How to add fractions with different denominators

A fraction names equal parts of a whole. The denominator tells you how many equal parts make the whole; the numerator tells you how many of those parts you have. Before adding, both fractions must refer to parts of the same size.

A worked example

Calculate 5/12 + 1/6. Twelfths and sixths are different-sized parts, so first rewrite 1/6 as 2/12. Multiplying its numerator and denominator by 2 preserves the fraction's value.

Now add equal-sized parts: 5/12 + 2/12 = 7/12. The numerator 7 and denominator 12 have no common factor greater than 1, so the result is already simplified.

Why adding denominators fails

Adding across would produce 6/18 = 1/3. But 5/12 is already greater than 1/3, and adding a positive number cannot make it smaller. This estimate exposes the mistake without repeating the calculation.

The common denominator does not have to be the smallest possible one. A smaller common denominator usually makes the arithmetic easier, while any valid common multiple can still give the correct result after simplification.

Try another question

Find 2/5 + 3/10 before reading on. Rewrite 2/5 as 4/10, then add 4/10 + 3/10 = 7/10. Explain why the denominator stays 10.

What should I practise next?

Check whether your difficulty is finding common multiples, making equivalent fractions or simplifying. Practise that step separately. Then use the original examples on the mathematics page or create one flashcard for the rule you forgot.