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

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

There we studied about concept of fraction in general with examples and exercises. We also introduced Like and Unlike Fractions which are used here.

The knowledge of

Equivalent Fractions,

Conversion of Improper to Mixed and Mixed to Improper Fractions

and

Least Common Multiple (L.C.M.)

is also used here.

Learn/Teach
Fractions through Fun Games.
For details, see near

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.

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

Examples :
(i) 2⁄7 + 4⁄7 = (2 + 4)⁄7 = 6⁄7

(ii) 1⁄13 + 2⁄13 + 4⁄13 + 5⁄13 = (1 + 2 + 4 + 5)⁄13 = 12⁄13

### Method of Adding Fractions with unlike denominators

Step 1 :
Find the L.C.M. of denominators of given fractions.

Step 2 :
Convert the given fractions into equivalent like fractions
with their L.C.M. as common denominator.

Step 3 :
Add the like fractions so obtained.

Step 4 :
Reduce the fraction obtained in step 3 to its
lowest terms and convert it into mixed fraction if required.

### Solved Example 1 of Adding Fractions

Find the sum 5⁄12 + 9⁄16

Solution :
Let us find the L.C.M. of the denominators.

```
4|    12    16
----------------
3     4

```

L.C.M. = 4 x 3 x 4 = 48.

5⁄12 + 9⁄16 = (5 x 4)⁄(12 x 4) + (9 x 3)⁄(16 x 3)
= 20⁄48 + 27⁄48 = (20 + 27)⁄48 = 47⁄48

## Solved Example 2 ofAdding Fractions

Find the sum 8⁄9 + 11⁄18 + 13⁄27 + 5⁄6

Solution :
Let us find the L.C.M.. of the denominators.

```
3|    9     18     27     6
-------------------------------
3|    3      6      9     2
-------------------------------
2|    1      2      3     2
-------------------------------
1      1      3     1

```

L.C.M. = 3 x 3 x 2 x 3 = 54.

8⁄9 + 11⁄18 + 13⁄27 + 5⁄6

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
= 152765427
= 76⁄27 = 2  2227. Ans.

### Solved Example 3 of Adding Fractions

Find the sum
2  512 + 1  1960 + 2  1140 .

Solution :
2  512 + 1  1960 + 2  1140
= (2 x 12 + 5)⁄12 + (1 x 60 + 19)⁄60 + (2 x 40 + 11)⁄40
= 29⁄12 + 79⁄60 + 91⁄40

Let us find the L.C.M.. of the denominators.

```
4|    12     60     40
-----------------------
5|     3     15     10
-----------------------
3|     3      3      2
-----------------------
1      1      2

```

L.C.M. = 4 x 5 x 3 x 2 = 120.

The required sum = 29⁄12 + 79⁄60 + 91⁄40

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  1120 . Ans.

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## Word Problems on Adding Fractions

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

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Do the Adding Fractions given below.

1. 1⁄5 + 3⁄5
2. 2⁄11 + 3⁄11 + 4⁄11 + 5⁄11
3. 7⁄15 + 4⁄9
4. 7⁄24 + 7⁄18 + 15⁄22
5. 4  89 + 2  13 + 1⁄4.

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