# How to divide decimals

In this post we will two different methods to divide decimal numbers.
(a) Long Division Method
(b) Division using Fraction Method

## Long Division with decimals

This method can be used when decimal is divided by whole number.

This division involves following steps:
(A) First divide the number before decimal point
(B) Insert the decimal in the quotient and involve digits after decimal.

Let us understand the concept with the help of examples:

Example 01
2.5 divided by 5

Solution
You can observe that:
2.5 (dividend) is a decimal number
5 (divisor) is whole number

Since divisor is whole number, we can use long division method

Long Division Steps
(a) Check division for number before decimal i.e 2
Dividing 2 by 5 results in:
⟹ Quotient = 0
⟹ Remainder = 2

(b) Put decimal in the quotient

(c) Use the next number of dividend (i.e. number 5)

(d) Now divide number 25 by 5

Hence 0.5 is the solution

This method is similar to the whole number division.
Only thing you have to careful is the placing of decimal point in the quotient.

Example 02
Divide 409.4 by 23

Observe that:
Dividend is decimal number (i.e. 409.4)
Divisor is whole number (i.e. 23)

Since Divisor is whole number, we can use long division method

Hence 17.8 is the solution of the division.

Let us understand the division step by step
(a) First divide the number before decimal point (i.e 409)

On dividing 409 by 23 we get:
⟹ 17 as quotient
⟹ 18 as remainder

Its now time to involve number after decimal point.

(b) Do the following Steps
⟹ Put decimal in the quotient
⟹ Involve number after decimal point (i.e. number 4) is the division

Hence, 17.8 is the final solution

Example 03
Divide 1.95 by 13

Notice that:
Divided (1.95) is a decimal number
Divisor (13) is a whole number

Since divisor is a whole number. Its possible to use Long Division Method.

Hence 0.15 is the solution of the division.

Let us understand the division process step by step
(a) First divide the number before decimal point

You can see that we got:
⟹ 0 as a quotient
⟹ 1 as remainder

Now involve the number after decimal point and do the rest of division

(b) Do the following steps
⟹ First put decimal point in the quotient
⟹ Divide rest of the number

From the above division, we found that 0.15 is the solution

## Division using Fraction Method

Step 01: Write the division in form of fraction
Step 02: Convert decimal into whole number by multiplying with 10, 100, 1000 etc..
Step 03: Divide the whole numbers to get final answer

Let us understand the process with examples

Example 01
18 divided by 0.2

Step 01: Writing in form of fraction
\Longrightarrow \ \frac{18}{0.2}\

Step 02: Convert decimal into whole number
18 ⟹ is already a decimal
0.2 ⟹ decimal with one decimal place value

To convert 0.2 into whole number, we multiply the fraction with 10
(Multiplication of new number is always done both on numerator & denominator)

\Longrightarrow \ \frac{18\times 10}{0.2\times 10}\\\ \\ \Longrightarrow \ \frac{180}{2}\\\ \\

Step 03: Simply divide the number

From the above division, we found 90 is the solution

Hence, \frac{18}{0.2} \ \Longrightarrow \ 90\

Let us see another example for this method:

Example 02
Divide 9.6 by 0.08

Step 01: Write the division in fraction form
\Longrightarrow \ \frac{9.6}{0.08}\

Step 02: Convert decimals into whole numbers
9.6 ⟹ contains one decimal place value
0.08 ⟹ contains two decimal place value

By Multiplying numerator & denominator by 100, both numbers become whole number

\Longrightarrow \ \frac{9.6\times 100}{0.08\times 100}\\\ \\ \Longrightarrow \ \frac{960}{8}\\\ \\

Step 03: Divide the whole numbers

Hence, 120 is the solution of the above division.
i.e. \frac{9.6}{0.08} \ \Longrightarrow \ 120\

Example 03
Divide 5.83 by 0.011

Step 01: Write the division in fraction form
\Longrightarrow \ \frac{5.83}{0.011}\

Step 02: Convert decimals into whole numbers
5.83 ⟹ contains two decimal place value
0.011 ⟹ contains three decimal place value

We multiply numerator and denominator by 1000 so that both numbers become whole numbers

\Longrightarrow \frac{5.83\times 1000}{0.011\times 1000} \\\ \\ \Longrightarrow \ \frac{5830}{11}

Step 03: Divide the whole numbers

Hence 530 is the solution of the problem
i.e. \frac{5.83}{0.011} \ \Longrightarrow \ 530\

I hope you have understood both the methods.
It is now time to solve some problems related to division of decimals

## Decimal Division Questions

(01) Divide 6.4 by 8

(a) 0.6
(b) 0.8
(c) 0.06
(d) 0.08

\Longrightarrow \frac{6.4}{8} \\\ \\ \Longrightarrow \ \frac{6.4\times 10}{8\times 10}\\\ \\ \Longrightarrow \ \frac{64}{8\times 10}\\\ \\

