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Divide: −2.89 ÷ ( 3.4 ) .

Solution

Determine the sign of the quotient. The quotient will be negative.
Make the divisor the whole number by 'moving' the decimal point all the way to the right. 'Move' the decimal point in the dividend the same number of places to the right. .
Divide. Place the decimal point in the quotient above the decimal point in the dividend. Add zeros as needed until the remainder is zero. .
Write the quotient with the appropriate sign. −2.89 ÷ ( 3.4 ) = −0.85
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Divide: −1.989 ÷ 5.1 .

−0.39

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Divide: −2.04 ÷ 5.1 .

−0.4

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Divide: −25.65 ÷ ( −0.06 ).

Solution

−25.65 ÷ ( −0.06 )
The signs are the same. The quotient is positive.
Make the divisor a whole number by 'moving' the decimal point all the way to the right.
'Move' the decimal point in the dividend the same number of places.
.
Divide.
Place the decimal point in the quotient above the decimal point in the dividend.
.
Write the quotient with the appropriate sign. −25.65 ÷ ( −0.06 ) = 427.5
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Divide: −23.492 ÷ ( −0.04 ) .

587.3

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Divide: −4.11 ÷ ( −0.12 ) .

34.25

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Now we will divide a whole number by a decimal number.

Divide: 4 ÷ 0.05 .

Solution

4 ÷ 0.05
The signs are the same. The quotient is positive.
Make the divisor a whole number by 'moving' the decimal point all the way to the right.
Move the decimal point in the dividend the same number of places, adding zeros as needed.
.
Divide.
Place the decimal point in the quotient above the decimal point in the dividend.
.
Write the quotient with the appropriate sign. 4 ÷ 0.05 = 80

We can relate this example to money. How many nickels are there in four dollars? Because 4 ÷ 0.05 = 80 , there are 80 nickels in $4 .

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Use decimals in money applications

We often apply decimals in real life, and most of the applications involving money. The Strategy for Applications we used in The Language of Algebra gives us a plan to follow to help find the answer. Take a moment to review that strategy now.

Strategy for applications

  1. Identify what you are asked to find.
  2. Write a phrase that gives the information to find it.
  3. Translate the phrase to an expression.
  4. Simplify the expression.
  5. Answer the question with a complete sentence.

Paul received $50 for his birthday. He spent $31.64 on a video game. How much of Paul’s birthday money was left?

Solution

What are you asked to find? How much did Paul have left?
Write a phrase. $50 less $31.64
Translate. 50 31.64
Simplify. 18.36
Write a sentence. Paul has $18.36 left.
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Nicole earned $35 for babysitting her cousins, then went to the bookstore and spent $18.48 on books and coffee. How much of her babysitting money was left?

$16.52

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Amber bought a pair of shoes for $24.75 and a purse for $36.90 . The sales tax was $4.32 . How much did Amber spend?

$65.97

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Jessie put 8 gallons of gas in her car. One gallon of gas costs $3.529 . How much does Jessie owe for the gas? (Round the answer to the nearest cent.)

Solution

What are you asked to find? How much did Jessie owe for all the gas?
Write a phrase. 8 times the cost of one gallon of gas
Translate. 8 ( $3.529 )
Simplify. $28.232
Round to the nearest cent. $28.23
Write a sentence. Jessie owes $28.23 for her gas purchase.
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Hector put 13 gallons of gas into his car. One gallon of gas costs $3.175 . How much did Hector owe for the gas. Round to the nearest cent.

$41.28

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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