When we divide two whole numbers using long division, we often get a remainder. In this lesson, we will learn how to use long division to express the quotient and remainder as a decimal.

To illustrate, let's compute 4 \div 5. We start by writing down 4\div 5 using long division notation:

\,\,0
5 \!\require{enclose}\enclose{longdiv}{\color{red}4}

Notice that \color{red}4 is less than the divisor 5. But we can proceed further by adding a \color{blue}0 after the decimal point in the dividend. We also add a decimal point in the quotient, as shown below:

\,0 {\bbox[2pt, lightgray]{\color{blue}.}}
5 \!\!\require{enclose}\enclose{longdiv}{{\color{red}4} {\bbox[2pt, lightgray]{\color{blue}.}} {\color{blue}0}}

Now we complete the division, as usual, stopping once we obtain a remainder of 0\mathbin{:}

\,0 {\,.\,} 8
5 \!\!\require{enclose}\enclose{longdiv}{4 {\, . \,} 0 }
-\!\!\!\!\! 4 0
\fbox{0}

Therefore, 4 \div 5 = 0.8\,.

FLAG

Calculate the value of 46 \div 5.

EXPLANATION

We start by going through the long division procedure as usual:

\,\,\phantom{0} {\:\phantom{|}} 9
5 \!\require{enclose}\enclose{longdiv}{4 {\:\phantom{|}} 6}
-\!\!\!\! 4 5
\color{red}1

Notice that the remainder \color{red}1 is less than the divisor 5. But we can proceed further by adding a \color{blue}0 after the decimal point in the dividend. We also add a decimal point in the quotient, as shown below:

\,\,\phantom{0} {\:\phantom{|}} 9 {\bbox[2px, lightgray]{\color{blue}.}}
5 \!\require{enclose}\enclose{longdiv}{4 {\:\phantom{|}} 6 {\bbox[2px, lightgray]{\color{blue}.}} {\color{blue}0}}
-\!\!\!\! 4 5 \color{lightgray}\downarrow
\color{red}1 \color{lightgray}0

Now we complete the division, as usual, stopping once we obtain a remainder of 0\mathbin{:}

\,\,\phantom{0} {\:\phantom{|}} 9 {\, . \,} 2
5 \!\require{enclose}\enclose{longdiv}{4 {\:\phantom{|}} 6 {\, . \,} 0}
-\!\!\!\! 4 5
1 0
-\!\!\!\!\! 1 0
\fbox{0}

Therefore, 46 \div 5 = 9.2\,.

FLAG

Calculate the value of $62 \div 5.$

a
$12$
b
$12.4$
c
$12.2$
d
$12.6$
e
$126$

Calculate the value of $33 \div 6 .$

a
$6.3$
b
$5.5$
c
$5.7$
d
$5.8$
e
$6.5$

Find 51 \div 4.

EXPLANATION

We start by going through the long division procedure as usual:

\,\,1 {\:\phantom{|}} 2
4 \!\require{enclose}\enclose{longdiv}{5 {\:\phantom{|}} 1}
-\!\!\!\! 4
1 1
-\!\!\!\! 8
\color{red}3

Notice that the remainder \color{red}3 is less than the divisor 4 , but we can proceed further by adding a \color{blue}0 after the decimal point in the dividend. We also add a decimal point in the quotient, as shown below:

\,\,1 {\:\phantom{|}} 2 {\bbox[2px, lightgray]{\color{blue}.}}
4 \!\require{enclose}\enclose{longdiv}{5 {\:\phantom{|}} 1 {\bbox[2px, lightgray]{\color{blue}.}} {\color{blue}0}}
-\!\!\!\! 4 \color{lightgray}\downarrow
1 1 \color{lightgray}\downarrow
-\!\!\!\! 8 \color{lightgray}\downarrow
\color{red}3 \color{lightgray}0

Now we complete the division, as usual, adding more zeros as needed but stopping once we obtain a remainder of 0\mathbin{:}

\,\,1 {\:\phantom{|}} 2 {\, . \,} 7 {\:\phantom{|}} 5
4 \!\require{enclose}\enclose{longdiv}{5 {\:\phantom{|}} 1 {\, . \,} 0 {\:\phantom{|}} 0}
-\!\!\!\! 4
1 1
-\!\!\!\!\!\!\! 8
3 0
-\!\!\!\! 2 8
2 0
-\!\!\!\! 2 0
\fbox{0}

Therefore, 51 \div 4 = 12.75\,.

FLAG

Find $78 \div 8.$

a
$9.75$
b
$8.95$
c
$8.75$
d
$9.25$
e
$9.05$

Find $41 \div 4.$

a
$10.75$
b
$11.25$
c
$10.35$
d
$10.55$
e
$10.25$

What is 79 \div 8?

