Home > Pre-algebra > Fractions > Adding Fractions

#### Introduction

In order to add fractions together, we find the highest common factor of the denominator, and add the equivalent numerators together.

#### Terms

Fraction - Fractions are used when using numbers to express parts of whole.
Least/Lowest Common Multiple - The lowest multiple of two or more numbers.
Equivalent Fraction - Equivalent fractions are fractions that have the same value.

## Lesson

When adding fractions together, we have to make sure the denominators are the same. So if we are given , in this case the denominators are the same, so we simply add the two numerators together:

When the denominators are different, we ‘make’ them the same by finding their lowest common multiple. So in the case of , the LCM of 3 and 7 is 21. So we need to make the denominator of each fraction equal to 21

These fractions now have the same denominators, so we simply add the numerators

So we know that

When adding mixed fractions, we follow the same procedure but we need to convert the mixed fraction to an improper fraction first. So if we are given , we convert to the improper fraction . Then we ‘make’ the denominators the same by finding the LCM, so we end up with:

Since the denominators are now the same, we add the numerators together:

## Examples

Since these fractions have different denominators, we need to find the least common multiple of the denominators
The least common multiple of 2 and 3 is 6, so we need to multiply to make each of the denominators = 6
Since these fractions have the same denominator, we can just add the numerators
Because is an improper fraction (the numerator is greater than the denominator), we need to convert it to a mixed number
Since these fractions have the same denominator, we can just add the numerators
Because is an improper fraction (the numerator is greater than the denominator), we need to convert it to a mixed number
Since these fractions have the same denominator, we can just add the numerators
can be reduced, since is a factor of both and :
The fraction is now in lowest terms
Since these fractions have the same denominator, we can just add the numerators
can be reduced, since is a factor of both and :
The fraction is now in lowest terms
More Examples