Solve Word Problems: Adding and Subtracting Fractions and Mixed Numbers

Students solve real-world and mathematical word problems involving addition and subtraction of fractions and mixed numbers with like denominators. They identify the operation needed, set up equations, and interpret answers in context.

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Grade 4 · Adding and Subtracting Mixed Numbers · question 1 of 3

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20 rungs. A star at the top.

A sandbox is 2/8 full of sand. Ivy dumps in 3/8 more. How full is the sandbox?

How it is taught

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A mixture problem adds like parts of the same whole.

Tenths plus tenths can make another whole liter.

Read it: Draw the story on one bar

A fence is 1/4 painted, then 2/4 more is painted. Draw a bar in 4 pieces: 1 is shaded, 2 more join it, and 3 are shaded now. So 3/4 of the fence is painted.

Find the fractions in the story and the size of a piece: here, fourths.
Decide whether pieces join or leave: more paint means 2 pieces join.
Count the shaded pieces and keep the bottom number: 1/4 + 2/4 = 3/4.

Every piece in the story is a fourth of the same fence, so the pieces can be counted together.

Words like more and in all mean pieces join; words like left and used mean pieces leave.

If 1 piece of paint is washed off, 1 piece leaves: 3/4 − 1/4 = 2/4 is still painted.

Draw the story on one bar, decide whether pieces join or leave, then count them and keep the bottom number.

Adding the bottom numbers too, and writing 1/4 + 2/4 = 3/8.

3/8 is 3 pieces of a bar cut into 8, smaller pieces than these. The fence was not cut again, so the answer is 3/4.

3/6 + 2/6 = ___/6 — 5. 3 pieces and 2 more are 5 pieces, and every piece is still 1/6: 5/6.

2 3/8 + 1 4/8

Maya ran two and three-eighths miles on Monday, and one and four-eighths miles on Tuesday. How far did she run in all?

We're putting two distances together — that means we need to add.

Let's write it out: two and three-eighths plus one and four-eighths.

First, add the whole numbers. Two plus one.

That's three wholes.

Now the fraction parts. Both bottoms — the denominators — are eight.

When denominators match, we just add the top numbers: three plus four is seven.

Grade 4 · Maya's running miles

So three-eighths plus four-eighths is seven-eighths.

Seven-eighths is less than one whole, so we don't need to regroup.

Maya ran three and seven-eighths miles in all. Nice work!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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