# How to Add Two Fractions Faster

Fractions whose denominators are the same are called similar fractions, otherwise they are called dissimilar fractions. The fractions 1/9 and 7/9 are similar fractions, while 3/4 and 2/3.

Adding similar fractions is easy. Just copy add the numerator and then copy the denominator. For example,

1/9 + 7/9 = 8/9.

Adding dissimilar fractions is a bit more complicated. You have to get the Least Common Multiple (LCM) of the denominators. For example, if we want to add 3/4 and 2/3, we get the LCM of 4 and 3 which is equal to 12. You then change the given to equivalent fractions. The addition becomes

9/12 + 8/12 = 17/12.

Shortcut: How to Add Two Fractions Faster

We can use a shortcut to add to two add fractions.  We will only discuss dissimilar fractions because similar fractions are too easy to add. Below are the steps for the shortcut 3/4 and 2/3

Example 1: 3/4 + 2/3

(1) Multiply the numerator of the first fraction by the denominator of the second fraction: 3 × 3 = 9.

(2) Multiply the denominator of the first fraction by the numerator of the second fraction: 4 × 2 = 8

(3) Add the results in (1) and (2). The sum is the numerator of the sum: 9 + 9 = 17.

(4) Multiply the denominators of the given. This will be the numerator of the sum: 4 × 3 = 12.

Example 2: 2/7 + 5/9

$\displaystyle \frac{2}{7} + \frac{5}{9} = \frac{(2 \times 9) + (7 \times 5)}{7 \times 9}$

$= \displaystyle \frac{18 + 35}{63} = \frac{63}{53}$

Example 3: 4/5 + 7/9

$\displaystyle \frac{4}{5} + \frac{7}{9} = \frac{(4 \times 9) + (5 \times 7)}{5 \times 9}$

$= \displaystyle \frac{36 + 35}{45} = \frac{71}{53}$

In the next post, we are going to discuss why this shortcut works.