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# Division of Decimals by Whole Numbers

## Decimal in quotient directly above decimal in dividend

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Division of Decimals by Whole Numbers
License: CC BY-NC 3.0

Jack has 15.62 yards of fabric leftover from a project. He wants to make blankets and donate them to the animal shelter. He thinks he can make 11 blankets. How long will each blanket be?

In this concept, you will learn how to divide decimals by whole numbers.

### Dividing Decimals by Whole Numbers

To divide means to split up into equal parts. Dividing a decimal number means splitting up the decimal value into sections.

Here is a division problem.

4.64÷2=\begin{align*}4.64 \div 2 = \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

In this problem, 4.64 is the dividend. The dividend is the number being divided. The divisor is the number of parts the dividend is being divided into. The divisor is 2. Remember that the divisor goes outside of the division box in long division.

24.64\begin{align*}\require{enclose} 2\enclose{longdiv}{4.64}\\\end{align*}

Dividing a decimal is similar to whole number division. First, divide the 2 into each number. Ignore the decimal for now.

23224.64 206   6  04 40\begin{align*}\require{enclose} \begin{array}{rcl} && \ \ \ \ \, 2 \, 3 2\\ && 2 \enclose{longdiv}{4.64}\\ && \ \underline{-2}\\ && \quad 06\\ && \ \ \ \underline{-6}\\ && \quad \ \ 04 \\ && \quad \ \underline{-4}\\ && \qquad 0 \end{array}\end{align*}

Then, insert the decimal point into the quotient. Bring the decimal point from its place in the division box directly up into the quotient.    2.3224.64\begin{align*}\require{enclose} \begin{array}{rcl} && \ \ \ \ \, 2 \color{red}{.} \color{black}{32}\\ && 2 \enclose{longdiv}{4.64}\\ \end{array}\end{align*}

The quotient of 4.64 divided by 2 is 2.32.

### Examples

#### Example 1

Earlier, you were given a problem about Jack and blankets.

Jack wants to make 11 blankets from 15.62 yards of fabric. Divide 15.62 by 11 to find the length of each blanket.

First, ignore the decimal and divide as if this were two whole numbers.

1421115.62   11    46 44 22   22   0\begin{align*}\require{enclose} \begin{array}{rcl} && \qquad \! 1 \, 42 \\ && 11 \enclose{longdiv}{15.62}\\ && \ \ \ \underline{-11}\\ && \quad \ \ \ \ 46\\ && \quad \ \underline{-44}\\ && \quad \quad \ 22\\ && \quad \ \ \ \underline{-22}\\ && \quad \quad \ \ \ 0 \end{array}\end{align*}

Then, add decimal point into the quotient. Bring the decimal point from its place in the division box up into the quotient.

1.421115.62\begin{align*}\require{enclose} \begin{array}{rcl} && \qquad \! 1{\color{red}.}42 \\ && 11 \enclose{longdiv}{15.62} \\ \end{array}\end{align*}

Each blanket will be 1.42 yards long.

#### Example 2

Find the quotient.

66.3÷3\begin{align*}66.3 \div 3\end{align*}

First, ignore the decimal and divide as if this were two whole numbers.

221366.3 606   6  03 30\begin{align*}\require{enclose} \begin{array}{rcl} &&\quad 22 \, 1 \\ && 3 \enclose{longdiv}{66.3}\\ && \ \underline{-6}\\ && \quad 06\\ && \ \ \ \underline{-6}\\ && \quad \ \ 03 \\ && \quad \ \underline{-3}\\ && \qquad 0 \end{array}\end{align*}

Then, add decimal point into the quotient. Bring the decimal point from its place in the division box up into the quotient.

22.1366.3\begin{align*}\require{enclose} \begin{array}{rcl} && \ \ \ \ 22 \color{red}. \! \color{black}{1} \\ && 3 \enclose{longdiv}{66.3} \end{array}\end{align*}

Find the quotient for the following problems.

#### Example 3

36.48÷12\begin{align*}36.48 \div 12\end{align*}

First, ignore the decimal and divide as if this were two whole numbers.

