Subtracting fractions is easier than you think since it is very similar to adding fractions. Just like adding fractions, you need to keep in mind the following four important rules.
- You cannot subtract the denominators, also called bottom numbers!
- You can only subtract the numerators, also called top numbers!
- You can subtract the numerators only when the denominators are the same!
- If the denominators are not the same, look for a common denominator before subtracting the numerators.
How to subtract fractions with like denominators
As shown in the figure above, the subtraction of 2/8 from 5/8 is simple. Since the denominator is the same, just subtract the numerators.
5/8 – 2/8 = (5 – 2)/8 = 3/8
A couple more examples showing how to subtract fractions with the same denominator
Example #1:
| 52 | − 12 = ? |
There is no need to look for a common denominator because they are already the same.
| So, 52 | − 12 | = 5 − 12 | = 42 = 2 |
Example #2:
9/4 – 3/4 = (9 – 3)/4 = 6/4
How to subtract fractions with different denominators
Just like adding fractions, if the denominators are different, you will first find equivalent fractions that give a common denominator for both fractions.
Example #3:
| 73 | − 36 = ? |
Here the denominators are not the same, so multiply 3 by 2 to get the same denominator.
Remember that we have to multiply 7 by 2 also in order not to change the problem.
| So, 73 | − 36 | = 7 × 23 × 2 | − 36 | = 146 | − 36 | = 116 |
Example #4:
| 35 | − 24 = ? |
| So, 35 | − 24 | = 3 × 45 × 4 | − 2 × 54 × 5 | = 1220 | − 1020 | = 220 |
How to subtract fractions with whole numbers
Here are the three simple steps to follow when subtracting fractions with whole numbers.
Step 1
Convert the whole number into a fraction. You do this by using 1 as a denominator for the whole number.
Step 2
Look for the lowest common denominator. You just need to multiply 1 and the other denominator to get the lowest common denominator.
Step 3
Multiply the numerator and the denominator of the fraction in step 1 by the lowest common denominator.
Step 4
Subtract the fractions.
Example #5:
Subtract: 5 – 1/3
5 – 1/3 = 5/1 – 1/3 = 15/3 – 1/3 = (15 – 1)/3 = 14/3
Subtracting fractions and mixed numbers
When subtracting fractions with mixed numbers, just convert the mixed number into an improper fraction before subtracting.
Example #6:
7/3 – 1 2/3 = 7/3 – [(3 × 1 + 2) / 3]
7/3 – 1 2/3 = 7/3 – (5/3)
7/3 – 1 2/3 = (7 – 5)/3
7/3 – 1 2/3 = 2/3
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