Adding Fractions with Like Denominators

Begin with a quick picture: three sixths plus two sixths is five sixths, five pieces of the same size. Then give the sheet. Twenty problems take about twelve minutes. Remind students to check whether each sum can be reduced or turned into a mixed number, since the key writes answers that way, for instance 5/6 + 4/6 as one and a half. Mark with the key and ask children to read their answers aloud as a full sentence. Choose twelve for a gentle start.

The idea is that fractions with the same denominator count the same kind of piece, so only the number of pieces changes. The most common error is adding the denominators too, writing 2/6 + 3/6 = 5/12. Students also forget to reduce, or leave an answer as an improper fraction when the key wants a mixed number. Identifying fractions and equivalent fractions come first. Adding unlike denominators comes after, and it adds a step of finding common pieces.

Up to 6 keeps sums small and easy to draw. Up to 10 and Up to 12 give more chances for sums that pass one whole. Use twelve problems the first day and twenty after. Have a student draw a bar for one problem to show why the denominator does not change. If the page is easy, try Missing number mode to ask for the second fraction.

Do any sums go over one whole?

Yes, on many problems. Numerators can add past the denominator, and the key writes the result as a mixed number in lowest terms. The Denominators control sets how large they get.

Why do students add the denominators?

It seems natural, since both numbers are being added. Show it with a picture: two eighths plus three eighths cannot become eighths of sixteen. The pieces stay the same size, so the bottom number does not change.

Do students need to simplify their answers?

The key shows lowest terms, so tell students ahead of time whether you require it. Many fourth grade programs expect it. A quick rule: check if the top and bottom share a factor.