Adding and subtracting fractions
Why you never add the bottom numbers
What is this about?
A fraction is pieces of a whole. In 3/4, the 4 tells you how many equal pieces the cake was cut into, and the 3 tells you how many you take. To add two fractions, the pieces must be the same size. If one cake is cut into quarters and another into eighths, the pieces don't match and you can't just put them together.
The rule to remember
If the denominators are the same, add only the numerators and keep the denominator. If they're different, find a common denominator first, then add.
Example 1
3/8 + 2/8
- 1The denominators are already the same (both are 8), so the pieces are the same size.
- 2Add only the top numbers: 3 + 2 = 5.
- 3The denominator stays untouched: it's still 8.
Result: 5/8
Example 2
1/2 + 1/6
- 1The denominators are different (2 and 6), so we need to match them.
- 26 is a multiple of 2, so the common denominator is 6.
- 3Turn 1/2 into sixths: multiply top and bottom by 3 to get 3/6.
- 4Now you can add: 3/6 + 1/6 = 4/6.
- 5Simplify by dividing top and bottom by 2: 2/3.
Result: 2/3
The most common mistake
Many people write
1/2 + 1/6 = 2/8
Why it's wrong
The numerators were added on one side and the denominators on the other. That doesn't work: notice that 2/8 is 0.25 while the correct answer, 2/3, is 0.66. Denominators are never added, only matched.
Did it click?
The best way to find out is to try. These exercises are exactly on this topic.
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