How to Add Fractions

Concept

When adding fractions, the first thing to check is if the denominators are the same.

Rules

To add like fractions:
1. Add all the numerators.
2. The denominator stays the same.
3. Simplify the answer by dividing the numerator and the denominator by their greatest common factor.

To add unlike fractions:
1. Find an equivalent fraction with a common denominator. To do this, find the least common multiple of the two denominators.
2. Rewrite the fractions with the common denominator.
3. Add all numerators. The denominator stays the same.
4. Simplify, if needed, by dividing the numerator and the denominator by their greatest common factor.

Example

Add. Write in the simplest form.
$\fn_phv \frac{1}{3}+ \frac{3}{6}$

Solution

1. If the denominators are not the same, find an equivalent fraction with a common denominator. (The denominators in this problem are 3 and 6.)
To do this, find the least common multiple of the two denominators.
Some multiples for the number 3 are: 3, 6, 9, 12
Some multiples for the number 6 are: 6, 12, 18, 24
The least common multiple for 3 and 6 is 6.
2. Change the numerators with the common denominator 6.
In order to rewrite $\fn_phv {\color{Red} \frac{1}{3}}$ so it has the common denominator 6, multiply the numerator and denominator by the factor 2.
$\fn_phv {\color{Red} \frac{1\times 2}{3\times 2} =\frac{2}{6}}$
$\fn_phv {\color{Red} \frac{3}{6}}$ already has the common denominator 6, so it doesn’t need to be rewritten.
3. Add all the numerators. The denominator stays the same.
$\fn_phv {\color{Red} \frac{2}{6}+\frac{3}{6}=\frac{5}{6}}$
4. Simplify, if needed. $\fn_phv {\color{Red} \frac{5}{6}}$ is already in simplest form.

Practice How to Add Fractions

Practice Problem 1

Add. Write the sum.

Practice Problem 2

Korbin spent $\fn_phv {\color{Teal} \frac{2}{9}}$ of an hour biking and $\fn_phv {\color{Teal} \frac{5}{9}}$ of an hour jogging. How much time did he spend on both activities altogether?

Practice Problem 3

Add.
Write in simplest form.

Practice Problem 4

Miley rode her bike for $\fn_phv {\color{Teal} \frac{2}{5}}$ of a kilometer on Monday and $\fn_phv {\color{Teal} \frac{3}{7}}$ of a kilometer on Tuesday. How many kilometers did she ride altogether?