# How to Add and Subtract Fractions with Different Denominators

## Instructions

• 1

Arranging the fractions

Whether you are adding or subtracting a fraction, the very first thing is to arrange them properly. The order does not really matter if the fractions are to be added, but if you have to subtract them, then write the greater fraction first. Remember that:

4 ≥ 3

but

¼ ≤ 1/3

• 2

Adding the Fraction

No matter how many fractions there are with different denominators, you may arrange them in any order as long as you have to add them. For example:

½ + 1/3 + ¼

Now think of three numbers that, when multiplied with the numerators and denominators of all the above three fractions, get the same number in the denominators. Hence,

Multiply numerator and denominator in ½ with 6 to get 6/12

Multiply numerator and denominator in 1/3 with 4 to get 4/12

Multiply numerator and denominator in ¼ with 3 to get 3/12

Now add:

6/12 + 4/12 + 3/12 = 6+4+3 / 12

= 13/12

• 3

Subtracting the Fractions

The same technique is followed while subtracting the fractions i.e. you multiply the numerators and denominators of the fractions (to be subtracted) with a number that equalizes the denominators. Besides, just ensure that the greater fraction is at the left side of the negative (-) sign. Hence:

½ - 1/5

Equate the denominators of two fractions by multiplying the first fraction with 5 to make it 5/10 and the other fraction by 2 to make it 2/10

Now subtract:

5/10 – 2/10 = 5 – 2 /10

= 3/10

• ## Tips & Warnings

When the denominator of 2 or more fractions to be added or subtracted is the same there is no need to take the L.C.M. You simply add or subtract the numbers in the numerators.

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