Subtracting fractions
The process of subtracting fractions is more or less the same as that for adding fractions. When adding or subtracting fractions, we cannot just perform the operations on both numerator and denominator separately. If the fraction(s) being subtracted already have a common denominator, subtract the numerators as you would whole numbers while keeping the denominator the same. Otherwise we need to find a common denominator before we can subtract.
So, to subtract fractions:
- Make sure that the fractions you are subtracting have a common denominator (the number below the fraction bar)
- If the fractions don't share a common denominator, find a common denominator
- Once all fractions share a denominator, subtract the numerators of the fractions while keeping the denominator the same
- Write the new numerator (the result of the subtraction) above the shared denominator
- Simplify the fraction if necessary
Examples
1. Find the value of 
.
The numerators in this example could be directly subtracted since the fractions already had a common denominator. After subtracting, we simplified the fraction.
2. Find the value of 
.
For this example, the least common denominator is 35, so we converted both fractions to equivalent fractions with a denominator of 35, then subtracted.
Note that it is not necessary to use the least common denominator (any common denominator can be used) to subtract (or add) fractions, but doing so usually makes the problem easier to handle and less likely to require simplification.