# Dividing Fractions

Turn the second fraction upside down, then multiply.

## There are 3 Simple Steps to Divide Fractions:

 Step 1. Turn the second fraction (the one you want to divide by) upside down (this is now a reciprocal). Step 2. Multiply the first fraction by that reciprocal Step 3. Simplify the fraction (if needed)

### Example:

 1 ÷ 1 2 6

Step 1. Turn the second fraction upside down (it becomes a reciprocal):

 1 becomes 6 6 1

Step 2. Multiply the first fraction by that reciprocal:

(multiply tops ...)

 1 × 6 = 1 × 6 = 6 2 1 2 × 1 2

(... multiply bottoms)

Step 3. Simplify the fraction:

 6 = 3 2

### With Pen and Paper

And here is how to do it with a pen and paper (press the play button):

"Dividing fractions, as easy as pie,
Flip the second fraction, then multiply.
And don't forget to simplify,
Before it's time to say goodbye"

 Another way to remember is: "leave me, change me, turn me over"

### How Many?

A question like 20 divided by 5 is asking "how many 5s in 20?" (=4)

So 1/2 divided by 1/6 is asking "how many 1/6s in 1/2"

 1 ÷ 1 is really asking: 2 6
 How many 1 in 1 ? 6 2

Now look at the pizzas below ... how many "1/6th slices" fit into a "1/2 slice"?

 How many in ? Answer: 3

 So now you can see why 1 ÷ 1 = 3 2 6

### Another Example:

 1 ÷ 1 8 4

Step 1. Turn the second fraction upside down (the reciprocal):

 1 becomes 4 4 1

Step 2. Multiply the first fraction by that reciprocal:

 1 × 4 = 1 × 4 = 4 8 1 8 × 1 8

Step 3. Simplify the fraction:

 4 = 1 8 2

## Fractions and Whole Numbers

What about division with fractions and whole numbers?

Make the whole number a fraction, by putting it over 1.

 Example: 5 is also 5 1

Then continue as before.

### Example:

 2 ÷ 5 3

Make 5 into 5/1 :

 2 ÷ 5 3 1

Step 1. Turn the second fraction upside down (the reciprocal):

 5 becomes 1 1 5

Step 2. Multiply the first fraction by that reciprocal:

 2 × 1 = 2 × 1 = 2 3 5 3 × 5 15

Step 3. Simplify the fraction:

The fraction is already as simple as it can be.

### Example:

 3 ÷ 1 4

Make 3 into 3/1 :

 3 ÷ 1 1 4

Step 1. Turn the second fraction upside down (the reciprocal):

 1 becomes 4 4 1

Step 2. Multiply the first fraction by that reciprocal:

 3 × 4 = 3 × 4 = 12 1 1 1 × 1 1

Step 3. Simplify the fraction:

 12 = 12 1

You can rewrite a division question like "20 divided by 5" into "how many 5s in 20" (=4)

So you can also rewrite "3 divided by ¼" into "how many ¼s in 3" (=12)

## Why Turn the Fraction Upside Down?

### Because dividing is the opposite of multiplying!

 A fraction says to: multiply by the top number divide by the bottom number

But for DIVISION we:

• divide by the top number
• multiply by the bottom number

### Example: dividing by 5/2 is the same as multiplying by 2/5

So instead of dividing by a fraction, it is easier to turn that fraction upside down, then do a multiply.