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## Texas Go Math Grade 4 Lesson 2.5 Answer Key Relate Fractions, Decimals, and Money

**Remember**

1 dollar = 100 cents

1 quarter = 25 cents

1 dime = 10 cents

1 penny = 1 cent

**Unlock the Problem**

Together, Julie and Sarah have $1.00 in quarters. They want to share the quarters equally. How many quarters should each girl get? How much money is this?

**Use the model to relate money, fractions, and decimals.**

So,

Each girl should get 2 quarters, or $ \(\frac{1}{2}\).

**Examples** Use the money to model decimals.

___________ cents

Answer:

The given model is:

Now,

We know that,

1 dollar = 100 cents

Hence, from the above,

We can conclude that

$1.00 = 100 cents

So,

$ 0.10, or 10 cents

So,

$ 0.01, or 1 cent

**Relate Money and Decimals Think of dollars as ones, dimes as tenths, and pennies as hundredths.**

Think: $1.56 = 1 dollar and 56 pennies

There are 100 pennies in 1 dollar

So,

$1.56 = 156 pennies.

Think: 1.56 = 1 one and 56 hundredths

There are 100 hundredths in 1 one.

So,

1.56 = 156 hundredths.

**Share and Show**

Question 1.

Write the amount of money as a decimal in terms of dollars.

5 pennies = \(\frac{5}{100}\) of a dollar = ___________ of a dollar.

Answer:

The given model is:

Now,

We know that,

1 dollar = 100 pennies

So,

1 penny = \(\frac{1}{100}\) dollar

So,

5 pennies = 5 × \(\frac{1}{100}\)

= 5 × 0.01

= 0.05 dollars

Hence, from the above,

We can conclude that

5 pennies is equal to 0.05 of a dollar

**Write the total money amount. Then write the amount as a fraction or a mixed number and as a decimal in terms of dollars.**

Question 2.

Answer:

The given model is:

Now,

From the above model,

We can observe that

There are 4 pennies, 3 dimes, and 3 Quarters

So,

The total amount of money in dollars = (4 × $0.01) + (3 × $0.1) + (3 × $0.25)

= $0.04 + $0.3 + $0.75

= $1.09

Now,

The representation of the total amount of money in the form of a mixed number is: 1\(\frac{9}{100}\)

Hence, from the above,

We can conclude that

The representation of the total amount of money in the form of a mixed number is: 1\(\frac{9}{100}\)

The representation of the total amount of money in the form of a decimal number is: $1.09

Question 3.

Answer:

The given model is:

Now,

From the above model,

We can observe that

There are 3 Quarters, 2 dimes, and 1 dollar

So,

The total amount of money in dollars = (3 × $0.75) + (2 × $0.1) + (1 × $1)

= $2.25 + $0.2 + $1

= $3.45

Now,

The representation of the total amount of money in the form of a mixed number is: 3\(\frac{45}{100}\)

Hence, from the above,

We can conclude that

The representation of the total amount of money in the form of a mixed number is: 3\(\frac{45}{100}\)

The representation of the total amount of money in the form of a decimal number is: $3.45

**Write as a money amount and as a decimal in terms of dollars.**

Question 4.

\(\frac{92}{100}\) ________ ________

Answer:

The given fraction is: \(\frac{92}{100}\)

Now,

The representation of the given fraction in the form of a decimal is: $0.92

Hence, from the above,

We can conclude that

The representation of \(\frac{92}{100}\) in the form of a decimal is: $0.92

Question 5.

\(\frac{7}{100}\) ________ ________

Answer:

The given fraction is: \(\frac{7}{100}\)

Now,

The representation of the given fraction in the form of a decimal is: $0.07

Hence, from the above,

We can conclude that

The representation of \(\frac{7}{100}\) in the form of a decimal is: $0.07

Question 6.

\(\frac{16}{100}\) ________ ________

Answer:

The given fraction is: \(\frac{16}{100}\)

Now,

The representation of the given fraction in the form of a decimal is: $0.16

Hence, from the above,

We can conclude that

The representation of \(\frac{16}{100}\) in the form of a decimal is: $0.16

Question 7.

\(\frac{53}{100}\) ________ ________

Answer:

The given fraction is: \(\frac{53}{100}\)

Now,

The representation of the given fraction in the form of a decimal is: $0.53

Hence, from the above,

We can conclude that

The representation of \(\frac{53}{100}\) in the form of a decimal is: $0.53

**Math Talk**

**Mathematical Processes**

Explain how $0.84 and \(\frac{84}{100}\) a dollar are related.

