Solve Subtraction Word Problems with Unlike Fraction Denominators

Students solve real-world subtraction problems involving fractions and mixed numbers with unlike denominators, including scenarios such as finding how much remains or how much more one quantity is compared to another.

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Grade 5 · Fraction Addition and Subtraction Word Problems · question 1 of 3

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20 rungs. A star at the top.

Finn ran 5/8 mile. Ava ran 1/4 mile farther than Finn. How far did Ava run?

How it is taught

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Unlike denominators must match before you subtract.

How much remains means start with what you had and take away what was used.

Read it: Stories with two cuts

Ana pours 1/6 cup, then 7/12 cup more. Cut each sixth in 2: 1/6 is 2/12, and 2/12 + 7/12 = 9/12, which is 3/4 cup. Pouring 1/6 cup back out leaves 9/12 − 2/12 = 7/12 cup.

Find the two amounts in the story, and whether they go together or one is taken away.
Cut both into the same pieces: 1/6 is 2/12, and 7/12 stays 7/12.
Add or take away the numerators, and keep the story's unit: 9/12 is 3/4 cup.

A story's amounts are fractions of the same whole, a cup here, so they can be counted together once the pieces match.

"In all" and "more" put the amounts together; "left", "used" and "how much more" take one away.

An answer is checked against the story: a total is more than either amount, and what is left is less than what there was.

Write both amounts in a common denominator, add or subtract as the story says, and give the answer in the story's unit.

Adding the tops and the bottoms: 1/6 + 7/12 = 8/18 cup.

8/18 cup is less than the 7/12 cup alone, so it cannot be the total. Cut both into twelfths: 2/12 + 7/12 = 9/12, which is 3/4 cup.

2/5 − 3/10 = ___ — 1/10. Cut both bars into 10: 2/5 is 4/10 and 3/10 stays 3/10. Take 3 tenths from 4: 1/10.

3/4 − 1/3

Maya had three-fourths of a cup of juice. She drank one-third of a cup. How much juice is left?

We can write this as three-fourths minus one-third.

But look closely — the denominators are different. Four and three. We can't subtract yet.

We need a common denominator. The smallest number that both four and three fit into is twelve.

Change three-fourths into twelfths. Multiply the top and bottom by three to get nine-twelfths.

Change one-third into twelfths. Multiply the top and bottom by four to get four-twelfths.

Now both fractions have the same denominator. We're ready to subtract.

Grade 5 · How much juice is left?

Subtract the numerators: nine minus four is five. Keep the denominator the same — twelve.

Five-twelfths means five out of twelve equal pieces of a cup.

So three-fourths minus one-third equals five-twelfths. Maya has five-twelfths of a cup left. 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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