# CLASS-4ADDITION OF MIX FRACTION WITH DIFFERENT DENOMINATOR

ADDITION OF MIX FRACTION WITH DIFFERENT DENOMINATOR -

Addition of mixed fraction with different denominator is near to similar of addition of mixed fraction with same denominator except one or two steps. Process of addition of mix fraction with different denominator is described below -

Process of addition of mix fraction with different denominator -

Step.1) Convert from mix fraction to improper fractions.

Step.2) Find LCM of denominator of given fraction

Step.3) Change both the fractions to equivalent fractions with common denominators.

Step.4) Make addition of given fraction.

Step.5) Reduce to lowest term if possible.

Step.6) Convert the improper fraction to mixed number as the denominator is smaller than the numerator.

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There are some examples are given below for your better understanding.

3         7

Example.1) Find The addition of following mix fraction 2----- + 2----

7         6

3            7

Ans.)     2 ------ + 2 ------

7            6

STEP 1: Convert to improper fractions.

17           19

= -------- + -------

7            6

STEP 2: Find LCM of denominator of given fraction

(17 X 6) + (19 X 7)

= ---------------------

42

102 + 133

= -------------

42

235

= --------

42

STEP 3: Reduce to lowest term if possible.

235

=  -------

40

STEP 4: Convert the improper fraction to mixed number as the denominator is smaller than the numerator.

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πΈπππππππ = -------------

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25

= 5 ------    (Ans.)

42

5          7

Example.2) Find The addition of following unlike Fraction ------ + ------

24        32

Ans.)            5           7

------- + -------

24          32

STEP.1) Find the L.C.M of the denominators 24 and 32.

L.C.M of 24 and 32 is 96.

Step.2) Change both the fractions to equivalent fractions with common denominators.

5             5 X 4            20

--------- = ----------- = --------

24            24 X 4           96

7              7 X 3             21

--------- =  ------------ = --------

32             32 X 3            96

20             21

--------- + ---------

96             96

Step.3)  Add the equivalent fractionsWhen we add or subtract fractions with same denominator, we just add or subtract the numerators and keep the denominator same.

(20 + 21)

=  ------------

96

41

=  ----------

96

41/96 is a proper fraction i.e denominator is greater than numerator. So, this is the answer.   (Ans.)

1            5           5

Example.3) Find the value of 1------ + 2------ + 3------

4            6           8

1           5           5

Ans.)   1------ + 2------ + 3------

4           6           8

Step.1) Convert from mix fraction to improper fractions.

5           17          29

=  ------- + ------- + --------

4            6           8

Step.2) Find LCM of denominator of given fraction

So, the LCM of the denominator is 4, 6, and 8 is 24.

Step.3) Change both the fractions to equivalent fractions with common denominators.

5             5 X 6           30

--------- = ----------- = --------

4             4 X 6           24

17            17 X 4           68

--------- = ----------- = --------

6             6 X 4            24

29             29 X 3           87

--------- = ------------ = --------

8              8 X 3            24

30             68            87

So,  --------- + --------- + ---------

24             24            24

Step.4) Make addition of given fraction.

(30 + 68 + 87)

= -------------------

24

185

=  ---------     Step.5) Reduce to lowest term if possible.

24

Step.6) Convert the improper fraction to mixed number as the denominator is smaller than the numerator.

πΉππππππππ

πΈπππππππ = -------------

π«ππππππ

17

=  7 --------     (Ans.)

24