Algebra Den

Addition of Fractions with Different Denominators

Explanation
To add fractions with different denominators,
Step 1 = Find equivalent fractions of given fraction with common denominator
Step 2 = Follow the process of addition of fractions with same denominator (topic available in above link)

As mentioned in Step 1 (above), we need to find :
Common denominator = LCM of the denominators of the given fractions (LCM topic is available in this site)
Equivalent Fractions = Involves following steps:
Step 1 = Divide the Common Denominator by the denominator of given fractions
Step 2 = Multiply the quotient with the numerator of the respective fractions.

e.g. add 2/7 and 3/5
The above fractions have different denominators, so we need to find :
Common Denominator = LCM of the denominators(7 & 5) of the given fractions = 35
Equivalent Fraction of given fraction 2/7 and 3/5: The proceed is as :-

Given fraction 2/7
Step 1 = Divide the Common Denominator(35) by the denominator of given fraction(7) = 35 ÷ 7 = 5
Step 2 = Multiply the quotient(5) with the numerator of the respective fraction(2) = 5 × 2 = 10
So, Equivalent Fractions of given fraction with common denominator 2/7 = 10/35

Given fraction 3/5
Step 1 = Divide the Common Denominator(35) by the denominator of given fraction(5) = 35 ÷ 5 = 7
Step 2 = Multiply the quotient(7) with the numerator of the respective fraction(3) = 3 × 7 = 21
So Equivalent Fractions of given fraction with common denominator 3/5 = 21/35

Now, we have equivalent fractions of given fraction with same denominators 2/7 & 3/5 = 10/35 & 21/35
so (2/7) + (3/5) = (10/35) + (21/35)
Add the numerators and denominator remains same:
= (10+21) / 35     = 31/35.

Alternative Method
The above discussed method is for Beginners. Once you understand the concept of addition of fractions with different denominators, you can directly apply the addition process in following ways:
(2/7) + (3/5)
Find LCM of denominators and divide the LCM by denominator & multiply its quotient with respective numerators and we get:
= { (2×5) + (3×7) } / 35
Solve the Parentheses and we get:
= {10 + 21} / 35
Solve Braces and we get:
= 31 / 35