How to Subtract two Fractions with Different Denominators
Fractions with different denominators cannot be subtracted directly. The following steps are required in order to subtract fractions with unlike denominators:
- Find the Lowest Common Multiple (lcm) of both denominators.
- Once the lcm has been determined, scale up the numerators and denominators of both fractions to get a common denominator.
- Once both fractions have the same denominator, the numerators can then simply be subtracted from eachother.
For example, to determine the difference of these fractions:
(two and three-quarters minus one and two-thirds)
Step 1 : Convert both fractions to vulgar fractions, by multiplying the whole number by the denominator and adding the result to its numerator:
|(2 x 4) + 3|
|(1 x 3) + 2|
Determine a common denominator for both fractions, by finding the Lowest Common Multiple (lcm) of the denominators (4 and 3).
In this example, since 3 is a prime number, this means that there are no common factors, and the lcm is simply 4 x 3 = 12. So we need to 'scale up' both fractions to a denominator of 12, by multiplying both numerator and denominator:
|11 x 3 - 5 x 4|
|3 x 4|
|33 - 20|
Step 3: As a final step for all types of fraction arithmetic, remember to check the result for fractions which can be reduced to its simplest form (i.e. where the numerator and denominator can be divided out by a common factor, and to extract any whole numbers if the result is an improper fraction).
In this example, the result 13/12 is an improper fraction, and the numerator needs to be divided through by the denominator:
And voila! Our two fractions with different denominators have been subtracted!
Check the answer to this, and other fraction problems by using our Fraction Calculator!