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Compute a Unit Fraction Divided by a Whole Number

Students calculate quotients of unit fractions divided by whole numbers. They apply the rule that dividing by a whole number n is the same as multiplying by 1/n, and verify results using diagrams. For example, (1/3) ÷ 4 = 1/3 × 1/4 = 1/12.

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Compute a Unit Fraction Divided by a Whole Number

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

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20 rungs. A star at the top.

1/5 ÷ 2 =

How it is taught

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Dividing a unit fraction by a whole splits it into smaller equal bits.

Dividing by a whole is multiplying by its reciprocal.

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.

1/5 ÷ 8 = ___ — 1/40. 5 rows, each cut into 8: 40 cells in the whole, so each share is 1/40 of it.

(1/3) ÷ 4 = 1/12

Imagine you have one-third of a pizza, and four kids want to share it equally.

Here's our pizza as a bar — the shaded part is one-third.

We can write this as one-third divided by four.

Let's split that one-third into four equal pieces — one for each kid.

Splitting the third into four makes twelve tiny pieces across the whole bar.

Each kid's piece is one out of twelve — that's one-twelfth.

Here's a handy shortcut: dividing by four is the same as multiplying by one-fourth.

So one-third divided by four becomes one-third times one-fourth.

Multiply the numerators on top: one times one is one.

Multiply the denominators on the bottom: three times four is twelve.

Share 13 among 4 kids — how much each?one-third of the pizzaeach piece = 112 of the whole13÷4÷ 4 = × 1413×14=112ANSWER112each kid's share
Grade 5 · Splitting one-third equally among four kids

Our answer is one-twelfth.

One-third divided by four is one-twelfth — each kid gets one-twelfth of the pizza.

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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