Compute a Whole Number Divided by a Unit Fraction

Students calculate quotients when dividing a whole number by a unit fraction. They apply the rule that dividing by 1/n is the same as multiplying by n, and use this to efficiently compute answers. For example, 5 ÷ (1/3) = 5 × 3 = 15.

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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.

Yusuf has 3 oranges at the beach. He cuts every orange into pieces that are each 1/2 of an orange. How many pieces does he get?

How it is taught

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Dividing by a unit fraction asks how many of those bits fit.

Dividing by 1/4 is the same as multiplying by 4.

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.

6 ÷ 1/3 = ___ — 18. 6 bars, each cut into 3: 18 pieces. More than 6, because the pieces are smaller than a bar.

3 ÷ 1/4 = 12

Imagine you have three whole pizzas, and you want to cut each one into quarters. How many slices will you have?

Let's split each pizza into four equal pieces — that's fourths.

Count them up: four, eight, twelve. Twelve slices in all!

In math, this is three divided by one-fourth.

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

So we can rewrite the problem as three times four.

Three times four equals twelve.

That matches the twelve slices we counted — the trick works!

Grade 5 · Dividing by a unit fraction means multiplying

So three divided by one-fourth is twelve. Dividing by one-over-n means multiplying by n.

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

Leads to

Solve Real-World Problems Dividing Unit Fractions and Whole Numbers

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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