Interpret Fraction Division in Context

Students solve real-world and mathematical problems by dividing fractions and mixed numbers, translating between the abstract computation and its meaning in the situation. They write equations, compute the answer, and verify it makes sense.

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Grade 6 · Number System: Fractions and Division · question 1 of 3

0 of 20

20 rungs. A star at the top.

÷ 1/2 = 14

How it is taught

0:00 of 5:02

Fraction division can ask how many groups of a size fit.

The answer can be greater than 1.

Read it: How many pieces fit?

4 bars, each cut into 3 equal pieces: 12 pieces of 1/3. So 4 ÷ 1/3 = 12, more than 4, because each piece is less than 1 bar.

Draw the amount you start with: 4 bars.
Cut every bar into pieces the size you divide by: 1/3 of a bar.
Count the pieces in every bar: 4 × 3 = 12.

Dividing by 1/3 asks how many thirds fit, not how to split 4 into 3 parts.

Each bar holds 3 pieces of 1/3, so 4 bars hold 4 × 3 = 12 of them.

Each piece is smaller than 1 bar, so there are more pieces than bars: 12 is more than 4.

To divide by a unit fraction, count the pieces that fit: 4 ÷ 1/3 = 4 × 3 = 12.

Reading 4 ÷ 1/3 as 4 split into 3 parts, and writing 4/3.

Count the thirds in 4 bars instead: 12 pieces, more than 4.

7 ÷ 1/4 = ___ — 28. 7 bars, each cut into 4: 28 pieces. More than 7, because the pieces are smaller than a bar.

3/4 ÷ 1/2

You have three-fourths of a cup of yogurt. Each serving is one-half of a cup. How many servings can you make?

We can write this as three-fourths divided by one-half.

Let's draw it. Here's a whole cup, split into four equal parts.

Three of those parts are filled — that's our three-fourths cup of yogurt.

One serving is one-half — that covers two of the four parts.

So how many one-half servings fit inside three-fourths? One full serving, plus a little more.

Grade 6 · How many 1/2-cup servings in 3/4 cup of yogurt?

To compute it, we use Keep–Change–Flip. Keep the first fraction the same.

Change divide into multiply.

And flip the second fraction — one-half becomes two over one.

Now multiply across: three times two is six, four times one is four.

Six-fourths simplifies to one and one-half.

So three-fourths divided by one-half is one and a half servings. The math matches our picture!

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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