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Understand Division of a Unit Fraction by a Whole Number

Students interpret what it means to divide a unit fraction by a non-zero whole number, such as (1/3) ÷ 4. Using visual models, they see that dividing 1/3 into 4 equal parts gives each part a size of 1/12. Students connect the operation to sharing scenarios.

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Understand Division of a Unit Fraction by a Whole Number

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

0 of 20

20 rungs. A star at the top.

(1/4) ÷ 3 =

How it is taught

0:00 of 3:44

A unit fraction has 1 on top.

Sharing that piece among more people makes a smaller unit fraction.

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.

1/6 ÷ 6 = ___ — 1/36. 6 rows, each cut into 6: 36 cells in the whole, so each share is 1/36 of it.

(1/3) ÷ 4

Imagine you have one-third of a pizza, and you want to share it equally between four friends. How much does each friend get?

Here's our whole pizza split into three equal parts. The orange piece is one-third.

We start with one-third — one out of three equal parts of the whole pizza.

To share with four friends, we cut that one-third into four equal slices.

Now the orange third has four tiny slices inside it. Each friend gets one slice.

Sharing 13 of a pizza with 4 friendsHow much does each friend get?(13) ÷ 4 = ?the whole pizza134 equal slices12 equal pieces in the whole11213 ÷ 4 = 112ANSWER112for each friend
Grade 5 · Sharing 1/3 of a pizza between 4 friends

But how big is each slice compared to the whole pizza? Let's cut every third the same way.

The whole pizza now splits into twelve equal pieces — twelfths.

Each friend's slice is one of those twelfths. So each friend gets one-twelfth of the whole pizza.

We write this as: one-third divided by four equals one-twelfth.

One-third divided by four is one-twelfth. Each friend gets a tiny twelfth-slice. Great thinking!

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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