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 .
There is a total of 4 blue fourths, which combine to make 1 whole, so .
Here is .
Now there is a total of 7 blue fifths, which combine to make 1 whole and 2 fifths, so .
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
|Add the numerators|
|Change into an improper fraction|
|Change to a mixed number|
|Subtract the numerators|
|Reduce the fraction|
Adding or Subtracting Fractions with Different Denominators
Try adding using pictures.
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.
- 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.
- 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.
The LCM of 4 and 5 is 20, so we need to convert the fractions so they each have a denominator of 20.
The LCM of 8 and 3 is 24, so we need to convert each fraction to one with a denominator of 24
The LCM of 7 and 6 is 42, so we need to convert each fraction to one with a denominator of 42.
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.