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Solve Addition Word Problems with Unlike Fraction Denominators

Students solve real-world addition problems involving fractions and mixed numbers with unlike denominators. They interpret the problem, select an operation, convert fractions to a common denominator, and evaluate the reasonableness of their answer.

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Solve Addition Word Problems with Unlike Fraction Denominators

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

0 of 20

20 rungs. A star at the top.

Lily ate 1/2 of a cracker bar at recess and 1/8 of the same bar after lunch. How much of the bar did she eat?

How it is taught

0:00 of 3:32

Unlike denominators need a common bottom before you add.

The total is the sum of the renamed fractions.

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.

  1. Find the two amounts in the story, and whether they go together or one is taken away.
  2. Cut both into the same pieces: 1/6 is 2/12, and 7/12 stays 7/12.
  3. 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.

1/5 + 7/10 = ___ — 9/10. Cut both bars into 10: 1/5 is 2/10 and 7/10 stays 7/10. Together that is 9/10.

1/2 + 1/3

Maya ran one-half of a mile, then jogged one-third of a mile more. How far did she run in all?

We need to add: one-half plus one-third equals what?

Look at the pieces. Halves are bigger than thirds, so we can't add them yet — they're not the same size!

We need a common denominator. The smallest number both two and three fit into is six.

Maya ran 12 mile, then 13 mile more.How far did she run in all?Add fractions with unlike denominators12+13=?12 mile13 mileDifferent-size pieces — can't add yet.Multiples of 2: 2, 4, 6Multiples of 3: 3, 6Common denominator: 6× 33× 223626+=5656 < 1 whole — and bigger than 12. ✓ANSWER56mile total
Grade 5 · Maya's morning run

Multiply one-half by three over three. One-half is the same as three-sixths.

Multiply one-third by two over two. One-third is the same as two-sixths.

Now we can add: three-sixths plus two-sixths.

Add the numerators: three plus two is five. The denominator stays six.

Does five-sixths make sense? Yes — it's less than one whole mile, and bigger than each piece we started with.

Maya ran five-sixths of a mile in all. Nicely done!

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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