⟹ First divide 64 by 8

The equation can be written as :

⟹ Now divide 8 by 10
\Longrightarrow \frac{8}{10} \\\ \\ \Longrightarrow \ 0.8\

Hence 0.8 is the solution
Option (b) is the right answer

(02) Divide 1.2 by 3

(a) 0.08
(b) 0.04
(c) 0.8
(d) 0.4

\Longrightarrow \frac{1.2}{3} \\\ \\ \Longrightarrow \ \frac{1.2\times 10}{3\times 10}\\\ \\ \Longrightarrow \ \frac{12}{3\times 10}\\\ \\

⟹ First Divide 12 by 3

The equation can be expressed as

⟹ Now divide 4 by 10
\Longrightarrow \frac{4}{10} \\\ \\ \Longrightarrow \ 0.4\

Hence 0.4 is the solution
Option (d) is the right answer

(03) Divide 5.2 by 0.4

(a) 12
(b) 11
(c) 13
(d) 14

\Longrightarrow \frac{5.2}{0.4} \\\ \\ \Longrightarrow \ \frac{5.2\times 10}{0.4\times 10}\\\ \\ \Longrightarrow \ \frac{52}{4}\\\ \\

On dividing 52 by 4 we get:

Hence 13 is the solution
Option (c) is the right answer

(04) Divide 4.9 by 7

(a) 0.7
(b) 0.8
(c) 0.9
(d) 0.6

\Longrightarrow \frac{4.9}{7} \\\ \\ \Longrightarrow \ \frac{4.9\times 10}{7\times 10}\\\ \\ \Longrightarrow \ \frac{49}{7\times 10}\\\ \\

Dividing 49 and 7, we get number 7 as quotient

The equation can be written as:

⟹ Now divide 7 by 10
\Longrightarrow \frac{7}{10} \\\ \\ \Longrightarrow \ 0.7\

Hence 0.7 is the solution
Option (a) is the right answer

(05) Divide 2.4 by 0.6

(a) 6
(b) 8
(c) 4
(d) 2

\Longrightarrow \frac{2.4}{0.6} \\\ \\ \Longrightarrow \ \frac{2.4\times 10}{0.6\times 10}\\\ \\ \Longrightarrow \ \frac{24}{6}\\\ \\

Hence, 4 is the solution of the division
Option (c) is the right answer

(06) Divide 8.64 by 1.8

(a) 4.2
(b) 4.8
(c) 3.6
(d) 3.8

\Longrightarrow \frac{8.64}{1.8} \\\ \\ \Longrightarrow \ \frac{8.64\times 100}{1.8\times 100}\\\ \\ \Longrightarrow \ \frac{864}{180}\\\ \\

Dividing 864 by 180

Hence, 4.8 is the solution
Option (b) is the right answer

(07) Divide 13.11 by 0.19

(a) 9.6
(b) 6.9
(c) 96
(d) 69

\Longrightarrow \frac{13.11}{0.19} \\\ \\ \Longrightarrow \ \frac{13.11\times 100}{0.19\times 100}\\\ \\ \Longrightarrow \ \frac{1311}{19}\\\ \\

Dividing 1311 by 19, we get:

Hence 69 is the solution
Option (d) is the right answer

(08) Divide 36.75 by 3.5

(a) 10.5
(b) 9.7
(c) 10.8
(d) 9.5

\Longrightarrow \frac{36.75}{3.5} \\\ \\ \Longrightarrow \ \frac{36.75\times 100}{3.5\times 100}\\\ \\ \Longrightarrow \ \frac{3675}{350}\\\ \\

Dividing 3675 by 350, we get:

Hence, 10.5 is the solution
Option (a) is the right answer

(09) Divide 60.2 by 70

(a) 8.6
(b) 0.89
(c) 0.95
(d) 0.86

\Longrightarrow \frac{60.2}{70} \\\ \\ \Longrightarrow \ \frac{60.2\times 10}{70\times 10}\\\ \\ \Longrightarrow \ \frac{602}{700}\\\ \\

Dividing 602 by 700 using Long Division Method

0.86 is the solution
Option (d) is the right answer

(10) Divide 3012.54 by 35.4

(a) 85.1
(b) 85.2
(c) 85.3
(d) 85.4

\Longrightarrow \frac{3012.54}{35.4} \\\ \\ \Longrightarrow \ \frac{3012.54\times 100}{35.4\times 100}\\\ \\ \Longrightarrow \ \frac{301254}{3540}\\\ \\

Dividing 301254 by 3540

Hence 85.1 is the solution
option (a) is the right answer