Plus and Minus (Different Denominators)
21 October 2026
Adding and subtracting different denominator fractions
When working with fractions that have different denominators, you cannot simply add or subtract the top numbers. The denominators must match before you can combine the fractions.
Finding a common denominator
To add or subtract fractions with different denominators, first find the lowest common denominator. This is the smallest number that both denominators divide into. For example, with 2/3 + 1/4, the denominators are 3 and 4. The lowest common denominator is 12.
Converting to equivalent fractions
Rewrite each fraction so that both have the common denominator. For 2/3, multiply the numerator and denominator by 4, giving 8/12. For 1/4, multiply the numerator and denominator by 3, giving 3/12.
Worked example
2/3 + 1/4
2/3 = 8/12 1/4 = 3/12
Add the numerators: 8 + 3 = 11 Keep the denominator: 12
The answer is 11/12.
Simplifying and subtracting
If the answer can be simplified, do so. The same method applies for subtraction: find the common denominator, convert the fractions, then subtract the numerators and keep the denominator the same.
Key insight: Always check that fractions have the same denominator before adding or subtracting. This ensures the pieces you are working with are the same size, making the calculation correct and clear.
