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Understand a Fraction as Division

Students learn that a fraction a/b represents the division a ÷ b. They connect fraction notation to division and explore this relationship using models such as sharing objects equally among groups.

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Understand a Fraction as Division

Grade 5 · Fractions as Division · question 1 of 3

0 of 20

20 rungs. A star at the top.

5/6 = 5 ÷

How it is taught

0:00 of 3:02

A fraction is a division.

The top is divided by the bottom.

Read it: A fraction is a division

3 ÷ 10 means 3 shared equally among 10. Cut each of the 3 bars into 10 pieces, and each share takes 1 piece from every bar: 3 pieces of 1/10, which is 3/10.

  1. Draw the amount being shared: 3 bars.
  2. Cut every bar into as many pieces as there are shares: 10.
  3. One share takes one piece from every bar: 3 pieces of 1/10 is 3/10.

Each bar gives every share 1 piece of 1/10, and there are 3 bars, so a share gets 3 tenths.

The amount shared goes on top and the number of shares goes underneath: 3 ÷ 10 = 3/10.

When there is more to share than there are shares, each share is more than 1 whole: 7 ÷ 4 = 7/4.

To divide a whole number by a whole number, write the amount shared over the number of shares: 3 ÷ 10 = 3/10.

Writing 3 ÷ 10 as 10/3, with the numbers backward.

The 3 bars are what is shared, so 3 goes on top: 3/10, less than 1 bar for each share.

2 ÷ 9 = ___ — 2/9. Cut each of the 2 bars into 9: one share takes 2 pieces of 1/9, which is 2/9.

3 ÷ 4 = 3/4

Imagine three sandwiches shared equally between four friends. How much does each friend get?

We can write this as three divided by four.

But three is smaller than four — how can we divide it?

Let's draw the three sandwiches as three bars.

We cut each sandwich into four equal pieces — one piece for each friend.

Each friend gets one piece from every sandwich. That's three pieces in all.

Each piece is one fourth, so each friend gets three fourths of a sandwich.

So three divided by four equals three fourths.

3 sandwiches, 4 friends — how much each?3 ÷ 4 = ?3 is smaller than 4 — can we still divide?1 piece + 1 piece + 1 piece = 3 pieces343 ÷ 4 = 34a/b = a ÷ ba fraction IS a divisionANSWER34per friend
Grade 5 · Sharing 3 sandwiches between 4 friends

The big idea: a fraction a over b means a divided by b.

Three divided by four is three fourths. Fractions are division!

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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