DECIMAL FRACTION

Decimal fraction is a fraction in which the denominator (the bottom number) is a power of ten (such as 10, 100, 1000, etc).

We will be able to write a decimal fraction with a decimal point (without denominator), which makes it easier to do calculations like addition and subtraction on fractions.

Examples :

3/10 is a decimal fraction and it can be written as 0.7

21/100 is a decimal fraction and it can written as 0.21

49/1000 is a decimal fraction and it can be written as 0.049.

Addition and Subtraction of Decimal Fractions

When we add or subtract decimal fraction, we have to write the decimal fraction with decimal point (without denominator) and add or subtract them. 

Example : 

Find the value of : 

3/10 + 21/100 - 2/1000

Solution : 

Write all the decimal fractions with decimal point. 

That is, 

3/10 + 21/100 - 2/1000  =  0.3 + 0.21 - 0.002

On the right side, make each value with same number of digits after decimal point by adding zeroes.  

3/10 + 21/100 - 2/1000  =  0.300 + 0.210 - 0.002

Simplify.

3/10 + 21/100 - 2/1000  =  0.510 - 0.002

3/10 + 21/100 - 2/1000  =  0.49

Change 0.49 as a fraction. 

3/10 + 21/100 - 2/1000  =  49/100

Multiplication of Decimal Fractions

When we multiply a decimal fraction by another decimal fraction, we have to multiply the numerator by numerator and denominator by denominator.  

Example : 

Find the value of : 

21/10 ⋅ 3/100

Solution : 

21/10 ⋅ 3/100  =  (21 ⋅ 3) / (10 ⋅ 100)

21/10 ⋅ 3/100  =  63/1000

Division of Decimal Fractions

Step 1 :

In division of two decimal fractions, change the division as multiplication. 

Step 2 :

Take reciprocal of the second fraction.

Step 3 :

Multiply the two fractions. (Numerator times numerator and denominator times denominator).

Example : 

Find the value of : 

7/100 ÷ 9/10

Solution : 

7/100 ÷ 9/10  =  7/100 ⋅ 10/9

7/100 ÷ 9/10  =  (7 ⋅ 10) / (100 ⋅ 9)

7/100 ÷ 9/10  =  (7 ⋅ 1) / (10 ⋅ 9)

7/100 ÷ 9/10  =  7/90

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