adding fractions

Two cases arise while adding fractions

Case I: Fractions with the same denominator

Let’s learn using an example – Add \(\frac{4}{5} \)and \(\frac{2}{5}\)

If the denominators of the fraction are the same, then simply add the numerators and place the result over the common denominator. 
\(\frac{4}{5} + \frac{2}{5} = \frac{4+2}{5} = \frac{6}{5}\)

Case II: Fractions with different denominators

For example, adding \(^4/_3 \) and \(^2/_5 \). In such cases, make denominators of both fractions the same. To solve such cases, find the denominators' Least Common Multiple.

The Least Common Multiple of 3, 5 is 15:

Multiple of 3 = 3,6,9,12,15,21

Multiple of 5 = 5,10,15,20

Now change fractions to equivalent fractions such that the denominator of both the fraction is 15.

\(\frac{4}{3} = \frac{4\times5}{3\times5} = \frac{20}{15}\)

\(\frac{2}{5} = \frac{2\times3}{5\times3} = \frac{6}{15}\)

Now you can add both fractions:
\(\frac{20}{15} + \frac{6}{15} = \frac{26}{15}\)