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Express Whole Number Division as a Fraction or Mixed Number

Students practice expressing the result of dividing two whole numbers as a fraction or mixed number. For example, 7 ÷ 4 = 7/4 = 1 and 3/4. Students convert between improper fractions and mixed numbers in this context.

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Express Whole Number Division as a Fraction or Mixed Number

Grade 5 · Fractions as Division · question 1 of 3

0 of 20

20 rungs. A star at the top.

2 3/4 = 11 ÷

How it is taught

0:00 of 2:58

A whole-number division can be written as a fraction.

The dividend sits on top, and the divisor sits on 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.

Write 7 ÷ 6 as a mixed number. — 1 1/6. 7 ÷ 6 = 1 with remainder 1, so the mixed number is 1 1/6.

7 ÷ 4

Imagine seven pizzas to share fairly among four friends. How much pizza does each friend get?

We can write this as seven divided by four.

Here's the cool trick: every division can be written as a fraction.

The number we are dividing — seven — becomes the top, the numerator.

The number we divide by — four — becomes the bottom, the denominator.

Seven-fourths is an improper fraction because the top is bigger than the bottom, so it's more than one whole.

Let's turn it into a mixed number. How many whole fours fit inside seven? Just one.

That leaves three left over, which is three-fourths of another whole.

So seven-fourths equals one and three-fourths.

Look — one whole pizza plus three-fourths of another. That's seven-fourths!

Seven divided by four equals seven-fourths, or one and three-fourths. Each friend gets one and three-fourths pizzas!

7 pizzas, 4 friends — how much each?7÷4=?74numerator (top)denominator (bottom)7 > 4 → more than 1 wholeHow many 4s fit in 7?1 whole, with 3 left over3 left over → 34 of another whole=1341 whole+34 moreANSWER134pizzas each
Grade 5 · 7 pizzas shared among 4 friends

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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