In this post we will learn methods to divide decimals by whole number.

Two methods are discussed in this chapter;

(a) Converting Division into multiplication

(b) Direct Division Methods

Both the methods are easy to understand. Choose the one which suits your temperament.

## How to divide decimals by whole number – Method 01

Follow the below steps;

(**a) Convert decimals and whole numbers into fraction form**.

**Decimal **

Remove decimal point and insert denominator 1.

Now add zeros in denominator same as the number of decimal places.

**Whole Number**

Insert the denominator 1 to convert the whole number into fraction.

**(b) Convert division into multiplication by taking reciprocal of the** **divisor**

**(c) Multiply the numerator and denominator.**

**(d) If possible, simplify the fractions.**

Given below are some solved examples for your understanding.

**Example 01**

Divide 0.25 ÷ 16

**Solution**

To divide the numbers, follow the below steps;

**(a) Convert the numbers into fraction.**

**Decimal Number 0.25 into fraction**

0.25 ⟹ 2 decimal places

Remove the decimal point and insert one in the denominator.

Since 0.25 contains two decimal places, insert two zeros in the denominator.

**Whole number into fraction**

Simply add the denominator 1 on the whole number 16.

Hence, the division can be represented as;

**(b) Convert the division into multiplication by taking reciprocal of divisor.**

Here 16/1 is the divisor.

The reciprocal of 16/1 is 1/16.

The above division can be represented as;

**(c) Multiplying the numerator and denominator separately**.

⟹ Number 25 in denominator can divide 100 in denominator leaving quotient 4.

Solving the remaining numbers we get;

Hence, 1/64 is the solution of division.

**Example 02**

Divide the numbers 9.1 ÷ 7

**Solution**

Follow the below steps;

**(a) Convert the number into fraction**

**Converting Decimal 9.1 into fraction**.

9.1 ⟹ contain one decimal place

Remove the decimal point and insert one in denominator.

**Converting whole number 7 into fraction.**

Insert 1 in the denominator.

(**b) Convert the division into fraction by taking reciprocal of divisor**.

Here fraction 7/1 is the divisor.

The reciprocal of 7/1 is 1/7.

**(c) Multiply numerator and denominator separately.**

Number 7 in denominator can divide 91 in numerator leaving 13 as quotient.

The fraction 13/10 can be written as;

\mathtt{\frac{13}{10} =\ 1.3}

Hence, 1.3 is the solution of given fraction.

**Example 03**Divide the numbers, 121 ÷ 0.011

**Solution****(a) Convert the numbers into fraction.**

Whole number 121 into fraction.

Insert the denominator 1 in the number 121.

**Convert decimal 0.011 into fraction**

0.011⟹ 3 decimal places

Remove the decimal point and insert 1000 in the denominator

Now the division can be represented as;

**(b) Convert division into multiplication by taking reciprocal of divisor.**

Here the divisor is 11/100.

The reciprocal of 11/100 is 100/11.

⟹ Number 11 can fully divide the numerator 121 and leave 11 as quotient.

Hence, 1100 is the solution of given division.

**Example 04**

Divide the numbers, 256 ÷ 0.12

**Solution**

**(a) Convert the numbers into fraction**.

**Converting whole number 256 into fraction.**

Insert the number 1 in the denominator.

**Converting 0.12 into fraction**

0.12 ⟹ contains 2 decimal places.

Remove the decimal point and insert 100 in denominator.

**(b) Convert division into multiplication by taking reciprocal of divisor.**

Here 12/100 is the divisor.

Reciprocal of 12/100 is 100/12.

The multiplication is represented as;

**(c) Multiply the numerator and denominator separately.**

⟹ Number 4 can divide numerator 256 and denominator 12 leaving quotient 64 and 3 respectively.

Multiplying the remaining numbers we get;

⟹ 6400 / 3

Hence, 6400/3 is the solution of given division.

## Dividing Decimals by Whole number – Method 2

This is a direct division of decimal number by whole number.

To divide the number, follow the below steps;

(**a) Remove the decimal point of the decimal number.**

**(b) Divide the given numbers**

**(c) Add back the decimal point to the quotient.**

The decimal point should have same decimal places as the decimal number given in questions.**Note;**

This method will only applicable when the dividend is decimal number and divisor is whole number.

Given below are examples for your understanding.**Example 01**

Divide the numbers, 0.015 ÷ 3

**Solution****(a) Remove the decimal point of given decimal number**

Decimal number ⟹ 0.015

Without decimal point ⟹ 15

We will add back the decimal points at the end.

(**b) Divide 15 by 3**

The quotient of division is 5.**(c) Add back the decimal points.**

0.015 ⟹ has three decimal points.

So our final answer will also have three decimal point.**Hence, 0.005 is the solution of division.**

**Example 02**

Divide the numbers, 27.2 ÷ 4

**Solution**

To divide the number follow below steps;

**(a) Remove the decimal point of given decimal number**

Decimal number ⟹ 27.2

Without decimal point ⟹ 272

Since we have removed the decimal points now, we will add it back at the **end. ****(b) Divide 272 by 4**

We get number 68 after division.

**(c) Add** **back the decimal points **

The decimal 27.2 contains one decimal place.

So we add decimal point after one place in the quotient.

**Hence, 6.8 is the final solution**.