Subtracting Fractions
Like fractions
Fractions with the same denominators are called like fractions.
For instance:
Example 1-In the picture below, all the fractions are like fractions.
Unlike fractions
Fractions with different denominators are known as unlike fractions.
Subtracting fractions
It is easier to add or subtract like fractions because either they are equal parts from the same whole or they are the parts of the same size.
Case 1- Subtracting like fractions
- Subtract the numerator and it will give us the answer.
- Simplify the fraction, if required.
For instance:
Example 2- Subtract from 3 15 from 12 15 .
Solution: As both, the fractions are like fractions
∴ 1215–315 = 12-3 15 = 9 15
As 9 15 can be simplified, ∴ the final answer is 3 5 .
Case 2- Subtracting unlike fractions
Below are the steps to subtract unlike fractions:
- Find the least common multiple (LCM) of the denominators.
- Change the denominator to the LCM by multiplying the numerator and the denominator by the same number.
- Once the fractions have the same denominators, subtract the numerators of the fractions.
- The difference between the numerator and the LCM will be the numerator and the denominator of the answer respectively.
- Simplify the fraction, if required.
- For instance:
Example 3- Subtract 4 7 from 3 5 .
Solution – We have to find, 3 5 – 4 7
As both the fractions are unlike fractions (different denominators), we need to make the denominators the same for subtraction.
The least common multiple of 7 and 5 is 35 .
To make the denominators 35, the fraction 3 5 can be written as 3×7 5×7 = 21 35 and the fraction 4 7 can be written as 4×5 7×5 = 20 35 .
Now, the question can be rewritten as 21 35 – 20 35 .
As the denominators are the same, &there 21 35 – 20 35 = 1 35
Since, 1 35 is in the simplest form, therefore the final answer is 1 35 .
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