Divide fractions by fractions · lesson

Divide by flipping

💡 Dividing by a fraction is the same as multiplying by its reciprocal.

To divide by a fraction, flip the second fraction upside down. Then multiply. The flipped fraction is called the reciprocal.

A whole number can be written over 1. So 4 is 4/1, and its reciprocal is 1/4.

Multiply tops together and bottoms together. Then simplify.

🧠 Let's work it out

Find 4/5 ÷ 2/3.

What do you think comes next?

💡 "How many pieces of size b fit in a?" is the division a ÷ b.

If you ask how many small parts fit in a big amount, you are dividing.

When the piece is less than 1, the answer is bigger than the amount you started with. That makes sense: small pieces, so many of them.

🧠 Let's work it out

How many 2/5-liter cups fill 4 liters?

What do you think comes next?

💡 Sharing equally and finding a missing side are both division.

If friends share an amount equally, divide the amount by the number of friends.

For a rectangle, area = length × width. If you know the area and the width, divide the area by the width to get the length.

🧠 Let's work it out

A rectangle has an area of 5/8 square foot. Its width is 1/2 foot. How long is it?

What do you think comes next?

💡 Change a mixed number into a fraction before you divide.

A mixed number like 3 1/3 has a whole part and a fraction part. You can't flip it as it is.

Change it to a fraction first. Multiply the whole by the bottom, add the top, and keep the bottom.

🧠 Let's work it out

Find 3 1/3 ÷ 2/3.

What do you think comes next?