Arithmetic Adding Fractions

A fraction is a part of a whole. A fraction can be altered to a decimal by dividing the upper number, or numerator, by the lower number, or denominator. Fractions are to indicate ratios, and to represent division which is one of the basic arithmetic operations. Thus the fraction 3/4 is also used to signify the ratio 3:4 (three to four) and the division 3 ÷ 4 as well.(three divided by four). Here in this topic we see about adding fractions.

Arithmetic adding Fractions with same denominator - Example problems:

Arithmetic adding Fractions - Example 1:

Add: 2/7   +    3/7

Solution

Here the denominator is equal

So we keep the denominator same as 7 and add the numerator alone

So the solution is   (2+3)/7 =  5/7

Arithmetic adding Fractions - Example 2:

Add:  5/8 +  3/8

Solution

Here the denominator is equal

So we keep the denominator same as 8 and add the numerator alone

So the solution is ,

(5+3) / 8 = 8 / 8  = 1.

Arithmetic adding Fractions with different denominator - Example problems:

Arithmetic adding Fractions - Example 1:

10/8   +    12/9


Answer:

Here the denominators are different that are 8 and 9. So take LCD of 8 and 9 first.

LCD of 8 and 9 is 72.

Therefore,
10 x 9        12 x 8          90      96       186
------------  +   ------------  =  -------- +  ------ = ----------
8 x 9          9 x 8          72       72        72


Simplifying this we get the answer as 31/12 .
Arithmetic adding Fractions - Example 2:

16/3     +   10/10

Answer:

Here the denominators are different that are 3 and 10. So take LCD of 3 and 10 first.

LCD of 3 and 10 is 30.

Therefore,
16 x 10       10 x 3       160       30       190
------------  +   ------------  =  -------- +  ------ = ----------
3 x 10          10 x 3       30       30        30


Simplifying this we get the answer as 190/30 .