Answer:

The given decimal number is: $0.84

Now,

We know that,

The number of digits after the decimal point represents the number of zeroes in the denominator after 1 i.e., 10 (or) 100

So,

The representation of $0.84 in the form of a fraction is: \(\frac{84}{100}\)

Hence, from the above,

We can conclude that

The representation of $0.84 in the form of a fraction is: \(\frac{84}{100}\)

**Problem Solving**

**H.O.T. Algebra Complete to tell the value of each digit.**

Question 8.

$1.05 = ________ dollar + ________ pennies, 1.05 = ________ ones + ________ hundredths

Answer:

The given number is: $1.05

Now,

We know that,

We will consider dollars as “Ones”, dimes as “Tenths”, and pennies as “Hundredths”

So,

$1.05 = 1 dollar + 0 dimes + 5 pennies

= 1 one + 5 hundredths

Hence, from the above,

We can conclude that

$1.05 = 1 dollar + 5 pennies

1.05 = 1 ones + 5 hundredths

Question 9.

$5.18 = ________ dollars + ________dime + ________ pennies

5.18 = ________ ones + ________ tenth + ________ hundredths

Answer:

The given number is: $5.18

Now,

We know that,

We will consider dollars as “Ones”, dimes as “Tenths”, and pennies as “Hundredths”

So,

$5.18 = 5 dollars + 1 dime + 8 pennies

= 5 ones + 1 tenth + 8 hundredths

Hence, from the above,

We can conclude that

$5.18 = 5 dollars + 1dime + 8 pennies

5.18 = 5 ones + 1 tenth + 8 hundredths

Question 10.

Sam has 3 dollar bills, 2 quarters, 3 dimes, and 2 pennies in her pocket. When this amount of money is written in terms of dollars, what is the value of the digit in the tenth place? hundredths place?

Answer:

It is given that

Sam has 3 dollar bills, 2 quarters, 3 dimes, and 2 pennies in her pocket

So,

The total amount of money = (3 × $1) + (2 × $0.25) + (3 × $0.1) + (2 × $0.01)

= $3 + $0.50 + $0.3 + $0.02

= $3.82

Now,

The representation of 3.82 in the place-value chart is:

Hence, from the above,

We can conclude that

The value of the digit in the tenths place is: 0.8

The value of the digit in the hundredths place is: 0.02

**Use the table for 11-12.**

Question 11.

**Use Diagrams** The table shows the coins three students have. Write Nick’s total amount as a decimal and as a fraction in terms of dollars.

Answer:

It is given that

The table shows the coins three students have

Now,

The given table is:

Now,

From the above table,

We can observe that

Nock has 2 Quarters, 4 dimes, 0 Nickels, and 2 pennies

So,

The total amount of money Nick has = ( 2 × $0.25) + (4 × $0.1) + (2 × $0.01)

= $0.50 + $0.4 + $0.02

= $0.92

So,

The representation of 0.92 in the form of a fraction is: \(\frac{92}{100}\)

Hence, from the above,

We can conclude that

The representation of the total amount of money Nick has in the form of a fraction is: \(\frac{92}{100}\)

The representation of the total amount of money Nick has in the form of a decimal number is: $0.92

Question 12.

**H.O.T.** Kim spent \(\frac{40}{100}\) of a dollar on a snack. Write as a money amount the amount she has left.

Answer:

It is given that

Kim spent \(\frac{40}{100}\) of a dollar on a snack

Now,

The given table is:

Now,

From the above table,

We can observe that

Kim has 1 Quarter, 3 dimes, 2 Nickels, and 3 pennies

So,

The total amount of money Kim has = (1 × $0.25) + (3 × $0.1) + (2 × $0.05) + (3 × $0.01)

= $0.25 + $0.3 + $0.1 + $0.03

= $0.68

= \(\frac{68}{100}\)

So,

The amount of money Kim has left = \(\frac{68}{100}\) – \(\frac{40}{100}\)

= \(\frac{68 – 40}{100}\)

= \(\frac{28}{100}\)

Hence, from the above,

We can conclude that

The amount of money Kim has left is: \(\frac{28}{100}\) of a dollar

Question 13.

Jane has 2 dimes, 6 nickels, and 10 pennies in her pocket. What fraction of a dollar does Jane have in her pocket?

