Dividing a Fraction by a Fraction

Step 1: Let's Learn

Read it, or press Listen and follow the words.

3/4 ÷ 1/8 asks how many eighths fit into three quarters.

Count them

3/4 is 6/8, and 6 eighths hold 6 single eighths. The answer is 6.

There is a shortcut, and it has a name.

Reciprocal is a fraction turned upside down. The reciprocal of 1/8 is 8.

Why turning it over works

Each whole holds 8 eighths, so counting eighths means multiplying by 8. That is the reciprocal.

How many of these fit into that

3/4 ÷ 1/8 asks how many eighths fit into three quarters. Since 3/4 is 6/8, the answer is 6. Reading division as a fitting question keeps it meaningful when the numbers stop being whole.

Multiply by the reciprocal

The rule is to flip the second fraction and multiply: 3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6. The reciprocal of a fraction is that fraction turned upside down, and multiplying by it undoes division by the original.

Why flipping works

Dividing by 1/8 asks how many eighths fit, and each whole holds 8 of them — so dividing by 1/8 is the same as multiplying by 8. In general, dividing by a/b is multiplying by b/a. The rule is not arbitrary; it is that observation generalised.

Predict the size first

Dividing by a fraction less than one gives a bigger answer; dividing by one greater than one gives a smaller one. 3/4 ÷ 1/8 should be considerably bigger than 3/4, and 6 is. Predicting the direction catches a flipped reciprocal immediately.

Step 2: Try It Yourself

Tap and try it out.

Set both fractions and see how many of the second fit into the first.

3/4

1/8

3/4 is greater than 1/8.

Compare how much of the whole each one covers.

First top number

First bottom number

Second top number

Second bottom number

Step 3: Watch an Example

One step at a time.

Watch Ana Work Out 2/3 ÷ 1/6

Ana divides one fraction by another.

Step 1
She reads it as: how many sixths fit into two thirds?

Step 4: Your Turn

Practice makes it stick.

The Ribbon

Problem 1 of 2

3/4 metre cut into pieces of 1/8 metre. How many pieces?

pieces

The Juice

Problem 2 of 2

2/3 litre poured into 1/12 litre cups. How many cups?

cups

How Many Fit?

1 of 4

1/2 ÷ 1/6 = ?

2 of 4

3/5 ÷ 1/10 = ?

3 of 4

2/3 ÷ 1/3 = ?

4 of 4

What is the reciprocal of 1/5?

Step 5: Quick Check

Show what you know.

Question 1 of 2

3/4 ÷ 1/12 = ?

Question 2 of 2

Why does dividing by a fraction mean multiplying by its reciprocal?

What You Learned

Dividing by a fraction asks how many fit.
Multiplying by the reciprocal is the shortcut.
The reciprocal counts how many pieces are in one whole.