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Solve Real-World Problems Dividing Unit Fractions and Whole Numbers

Students solve real-world and mathematical problems involving division of unit fractions by whole numbers and whole numbers by unit fractions. They interpret division situations as fair-sharing or measurement, set up equations, and explain their solutions in context.

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Solve Real-World Problems Dividing Unit Fractions and Whole Numbers

Grade 5 · Dividing with Unit Fractions · question 1 of 3

0 of 20

20 rungs. A star at the top.

Diego has 2 pints of cream. He pours one fourth of a pint into each tart. How many tarts can he fill?

How it is taught

0:00 of 3:38

Measurement division asks how many unit-size groups fit.

A unit fraction as the serving size makes more groups than the whole.

Read it: Share one piece

1/3 of a whole is shared among 4. Cut every row into 4 and the whole holds 12 equal cells, so each share is 1/12 of the whole: 1/3 ÷ 4 = 1/12.

  1. Shade the piece you start with: 1 row out of 3 is 1/3.
  2. Cut that row into as many shares as you divide by: 4.
  3. Cut every row the same way and count the cells: 3 × 4 = 12, so one share is 1/12.

A share is a part of the whole, so count every cell in the whole, not only the cells in the one row.

3 rows of 4 make 12 equal cells, and one cell is 1/12 of the whole.

Sharing makes each share smaller than the piece: 1/12 is less than 1/3.

To divide a unit fraction by a whole number, multiply its denominator by that number: 1/3 ÷ 4 = 1/12.

Reading 1/3 ÷ 4 as 1/3 taken 4 times, and writing 4/3.

Dividing shares the 1/3 out, so each share is smaller than 1/3: 1/3 ÷ 4 = 1/12.

Elise splits one fifth of a mile of path equally among 6 walkers. How much of a mile does each walker cover? — 1/30. 5 rows, each cut into 6: 30 cells in the whole, so each share is 1/30 of it.

2 ÷ 1/4

Maya has two cups of trail mix. She wants to scoop it into bags, with one-fourth cup in each bag. How many bags will she fill?

We can write this as a division: two divided by one-fourth equals what?

Let's draw a number line from zero to two — Maya's two cups of trail mix.

Each whole cup splits into four equal one-fourth pieces.

We count the scoops: one, two, three, four in the first cup.

Five, six, seven, eight in the second cup.

Eight one-fourths fit inside two. So two divided by one-fourth is eight.

Quick check — dividing by one-fourth is the same as multiplying by four. Two times four is eight.

2 cups → 14-cup scoops?How many bags can Maya fill?2÷14=?8021021cup 1cup 212345678÷ 14 is the same as × 42 × 4 = 8ANSWER8bags
Grade 5 · 2 cups of trail mix into ¼-cup scoops

Maya fills eight bags. Great job thinking with fractions!

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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