Answer:

It is given that

Jane has 2 dimes, 6 nickels, and 10 pennies in her pocket

Now,

According to the given information,

The fraction of a dollar Jane has in her pocket = (2 × $0.1) + (6 × $0.05) + (10 × $0.01)

= $0.2 + $0.3 + $0.1

= $0.6

= \(\frac{6}{10}\)

= \(\frac{60}{100}\) of a dollar

Hence, from the above,

We can conclude that

The fraction of a dollar Jane has in her pocket is: \(\frac{60}{100}\) of a dollar

Question 14.

**H.O.T. Multi-Step** Travis has \(\frac{50}{100}\) of a dollar. He has at least two different types of coins in his pocket. Draw two possible sets of coins that Travis could have.

Answer:

It is given that

Travis has \(\frac{50}{100}\) of a dollar. He has at least two different types of coins in his pocket.

Now,

The representation of \(\frac{50}{100}\) in the form of a decimal number is: $0.50

Now,

According to the given information,

$0.50 = (3 × $0.1) + (4 × $0.05)

= 3 dimes + 4 nickels

Now,

$0.50 = 2 × $0.25

= 2 Quarters

Hence, from the above,

We can conclude that

The two possible sets of coins that Travis could have is:

a. 3 dimes and 4 nickels

b. 2 Quarters

**Daily Assessment Task**

**Fill in the bubble completely to show your answer.**

Question 15.

The price written on a puzzle at a garage sale is \(\frac{85}{100}\). What is this amount written as a decimal in terms of dollars?

(A) 0.85

(B) 8.05

(C) 8.5

(D) 85.00

Answer:

It is given that

The price written on a puzzle at a garage sale is \(\frac{85}{100}\).

Now,

The representation of \(\frac{85}{100}\) in the form of a decimal is: 0.85

Hence, from the above,

We can conclude that

The representation of \(\frac{85}{100}\) in the form of a decimal is:

Question 16.

The coins below show how much money Debbie gave her brother.

What is the amount written as a decimal in terms of dollars?

(A) 0.70

(B) 0.27

(C) 0.72

(D) 7.2

Answer:

The given money is:

Now,

From the above,

We can observe that

The amount of money Debbie gave her brother is: 7 dimes, and 2 pennies

So,

The total amount of money Debbie gave her brother = (7 × $0.1) + (2 × $0.01)

= $0.7 + $0.02

= $0.72

Hence, from the above,

We can conclude that

The total amount of money Debbie gave her brother is:

Question 17.

David has $0.68 left after buying lunch at school. Which shows the money amount written as a fraction in terms of dollars?

(A) \(\frac{68}{10}\)

(B) \(\frac{8}{10}\)

(C) \(\frac{6}{100}\)

(D) \(\frac{68}{100}\)

Answer:

It is given that

David has $0.68 left after buying lunch at school

Now,

The representation of $0.68 in the form of a fraction = \(\frac{68}{100}\)

Hence, from the above,

We can conclude that

The representation of $0.68 in the form of a fraction is:

**Texas Test Prep**

Question 18.

Mia has two dollars and fifteen cents. What decimal names this money amount in terms of dollars?

(A) 2.50

(B) 2.15

(C) 21.50

(D) 0.15

Answer:

It is given that

Mia has two dollars and fifteen cents

Now,

We know that,

1 dollar = 100 cents

So,

The total amount of money Mia has = (2 × 100) + 15

= 200 + 15

= 215 cents

= \(\frac{215}{100}\) of a dollar

= $2.15

Hence, from the above,

We can conclude that

The total amount of money Mia has is:

### Texas Go Math Grade 4 Lesson 2.5 Homework and Practice Answer Key

**Complete to tell the value of each digit.**

Question 1.

$4.38 = ________ dollars + ________ dimes + ________ pennies

$4.38 = ________ ones + ________ tenths + ________ hundredths

Answer:

The given number is: $4.38

Now,

We know that,

We will consider dollars as “Ones”, dimes as “Tenths”, and pennies as “Hundredths”

So,

$4.38 = 4 dollars + 3 dimes + 8 pennies

= 4 ones + 3 tenths + 8 hundredths

Hence, from the above,

We can conclude that

$4.38 = 4 dollars + 3 dimes + 8 pennies

$4.38 = 4 ones + 3 tenths + 8 hundredths

Question 2.

$2.05 = ________ dollars + ________ dimes + ________ pennies

$2.05 = ________ ones + ________ tenths + ________ hundredths

Answer:

The given number is: $2.05

Now,

We know that,

We will consider dollars as “Ones”, dimes as “Tenths”, and pennies as “Hundredths”

So,

$2.05 = 2 dollars + 0 dimes + 5 pennies

= 2 ones + 0 tenths + 5 hundredths

Hence, from the above,

We can conclude that

$2.05 = 2 dollars + 0 dimes + 5 pennies

$2.05 = _2 ones + 0 tenths + _5 hundredths

**Write as a money amount and as a decimal in terms of dollars.**

Question 3.

