Adding Three Fractions

A fraction will always be a form of a / b where b cannot divide a completely and b ≠ 0. Fraction is also known as rational number.

Steps to add three fractions: - Suppose if we wants to add three fractions
4/9, 2/3, 1/6.

Step 1:- Find the L. C.M. of the denominators 9, 3 and 6.
Factors of 9 = 3 * 3
Factors of 3 = 3
Factors of 6 = 3 * 2

At first find the common of all three numbers which is 3 and other two numbers 3 and 2 which are left.
Product of 3, 3 and 2 is 18
So Least common factor = 18.

Step 2: - Divide the L.C.M. = 18 by each of the denominator 9, 3 and 6 then multiply the obtained quotient with their respective numerators.
So,
For the first fraction 4/9: 18/ 9= 2 and 2 * 4 = 8
For the second fraction 2/3: 18 / 3 = 6 and 6 * 2 = 12
Similarly for the third fraction: 1/ 6: 18 / 6= 3 and 3 * 1= 3

Step 3: Now add 8, 12 and 3 which gives 23

Step 4: 23/ 18

Another example:- Simplify 1 / 2 + 3 / 8 + 5 / 6.

Solution: -

            1 / 2 + 3 / 8 + 5 / 6.=(1 * 12 + 3 * 3 + 5 * 4) / 24
                                            = (12 + 9 + 20) /24
                                            = 41 / 24


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