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.

Also study Fractions Made Easy.

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
the bottom of this page.

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)

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

Adding of Unlike Fractions

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     
       

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
       

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
= 152⁷⁶⁄54²⁷
= 76⁄27 = 2  ²²⁄₂₇. Ans.

Solved Example 3 of Adding Fractions

Find the sum
2  ⁵⁄₁₂ + 1  ¹⁹⁄₆₀ + 2  ¹¹⁄₄₀ .

Solution :
2  ⁵⁄₁₂ + 1  ¹⁹⁄₆₀ + 2  ¹¹⁄₄₀
= (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

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  ¹⁄₁₂₀ . Ans.

Word Problems on Adding Fractions

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

Learning/Teaching Math Can Be Fun

Here is a collection of kids math
games and fun math activities for
the class room or for the home, to
make math exciting and easy to learn.

They help you

* To save you time and money to be
spent on resources, games and books.

* To become a wonderful, fun teacher
or parent who knows how to make math
fun, interesting and effective.

* To cater for all different ability
levels and cater for different
learning styles.

* To see your kids math skills soar
and their grades in math going
up and up.

This Collection of Fun Math Games
are electronic books (e-books)
that are downloaded to your computer
in a flash. You can start printing
games right away. You get to print
only what you want and as many
copies as you need.

For more information or to have
some FREE samples or to order
click HERE.

Exercise on Adding Fractions

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  ⁸⁄₉ + 2  ¹⁄₃ + 1⁄4.

Answers to Exercise on Adding Fractions

1. 4⁄5
2. 1  ³⁄₁₁
3. 41⁄45
4. 1  ²⁸⁷⁄₇₉₂
5. 7  ¹⁷⁄₃₆