Understand Division of a Whole Number by a Unit Fraction

Students interpret what it means to divide a whole number by a unit fraction, such as 3 ÷ (1/4). Using models, they understand this as asking 'how many one-fourths fit into 3?' and connect the operation to measurement/grouping division.

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

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20 rungs. A star at the top.

6 ÷ (1/8) = .

How it is taught

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A unit fraction is one equal part of a whole.

One part of 5 equal parts is 1/5.

Read it: How many unit fractions fit?

4 ÷ 1/4 asks how many pieces of 1/4 fit in 4. Each bar holds 4 fourths, so 4 bars hold 4 × 4 = 16 of them: 4 ÷ 1/4 = 16.

Draw the whole number as bars: 4 bars.
Cut every bar into pieces the size of the unit fraction: fourths.
Count every piece: 4 bars of 4 pieces is 4 × 4 = 16.

Dividing by 1/4 asks how many fourths fit in 4, not how to share 4 into 4 parts.

Each bar holds 4 pieces of 1/4, so 4 bars hold 4 × 4 = 16 of them.

Each piece is smaller than 1 bar, so there are more pieces than bars: 16 is more than 4.

To divide a whole number by a unit fraction, multiply it by the denominator: 4 ÷ 1/4 = 4 × 4 = 16.

Reading 4 ÷ 1/4 as 4 shared into 4 parts, and writing 1.

Count the fourths in 4 bars instead: 16 pieces, more than 4.

5 ÷ 1/5 = ___ — 25. 5 bars, each cut into 5: 25 pieces. More than 5, because the pieces are smaller than a bar.

3 ÷ 1/4

Imagine three big pancakes. We slice each one into quarter-pieces. How many pieces do we get in all?

We can write this as three divided by one-fourth. Dividing by a fraction asks a question: how many one-fourths fit inside three?

Here's our first whole pancake, cut into four equal quarters.

That's four one-fourths so far.

Now the second pancake — also cut into four quarters.

Four plus four more — that's eight one-fourths.

And the third pancake — four more quarters.

Eight plus four more — twelve one-fourths altogether.

So three divided by one-fourth equals twelve. Twelve quarter-pieces from three pancakes!

Grade 5 · How many one-fourths fit in 3?

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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Standards

CCSS.5.NF.B.7

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions

CCSS.5.NF.B.7b

Interpret division of a whole number by a unit fraction, and compute such quotients

Grade 5

Quoted from the Common Core State Standards.

Where this sits

Comes after

Understand Division of a Unit Fraction by a Whole Number

Leads to

Compute a Whole Number Divided by a Unit Fraction

What a star here means

A star here is the top of a twenty-rung ladder, in four blocks of equal length — three of facts and one of the skill used in a real question — where a right answer climbs one rung and a wrong one drops back to the start of the block, never below it. The star is kept for good. How we grade

All of Grade 5

This is one rung of 81 in Grade 5 mathematics, in the order they build on each other.

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