# Dividing decimals by whole numbers

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

(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

(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.