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## Subtracting Fractions

#### Introduction

In order to subtract fractions, we find the highest common factor of the denominator, and subtract one equivalent numerator from the other.

#### 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 subtracting fractions, 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 subtract 1 from 5

, which reduces to

When the denominators are different, we ‘make’ them the same by finding their least common multiple (LCM).

For example, in the problem , the LCM of 7 and 2 is 14

So to make the denominator of 6/7 = x/14, we have to multiply the denominator by 2 (don’t forget to multiply the numerator by 2 as well!). We then get 6*2 / 7*2 = 12/14. Similarly for 1/2, we multiply the numerator and denominator by 7 to get 1*7 / 2*7 = 7/14. The equivalent fractions of 6/7 (12/14) and 1/2 (7/14) now have the same denominators, so we simply subtract 7 from 12 to get 5/14.
When subtracting 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 1 2/3 – 1/4, we convert 1 2/3 to the improper fraction 5/3. Then we ‘make’ the denominators the same by finding the LCM, so we end up with 5*4/3*4 – 1*3/4*3 = 20/12 – 3/12. Since the denominators are now the same, we subtract 3 from 20 to get 17/12, or 1 5/12 (expressed as a mixed fraction).

## Examples

Since these fractions have the same denominator, we can just subtract the numerators
Since these fractions have different denominators, we need to find the least common multiple of the denominators
The least common multiple of 3 and 4 is 12, so we need to multiply to make each of the denominators = 12
Since these fractions have the same denominator, we can just subtract the numerators
Since these fractions have the same denominator, we can just subtract the numerators
can be reduced, since is a factor of both and :
The fraction is now in lowest terms