HOW TO ADD FRACTIONS, ADDING FRACTIONS WITH UNLIKE DENOMINATORS, SOLVED EXAMPLES

Please study Fractions before Adding Fractions if you have not already done so.
There we studied about
half, quarter, three fourth
with examples and exercises.

Here, we explain How to add fractions in general,
adding of fractions with unlike denominators
in particular in a lucid way.
We include solved examples and
problems for practice with answers.

Adding of Like Fractions

Sum of like fractions
= (Sum of their numerators)⁄(Common denominator)

Now 54 is taken as the common denominator.
The number with which we have to multiply each
denominator to get 54, is taken and that number
multiplies each numerator as shown below.

= ( 8 x 6 + 11 x 3 + 13 x 2 + 5 x 9)⁄54
= (48 + 33 + 26 + 45)⁄54 = 152⁄54
= 152^{76}⁄54^{27}
= 76⁄27 = 2 ^{22}⁄_{27}.
Ans.

Solved Example 3 of Adding Fractions

Find the sum
2 ^{5}⁄_{12} +
1 ^{19}⁄_{60} +
2 ^{11}⁄_{40} .

Now 120 is taken as the common denominator.
The number with which we have to multiply each
denominator to get 120, is taken and that number
multiplies each numerator as shown below.

= (29 x 10 + 79 x 2 + 91 x 3)⁄120
= (290 + 158 + 273)⁄120 = 721⁄120
= 6 ^{1}⁄_{120} . Ans.

For Application of various topics of Fractions
including Adding Fractions to Word Problems
go to Fraction Word problems.

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Exercise on Adding Fractions

Do the Adding Fractions given below.

1⁄5 + 3⁄5

2⁄11 + 3⁄11 + 4⁄11 + 5⁄11

7⁄15 + 4⁄9

7⁄24 + 7⁄18 + 15⁄22

4 ^{8}⁄_{9} +
2 ^{1}⁄_{3} +
1⁄4.

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