\(\frac{74}{100}\) _________ _________

Answer:

The given fraction is: \(\frac{74}{100}\)

Now,

The representation of the given fraction in the form of a decimal is: $0.74

Hence, from the above,

We can conclude that

The representation of \(\frac{74}{100}\) in the form of a decimal is: $0.74

Question 4.

\(\frac{31}{100}\) _________ _________

Answer:

The given fraction is: \(\frac{31}{100}\)

Now,

The representation of the given fraction in the form of a decimal is: $0.31

Hence, from the above,

We can conclude that

The representation of \(\frac{31}{100}\) in the form of a decimal is: $0.31

Question 5.

\(\frac{69}{100}\) _________ _________

Answer:

The given fraction is: \(\frac{69}{100}\)

Now,

The representation of the given fraction in the form of a decimal is: $0.69

Hence, from the above,

We can conclude that

The representation of \(\frac{69}{100}\) in the form of a decimal is: $0.69

Question 6.

\(\frac{58}{100}\) _________ _________

Answer:

The given fraction is: \(\frac{58}{100}\)

Now,

The representation of the given fraction in the form of a decimal is: $0.58

Hence, from the above,

We can conclude that

The representation of \(\frac{58}{100}\) in the form of a decimal is: $0.58

Question 7.

\(\frac{83}{100}\) _________ _________

Answer:

The given fraction is: \(\frac{83}{100}\)

Now,

The representation of the given fraction in the form of a decimal is: $0.83

Hence, from the above,

We can conclude that

The representation of \(\frac{83}{100}\) in the form of a decimal is: $0.83

Question 8.

\(\frac{95}{100}\) _________ _________

Answer:

The given fraction is: \(\frac{95}{100}\)

Now,

The representation of the given fraction in the form of a decimal is: $0.95

Hence, from the above,

We can conclude that

The representation of \(\frac{95}{100}\) in the form of a decimal is: $0.95

Question 9.

\(\frac{12}{100}\) _________ _________

Answer:

The given fraction is: \(\frac{12}{100}\)

Now,

The representation of the given fraction in the form of a decimal is: $0.12

Hence, from the above,

We can conclude that

The representation of \(\frac{12}{100}\) in the form of a decimal is: $0.12

Question 10.

\(\frac{26}{100}\) _________ _________

Answer:

The given fraction is: \(\frac{26}{100}\)

Now,

The representation of the given fraction in the form of a decimal is: $0.26

Hence, from the above,

We can conclude that

The representation of \(\frac{26}{100}\) in the form of a decimal is: $0.26

**Problem Solving**

**Use the table for 11-13**

Question 11.

The table tells the coins three people have. Write Mike’s total amount as a decimal and as a fraction in terms of a dollar.

Answer:

It is given that

The table tells the coins three people have

Now,

The given table is:

Now,

From the above table,

We can observe that

Mike has 1 Quarter, 1 Dime, 2 Nickels, and 2 pennies

So,

The total amount of money Mike has = (1 × $0.25) + (1 × $0.1) + (2 × $0.05) + (2 × $0.01)

= $0.25 + $0.1 + $0.1 + $0.02

= $0.47

Now,

The representation of 0.47 in the form of a fraction is: \(\frac{47}{100}\)

Hence, from the above,

We can conclude that

The representation of the total amount of money Mike has in the form of a fraction is: \(\frac{47}{100}\) of a dollar

The representation of the total amount of money Mike has in the form of a decimal is: $0.47

Question 12.

Write Jeannie’s total amount. Then write the amount as a fraction of a dollar and as a decimal in terms of dollars.

Answer:

The given table is:

Now,

From the above table,

We can observe that

Jeannie has 2 Quarters, 2 Dimes, 0 Nickels, and 1 penny

So,

The total amount of money Mike has = (2 × $0.25) + (2 × $0.1) + (0 × $0.05) + (1 × $0.01)

= $0.5 + $0.2 + $0 + $0.01

= $0.71

Now,

The representation of 0.71 in the form of a fraction is: \(\frac{71}{100}\)

Hence, from the above,

We can conclude that

The representation of the total amount of money Jeannie has in the form of a fraction is: \(\frac{71}{100}\) of a dollar

The representation of the total amount of money Jeannie has in the form of a decimal is: $0.71

Question 13.

