Solve Division Word Problems with Fraction or Mixed Number Answers

Students solve real-world problems where dividing whole numbers produces a fractional or mixed number answer. They interpret what the fraction means in context — for instance, splitting 5 sandwiches equally among 8 people means each person gets 5/8 of a sandwich.

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Grade 5 · Fractions as Division · question 1 of 3

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20 rungs. A star at the top.

Three loaves are shared equally among 5 children. How much of a loaf does each child get?

How it is taught

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Sharing can leave a fraction for each person.

The quotient is the dividend over the divisor.

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.

Draw the amount being shared: 3 bars.
Cut every bar into as many pieces as there are shares: 10.
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.

4 pizzas are shared equally among 7 friends. How much pizza does each friend get? — 4/7. 4 ÷ 7 = 4/7: each friend gets 1 piece of 1/7 from each of the 4 pizzas.

5 candy bars shared among 4 friends

Four friends want to share five candy bars equally. How much does each friend get?

We can write the problem as five divided by four.

Here are our five candy bars, lined up in a row.

First, give each friend one whole bar. That uses four of the five bars.

One bar is still left over, and all four friends still want their fair share.

Cut the leftover bar into four equal pieces, one piece for each friend.

Each friend gets one extra piece — that's one-fourth of a bar.

Grade 5 · When dividing whole numbers gives a mixed number

Add it up: one whole bar plus one-fourth equals one and one-fourth bars.

We can also write the answer as five-fourths — five pieces, each one-fourth of a bar.

So five divided by four equals one and one-fourth. Each friend gets one and one-fourth candy bars.

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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