OPERATIONS WITH FRACTIONS

In this section, you will learn, how to do the four binary operations with fractions. 

(i) Addition

(ii) Subtraction

(iii) Multiplication

(iv) Division

Addition and Subtraction of Fractions with Same Denominator

If we add or subtract two or more fractions with the same denominator, we have to take the denominator once and simplify the values in numerator. 

Example : 

Find the value of : 

1/7 + 3/7 - 2/7

Solution : 

In all the above fractions, the denominator is same. 

So take the denominator once and simplify the values in numerator. 

1/7 + 3/7 - 2/7  =  (1 + 3 - 2) / 7

1/7 + 3/7 - 2/7  =  2/7

Addition and Subtraction of Fractions with Different Denominators

If we add or subtract two or more fractions with different denominators, we have to follow the steps given below. 

Step 1 : 

Find the least common multiple (LCM) of the denominators. 

Step 2 : 

Mae the result of step 1 (LCM) as denominator for each fraction using multiplication.

Step 3 : 

In step 2, all the fractions will have the same denominator. Now take the denominator once and simplify the values in numerator.  

Example : 

Find the value of : 

1/4 + 5/6 - 3/8

Solution : 

Find the least common multiple of the denominators.

LCM of (4, 6, 8)  =  24

Make the denominator of each fraction as 24 using multiplication. 

1/4  =  (1 ⋅ 6) / (4 ⋅ 6)  =  6/24

5/6  =  (5 ⋅ 4) / (6 ⋅ 4)  =  20/24

3/8  =  (3 ⋅ 3) / (8 ⋅ 3)  =  9/24

Then, we have

1/4 + 5/6 - 3/8  =  6/24 + 20/24 + 9/24

1/4 + 5/6 - 3/8  =  (6 + 20 + 9)/24

1/4 + 5/6 - 3/8  =  35/24

Multiply a Fraction by a Whole Number

To multiply a proper or improper fraction by a whole number, first, we have to multiply the whole number and numerator of the fraction, keeping the denominator same.

For example, 

2 ⋅ 3/5   =  (2 ⋅ 3)/5  =  6/5

3 ⋅  7/11  =  (3 ⋅ 7)/11  =  21/11

Multiply a Fraction by a Fraction

To multiply a proper or improper fraction by another proper or improper fraction, we have to multiply the numerators and denominators. 

For example, 

2/3 ⋅ 4/5   =  8/15

1/3 ⋅  7/11  =  7/33

Divide a Whole Number by a Fraction 

To divide a whole number by any fraction, multiply the whole number by the reciprocal of the fraction.

For example, 

6 ÷ 2/5  =  6 ⋅ 5/2

6 ÷ 2/5  =  (6 ⋅ 5)/2

6 ÷ 2/5  =  (3 ⋅ 5)/1

6 ÷ 2/5  =  15  

Divide a Fraction by a Whole Number

To divide a fraction by a whole number, we have to multiply the denominator of the fraction by the whole number and simplify, if possible. 

For example, 

2/5 ÷ 6  =  2/(5 ⋅ 6)

2/5 ÷ 6  =  1/(5 ⋅ 3)

2/5 ÷ 6  =  1/15

Divide a Fraction by a Fraction

To divide a fraction by another fraction, multiply the first fraction by the reciprocal of the second fraction.

For example,

1/5 ÷ 3/7  =  1/5 ⋅ 7/3

1/5 ÷ 3/7  =  (1 ⋅ 7) / (5 ⋅ 3)

1/5 ÷ 3/7  =  7/15

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