If Alex spends \(\frac{63}{100}\) of a dollar, how much money will he have left?

Answer:

It is given that

Alex spends \(\frac{63}{100}\) of a dollar

Now,

The given table is:

Now,

From the above table,

We can observe that

Alex has 3 Quarters, 1 Dime, 1 Nickel, and 3 Pennies

So,

The total amount of money Alex has = (3 × $0.25) + (1 × $0.1) + (1 × $0.05) + (3 × $0.01)

= $0.75 + $0.1 + $0.05 + $0.03

= $0.93

Now,

The representation of 0.93 in the form of a fraction is: \(\frac{93}{100}\)

So,

The amount of money Alex has left = \(\frac{93}{100}\) – \(\frac{63}{100}\)

= \(\frac{93 – 63}{100}\)

= \(\frac{30}{100}\) of a dollar

= $0.30

Hence, from the above,

We can conclude that

The amount of money Alex has left is: \(\frac{30}{100}\) of a dollar

**Lesson Check**

**Fill in the bubble completely to show your answer.**

Question 14.

Which shows $0.87 written as a fraction in terms of dollars?

(A) 8\(\frac{7}{10}\)

(B) 8\(\frac{7}{100}\)

(C) \(\frac{87}{10}\)

(D) \(\frac{87}{100}\)

Answer:

The given number is: $0.87

Now,

The representation of the given decimal in the form of a fraction is: \(\frac{87}{100}\)

Hence, from the above,

We can conclude that

The representation of $0.87 in the form of a fraction is:

Question 15.

Write the total value of these coins as a decimal in terms of dollars.

(A) 0.56

(B) 0.056

(C) 5.06

(D) 56

Answer:

The given coins are:

Now,

From the above coins,

We can observe that

The total value of the given coins = (1 × $0.25) + (1 × $0.01) + (2 × $0.05) + (2 × $0.1)

= $0.25 + $0.01 + $0.1 + $0.2

= $0.56

Hence, from the above,

We can conclude that

The total value of the given coins is:

Question 16.

Roxanna has \(\frac{42}{100}\) of a dollar in change. Which shows the amount of change she has?

(A) $4.20

(B) $42

(C) $0.42

(D) $1.00

Answer:

It is given that

Roxanna has \(\frac{42}{100}\) of a dollar in change

Now,

The representation of \(\frac{42}{100}\) as a decimal is: 0.42

Hence, from the above,

We can conclude that

The amount of change Roxanna has is:

Question 17.

Jimmy has \(\frac{30}{100}\) of a dollar. Which shows this amount in decimal form?

(A) 0.33

(B) 1.03

(C) 1.3

(D) 0.3

Answer:

It is given that

Jimmy has \(\frac{30}{100}\) of a dollar

Now,

The representation of \(\frac{30}{100}\) as a decimal is: 0.30

Hence, from the above,

We can conclude that

The representation of \(\frac{30}{100}\) as a decimal is:

Question 18.

**Multi-Step** Jesse has 3 quarters and 4 dimes. If he spends \(\frac{1}{2}\) of a dollar, how much money will he have left?

(A) $0.65

(B) $0.50

(C) $0.55

(D) $0.60

Answer:

It is given that

Jesse has 3 quarters and 4 dimes and he spends \(\frac{1}{2}\) of a dollar

Now,

The representation of \(\frac{1}{2}\) of a dollar in the decimal form is: $0.5

The total amount of money Jesse has = (3 × $0.25) + (4 × $0.1)

= $0.75 + $0.4

= $1.15

Now,

The amount of money Jesse has left = $1.15 – $0.5

= $0.65

Hence, from the above,

We can conclude that

The amount of money Jesse has left is:

Question 19.

**Multi-Step** Jenny has 4 dollar hills, 2 quarters, 1 dime, and 3 pennies. When this amount of money is written as a decimal in terms of dollars, which digit is in tenths place?

(A) 3

(B) 6

(C) 4

(D) 5

Answer:

It is given that

Jenny has 4 dollar hills, 2 quarters, 1 dime, and 3 pennies

Now,

The total amount of money Jenny has = (4 × $1) + (2 × $0.25) + (1 × $0.1) + (3 × $0.01)

= $4 + $0.5 + $0.1 + $0.03

= $4.63

Now,

The representation of 4.63 in the place-value chart is:

Hence, from the above,

We can conclude that

The digit that is present in tenths place in the total amount of Jenny has is: