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How to Subtract Fractions
The numerator of a fraction tells us the number of parts of the whole that we have. It is written above the line in a fraction. The denominator of a fraction tells us the total number of equal parts that something has been divided into. It is written below the line in a fraction.
In order to subtract fractions, the fractions need to have the same denominator. We call this a common denominator. We can subtract fractions with a common denominator easily because the whole is divided into parts of the same size.
In the equation above, we are subtracting two quarters from three quarters. Our answer is going to tell us how many quarters we have left. The denominator stays the same since both fractions are shown in quarters and we subtract 2 from 3 to find out the numerator. This gives us an answer of 1/4 (one quarter).
As you can see below, the same process applies when subtracting any improper fractions.
If the fractions have different denominators, it is harder to subtract them because the parts are not the same size. As you can see in the picture below, 2/3 can be subtracted from 3/4, however, the remaining amount is neither in quarters or thirds. We need to find a common unit for the amounts we're working with.
We can do this by finding the Lowest Common Multiple (LCM) of our denominators. This number will need to be a multiple of both 3 and 4.
Multiples of 3: 3, 6, 9, 12, 15
Multiples of 4: 4, 8, 12, 16, 20
LCM of 3 & 4: 12
Now we multiply each fraction by a fraction equivalent to 1 to get that LCM as the denominator for each fraction. In this case we multiply by 3/3 and 4/4:
9/12 is equivalent to 3/4 and 8/12 is equivalent to 2/3. The difference now is that both of our fractions have the same denominator. With common denominators, we can subtract the numerators to find out how many parts we have left:
9/12 - 8/12 gives us 1/12, which is our answer!
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