3041236.48  3604   0  48   480\begin{align*}\require{enclose} \begin{array}{rcl} && \qquad \! 3 \, 04 \\ && 12 \enclose{longdiv}{36.48}\\ && \ \ \underline{-36}\\ && \qquad 04\\ && \quad \ \ \ \underline{-0}\\ &&\qquad \ \ 48 \\ && \quad \ \ \ \underline{-48}\\ && \quad \qquad 0 \end{array}\end{align*}

Then, add decimal point into the quotient. Bring the decimal point from its place in the division box up into the quotient.

3.041236.48\begin{align*}\require{enclose} \begin{array}{rcl} && \qquad \! 3.04 \\ && 12 \enclose{longdiv}{36.48} \end{array}\end{align*}

The quotient of 36.48 divided by 12 is 3.04.

#### Example 4

2.46÷3\begin{align*}2.46 \div 3\end{align*}

First, ignore the decimal and divide as if this were two whole numbers.

8232.46  24   06  6 0\begin{align*}\require{enclose} \begin{array}{rcl} && \quad \ \ \ 82 \\ && 3 \enclose{longdiv}{2.46}\\ && \ \ \underline{-24}\\ && \quad \ \ \ 06\\ && \quad \ \ \underline{-6}\\ && \quad \quad \ 0 \end{array}\end{align*}

Then, add decimal point into the quotient. Bring the decimal point from its place in the division box up into the quotient.

0.8232.46\begin{align*}\require{enclose} \begin{array}{rcl} && \quad 0.82 \\ && 3 \enclose{longdiv}{2.46} \end{array}\end{align*}

The quotient of 2.46 divided by 3 is 0.82.

#### Example 5

11.5÷5\begin{align*}11.5 \div 5\end{align*}

First, ignore the decimal and divide as if this were two whole numbers.

23511.5 10 15150\begin{align*}\require{enclose} \begin{array}{rcl} && \quad \ \ 2 \, 3 \\ && 5 \enclose{longdiv}{11.5}\\ && \ \underline{-10}\\ && \quad \ 1 \, 5\\ && \quad \! \underline{-15}\\ && \quad \quad \! 0 \end{array}\end{align*}

Then, add decimal point into the quotient. Bring the decimal point from its place in the division box up into the quotient.

2.3511.5\begin{align*}\require{enclose} \begin{array}{rcl} && \quad \ \ 2.3 \\ && 5 \enclose{longdiv}{11.5} \end{array}\end{align*}

The quotient of 11.5 divided by 5 is 2.3.

### Review

Find the quotient for the following problems.

1. 36.48÷2\begin{align*}36.48 \div 2\end{align*}
2. 5.4÷3\begin{align*}5.4 \div 3\end{align*}
3. 14.16÷6\begin{align*}14.16 \div 6\end{align*}
4. 18.63÷3\begin{align*}18.63 \div 3\end{align*}
5. 11.6÷4\begin{align*}11.6 \div 4\end{align*}
6. 11.26÷2\begin{align*}11.26 \div 2\end{align*}
7. 27.6÷4\begin{align*}27.6 \div 4\end{align*}
8. 18.5÷5\begin{align*}18.5 \div 5\end{align*}
9. 49.2÷4\begin{align*}49.2 \div 4\end{align*}
10. 27.09÷7\begin{align*}27.09 \div 7\end{align*}
11. 114.4÷8\begin{align*}114.4 \div 8\end{align*}
12. 325.8÷9\begin{align*}325.8 \div 9\end{align*}
13. 107.6÷4\begin{align*}107.6 \div 4\end{align*}
14. 115.7÷5\begin{align*}115.7 \div 5\end{align*}
15. 192.6÷6\begin{align*}192.6 \div 6\end{align*}

To see the Review answers, open this PDF file and look for section 4.10.

### Vocabulary Language: English

Divide

To divide is split evenly into groups. The result of a division operation is a quotient.

Dividend

In a division problem, the dividend is the number or expression that is being divided.

divisor

In a division problem, the divisor is the number or expression that is being divided into the dividend. For example: In the expression $152 \div 6$, 6 is the divisor and 152 is the dividend.

Quotient

The quotient is the result after two amounts have been divided.