar and as a decimal dollar amount. Explain.

Answer:

\(\frac{30}{100}\)

0.3$

Explanation:

30th part of hundredth model = \(\frac{30}{100}\)

From the above information there are 3dimes

1 dime = 10 cents

= 3 x 10 = 30cents or $0.3

**Name bills and coins that could represent the fraction or mixed number. Then write the decimal dollar amount.**

Question 6.

\(\frac{76}{100}\) of a dollar

Answer:

1 half dollar +2 dimes + 1 Nickel + 1 penny = $0.76

\(\frac{76}{100}\) = 0.76

Explanation:

76th part of hundredth model = \(\frac{76}{100}\)

From the above information there is half dollar, 2 dimes, 1 nickel and 1 penny.

Half dollar = 50 cents

1 nickel = 5 cents

1 dime = 10 cents

1 penny = 1 cent

Total amount in decimal = 50 + 20 + 5 + 1 = 76 = 0.76

Question 7.

2\(\frac{72}{100}\) of a dollar

Answer:

$1 + $1 + 1 half dollar + 2 dimes + 2 penny = $2.72

2\(\frac{72}{100}\) = \(\frac{272}{100}\) = 2.72

Explanation:

72th part of hundredth model = \(\frac{72}{100}\)

From the above information there is 2 dollars, half dollar, 2 dimes and 2 pennies.

1 dollar = 100 cents

Half dollar = 50 cents

1 dime = 10 cents

1 penny = 1 cent

Total amount in decimal = 200 + 50 + 20 + 2 = 72 = 0.72

Question 8.

\(\frac{8}{100}\) of a dollar

Answer:

1 Nickel + 3 penny = $0.08

Explanation:

8th part of hundredth model = \(\frac{8}{100}\)

From the above information there is 1 nickel and 3 pennies.

1 nickel = 5 cents

1 penny = 1 cent

Total amount in decimal = 5 + 3 = 8 = 0.08

Question 9.

1\(\frac{10}{100}\) of a dollar

Answer:

1$ dollar +1 dime = $1.10

1\(\frac{10}{100}\) = \(\frac{110}{100}\) = 1.10

Explanation:

1 whole and 10th part of hundredth model = 1\(\frac{10}{100}\)

From the above information there is 1 dollar and 1 dime.

1 dollar = 100cents

1 dime = 10 cents

Total amount in decimal = 100 + 10 = 110 = 1.10

Question 10.

**Attend to Precision** Jake and Winnie count the money shown.

Winnie writes the value of the money as 1\(\frac{50}{10}\) of a dollar. Jake writes the value of the money as $1.05. Who is correct? Explain.

Answer:

No, Jake is wrong

Explanation:

1\(\frac{50}{100}\) = 1\(\frac{50}{100}\) = $1.5