Fraction Flip

Dividing Fractions by Fractions

NCSCOS 6.NS.1

The Big Question

When we divide whole numbers, we ask:
"How many groups of [X] fit into [Y]?"

\( 6 \div 2 = ? \)

How many 2s are in 6? (The answer is 3!)

Division with fractions is exactly the same!

The Area Model

\( \frac{1}{2} \div \frac{1}{4} \)

"How many one-fourths are in one-half?"

1 Draw a whole unit and shade \( \frac{1}{2} \).
2 Divide the entire whole into fourths.
3 Count how many fourths are in the shaded half.

1/2

1/4

There are 2 fourths! So, \( \frac{1}{2} \div \frac{1}{4} = 2 \)

The Number Line Model

\( \frac{3}{4} \div \frac{1}{8} \)

"How many jumps of \( \frac{1}{8} \) can I take to reach \( \frac{3}{4} \)?"

0

1/4

1/2

3/4

1

Count the jumps: 6 jumps of \( \frac{1}{8} \)!

So, \( \frac{3}{4} \div \frac{1}{8} = 6 \)

Procedural Power: Fraction Flip

Keep

The Dividend

Leave the first fraction exactly as it is.

Change

The Sign

Change division (\(\div\)) to multiplication (\(\times\)).

Flip

The Divisor

Flip the second fraction to find its reciprocal.

Why does flipping work?

Dividing by a fraction is the same as multiplying by how many of those fractions fit into a whole.

Think about \( 10 \div \frac{1}{2} \):

Every whole has 2 halves.
So 10 wholes have 10 × 2 halves.
\( 10 \div \frac{1}{2} = 10 \times 2 = 20 \).

The Secret Reciprocal

Original 2/3

Reciprocal 3/2

"When you multiply a number by its reciprocal, you always get 1!"

Real World: Sharing Snacks

Maya has \( \frac{2}{3} \) of a pound of granola. She wants to put them into bags that hold \( \frac{1}{6} \) of a pound each.

How many bags can she fill?

Set it up:

\( \frac{2}{3} \div \frac{1}{6} = ? \)

Flip & Solve:

\( \frac{2}{3} \times \frac{6}{1} = \frac{12}{3} = 4 \)

Answer: 4 Bags

Ready to Flip?

Try this one with a Number Line:

\( \frac{1}{2} \div \frac{1}{8} \)

Hint: How many 1/8s fit in 1/2?

Try this one with the Flip Method:

\( \frac{3}{5} \div \frac{1}{2} \)

Hint: Mixed number alert!

TIME TO PRACTICE!

Fraction Flip

Fraction Flip Slides

Fraction Flip Worksheet

Fraction Flip Teacher Guide

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