Adding and subtracting fractions with same denominator

When both fractions count the same size of piece, adding them is just counting pieces. Three fourths and two fourths make five fourths, the way three apples and two apples make five apples. The denominator names the piece, so it does not get added.

What the page adds is the second step. Problem 1 shows 5/4 becoming 1 1/4 by a short long division, and problems 3 and 5 ask for the same move after simplifying, so 16/10 becomes 8/5 and then 1 3/5.

The standard is 4.NF.B.3.a, joining and separating parts of the same whole, a Grade 4 idea that 6th graders revisit here before unlike denominators.

Before you hand the sheet over, look at page 1. Only problem 1 shows its fractions; problems 2 to 6 print the instruction and nothing else. The fractions for those five appear only on the answer page, so copy them onto page 1 yourself and keep page 2 folded away.

At the table, watch problem 3. Most slips here come from adding tops and bottoms: 7/10 + 9/10 written as 16/20. Ask, "If you add tenths to tenths, what size are the pieces?" Your child usually catches it alone.

A note for parents on problem 4: the answer box prints a plus sign, yet the work above it is 13/7 - 9/7 = 4/7, which is right.

Cut the next pizza into eight slices and keep score as it disappears. "We had 8/8 and someone ate 3/8. What is left?" The answer stays in eighths, which is the whole point of this page.

In the kitchen, a measuring cup marked in fourths does the same job: pour 3/4 cup, add 2/4 more, and let your child explain why one cup is not enough.

Full House: An Invitation to Fractions by Dayle Ann Dodds follows one cake shared among the guests of an inn, slice by slice, a gentle story about parts of the same whole.

Name the effort you saw: "You kept the denominator and counted the pieces." Next in the series: adding and subtracting fractions with unlike denominators.