Adding Fractions with Unlike Denominators

Begin with one worked example in full: list multiples of each denominator, pick the first shared one, convert both fractions, add, then simplify. Hand out the page and plan for about twenty minutes. Ask students to write the common denominator on the side so the work is easy to read. When checking, accept any correct common denominator, because the key shows only the final answer in lowest terms. Make five versions to give a second try.

This is the step where fraction arithmetic gets harder. Children need equivalent fractions, multiples and adding like denominators all at once. The usual slip is adding the tops and the bottoms separately, so 1/2 + 1/3 becomes 2/5. Another is stopping at an unreduced or improper answer. At Up to 6 some pairs have one denominator that divides the other, as in 1/2 + 3/8, which needs just one conversion. Larger settings use pairs with no shared factor.

Begin with Up to 6, where denominators are small and the common one is easy to see. Move to Up to 10 or Up to 12 once the routine is steady. Multiplying the two denominators always works, even if the answer then needs a bigger reduction. Twelve problems are enough on the first day. Missing number mode asks the student to find an unknown fraction, which is a good test of understanding.

Does the key use the least common denominator?

The key shows the final answer in lowest terms, whichever common denominator the student used. Multiplying the denominators works on every problem here, but may leave a bigger reduction at the end.

Why is 1/2 + 1/3 not 2/5?

Because halves and thirds are different sized pieces, so the pieces cannot be counted together. Convert both to sixths first: 3/6 + 2/6 makes 5/6. A picture with two bars makes the point fast.

What makes some problems easier than others?

When one denominator divides the other, only one fraction needs converting, as in 1/2 + 3/8. With pairs like 2/3 + 3/4, both fractions change, which takes more steps.