Addition of fractions

Pure mathematics is, in its way, the poetry of logical ideas.  ~Albert Einstein

 

Fraction addition

Thumb rule in fractions: Simplification is easy if all denominators in fractions are equal. So try to make all denominators same. The purpose of finding LCM is making all denominators same.

Ex : 1/2 + 1/3

1/2 means 1 part out of 2 parts

1/3 means 1 part out of 3 parts

Total no of parts should be same to do addition or subtraction

so what we will do is

 1/2 = 1x3/2x3 = 3/6 means 3 parts out of 6 parts

 1/3 = 1x2/3x2 = 2/6 means 2 parts out of 6 parts

As total parts are same for both fractions, result is addition of two numerators 

result = 1/2 + 1/3 = 3/6 + 2/6 = 5/6

Conclusion is 1/a + 1/b = (a+b)/ axb

We can do this by simply memorizing above formula. But how many formulas you can remember. Try to learn simplification through mental calculation.

Let us try one more example.

Ex 2: 5/6 + 2/3 + 1/2

5/6 + 2/3 + 1/2 = 5/6 + (2x2)/(3x2) + (1x3)/(2x3)       -- making all denominators same

 = 5/6 + 4/6 + 3/6 = 12/6 = 2

Please remember if you multiply numerator and denominator with the same number, there is no change in value of fraction.

Try following examples: 

Ex 3 : 1/3 + 1/7 = ?

Ex 4 : 2/3 + 1/4 + 1/2 = ?