## Dividing Decimals

Read this text. Pay attention to the "How To" boxes which give brief step-by-step summaries of how to divide decimals. Complete the practice problems and check your answers.

### Answers

#### EXAMPLE 5.19

##### Solution
 $0.12 \div 3$ Write as long division, placing the decimal point in the quotient above the decimal point in the dividend. Divide as usual. Since 3 does not go into 0 or 1 we use zeros as placeholders. $0.12 \div 3 = 0.04$

#### TRY IT 5.37

$0.07$

#### TRY IT 5.38

$0.08$

#### EXAMPLE 5.20

##### Solution
 $\ 3.99 \div 24$ Place the decimal point in the quotient above the decimal point in the dividend. Divide as usual. When do we stop? Since this division involves money, we round it to the nearest cent (hundredth). To do this, we must carry the division to the thousandths place. Round to the nearest cent. $\ 0.166 \approx \ 0.17$ $\ 3.99 \div 24 \approx \ 0.17$

This means the price per bottle is $17$ cents.

#### TRY IT 5.39

$\ 0.19$

#### TRY IT 5.40

$\ 0.42$

#### EXAMPLE 5.21

##### 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. $-2.89 \div(3.4)=-0.85$

#### TRY IT 5.41

$-0.39$

#### TRY IT 5.42

$-0.4$

#### EXAMPLE 5.22

##### Solution
 $-25.65 \div(-0.06)$ 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. $-25.65 \div(-0.06)=427.5$

#### TRY IT 5.43

$587.3$

#### TRY IT 5.44

$34.25$

#### Example 5.23

##### Solution
 $4 \div 0.05$ 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. $4 \div 0.05=80$

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

#### TRY IT 5.45

$200$

#### TRY IT 5.46

$350$