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Fractions & Decimals

Fractions & Decimals

At a Glance - Adding & Subtracting Fractions

Adding and subtracting fractions can be time-consuming because it often involves a few extra steps. This is a really important and commonly-used skill, though. So let's get to it.

Here is 3/4 + 1/4.

3/4 + 1/4 circles

There is a total of 4 blue fourths, which combine to make 1 whole, so 3/4 + 1/4 = 1.

Here is 4/5 + 3/5.

4/5 + 3/5 circles

Now there is a total of 7 blue fifths, which combine to make 1 whole and 2 fifths, so 4/5 + 3/5 = 1 2/5.

The most important thing to remember when adding or subtracting fractions is that we must have a common denominator. 

When the denominators are the same, all you have to do is add or subtract the numerators and keep the denominator the same. 

Examples with common denominators

Example 1
 7/8 + 3/8Add the numerators
  11/8Change into an improper fraction
5/4Simplify
1 3/8Change to a mixed number
Example 2
5/6 - 1/6Subtract the numerators
4/6Reduce the fraction
2/3

Adding or Subtracting Fractions with Different Denominators

Try adding 2/3 + 1/4 using pictures.

2/3 + 1/4 circles

This can be a little tricky at first, but once you get the hang of it, it’s a breeze.

To add two fractions with different denominators, we need to convert one or both fractions so they have matching - or common - denominators.

  1. Use the Least Common Multiple of the denominators and use it as your common denominator
    • Or, if you can't easily find the LCM, just multiply the denominators together. This will usually create a little more work, as you'll have to reduce the fraction later. The LCM is your best bet, but both will lead you to a correct answer.
  2. Once the original fractions are converted to two fractions with common denominators, just add the numerators and keep the denominator.

Look Out: when adding fractions, don't fall into the trap of mistakenly adding the denominators together. Here's a quick way to remember: we all know that two halves make one whole. If we made the mistake of adding denominators, we would get ½ + ½ = 2/4 = ½, which is obviously wrong.

Example 1

3/4 + 2/5 =

The LCM of 4 and 5 is 20, so we need to convert the fractions so they each have a denominator of 20.

3/4 = 15/20 and 2/5 = 8/20


Example 2

7/8 - 2/3 =

The LCM of 8 and 3 is 24, so we need to convert each fraction to one with a denominator of 24

7/8 = 21/24 and 2/3 = 16/24


Example 3

4/7 + 2/6

The LCM of 7 and 6 is 42, so we need to convert each fraction to one with a denominator of 42.

8/9 - 2/3 and 8/9 - 6/9 =


Example 4

8/9 - 2/3 =

The LCM of 9 and 3 is 9. Since the first fraction already has a denominator of 9, we only need to convert the second one.

2/3 = 6/9


Exercise 1

4/7 + 1/3


Exercise 2

3/4 - 1/6


Exercise 3

4/5 + 3/10


Exercise 4

7/12 - 1/3


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