EXPLANATION

We start by going through the long division procedure as usual:

\,\phantom{0}{\:\phantom{|}} 9
8 \!\!\require{enclose}\enclose{longdiv}{7 {\:\phantom{|}} 9}
-\!\!\!\!\! 7 2
{\color{red}7}

Notice that the remainder \color{red}7 is less than the divisor 8 , but we can proceed further by adding a \color{blue}0 after the decimal point in the dividend. We also add a decimal point in the quotient, as shown below:

\,\,\phantom{0} {\:\phantom{|}} 9 {\bbox[2px, lightgray]{\color{blue}.}}
8 \!\require{enclose}\enclose{longdiv}{7 {\:\phantom{|}} 9 {\bbox[2px, lightgray]{\color{blue}.}} {\color{blue}0}}
-\!\!\!\!\! 7 2 \color{lightgray}\downarrow
\color{red}7 \color{lightgray}0

Now we complete the division, as usual, adding more zeros as needed but stopping once we obtain a remainder of 0\mathbin{:}

\,\,{\phantom{0}} {\:\phantom{|}} 9 {\, . \,} 8 {\:\phantom{|}} 7 {\:\phantom{|}} 5
8 \!\require{enclose}\enclose{longdiv}{7 {\:\phantom{|}} 9 {\, . \,} 0 {\:\phantom{|}} 0 {\:\phantom{|}} 0}
-\!\!\!\!\! 7 2
7 0
-\!\!\!\! 6 4
6 0
-\!\!\! 5 6
4 0
-\!\!\! 4 0
\fbox{0}

Therefore, 79 \div 8 = 9.875\,.

FLAG

What is $97 \div 8?$

a
$11.125$
b
$11.625$
c
$12.625$
d
$12.175$
e
$12.125$

What is $25 \div 8?$

a
$3.125$
b
$3.215$
c
$3.135$
d
$3.175$
e
$2.175$

Cameron spent \[math]607 in five days. If she spent an equal amount each day, how much did Cameron spend per day?

EXPLANATION

To determine the amount Cameron spent each day, we need to divide 607 by 5.

We start by going through the long division procedure as usual:

\,\,1 {\:\phantom{|}} 2 {\:\phantom{|}} 1
5 \!\require{enclose}\enclose{longdiv}{6 {\:\phantom{|}} 0 {\:\phantom{|}} 7 }
-\!\!\!\! 5
1 0
-\!\!\!\! 1 0
0 7
-\!\!\!\! 5
\color{red}2

Notice that the remainder \color{red}2 is less than the divisor 5. But we can proceed further by adding a \color{blue}0 after the decimal point in the dividend. We also add a decimal point in the quotient, as shown below:

\,\,1 {\:\phantom{|}} 2 {\:\phantom{|}} 1 {\bbox[2px, lightgray]{\color{blue}.}}
5 \!\require{enclose}\enclose{longdiv}{6 {\:\phantom{|}} 0 {\:\phantom{|}} 7{\bbox[2px, lightgray]{\color{blue}.}}\color{blue}0}
-\!\!\!\! 5 \color{lightgray}\downarrow
1 0 \color{lightgray}\downarrow
-\!\!\!\! 1 0 \color{lightgray}\downarrow
0 7 \color{lightgray}\downarrow
-\!\!\!\! 5 \color{lightgray}\downarrow
\color{red}2 \color{lightgray}0

Now we complete the division, as usual, stopping once we obtain a remainder of 0\mathbin{:}

\,\,1 {\:\phantom{|}} 2 {\:\phantom{|}} 1 {\,.\,} 4
5 \!\require{enclose}\enclose{longdiv}{6 {\:\phantom{|}} 0 {\:\phantom{|}} 7 {\,.\,} 0}
-\!\!\!\! 5
1 0
-\!\!\!\! 1 0
0 7
-\!\!\!\! 5
2 0
-\!\!\!\! 2 0
\fbox{0}

Therefore, 607 \div 5 = 121.4 \, .

We conclude that Cameron spent \[math]121.40 each day.

FLAG

A bottle contains $9$ ounces of vanilla extract. Maggy wants to divide the contents of the bottle into $4$ equal parts to make ice cream. How many ounces of vanilla extract will there be in each part?

a
$2.25$ ounces
b
$1.75$ ounces
c
$2.15$ ounces
d
$2.75$ ounces
e
$2.05$ ounces

Martha needs to cut a piece of ribbon that is $9$ inches long into $6$ smaller pieces of equal length. How long should each piece be?

a
$1.5$ inches
b
$1.6$ inches
c
$1.25$ inches
d
$1.4$ inches
e
$1.3$ inches
Flag Content
Did you notice an error, or do you simply believe that something could be improved? Please explain below.
SUBMIT
CANCEL