# 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 reciprocalStep 3. Simplify the fraction (if needed)

### Example:12  ÷  16

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

16 becomes 61

Step 2. Multiply the first fraction by that reciprocal:

(multiply tops ...)

12 × 61  =  1 × 62 × 1  =  62

(... multiply bottoms)

Step 3. Simplify the fraction:

62  =  3

### 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?

20 divided by 5 is asking "how many 5s in 20?" (=4) and so:

12  ÷  16 is really asking:

how many 16s in 12 ?

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 12  ÷  16 = 3

In other words "I have half a pizza, if I divide it into one-sixth slices, how many slices is that?"

### Another Example:18  ÷  14

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

14  becomes  41

Step 2. Multiply the first fraction by that reciprocal:

18  ×  41 = 1 × 48 × 1 = 48

Step 3. Simplify the fraction:

48  =  12

## 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 51

Then continue as before.

### Example:23  ÷  5

Make 5 into 51 :

23  ÷  51

Then continue as before.

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

51 becomes 15

Step 2. Multiply the first fraction by that reciprocal:

23 × 15 = 2 × 13 × 5 = 215

Step 3. Simplify the fraction:

The fraction is already as simple as it can be.

### Example:3  ÷  14

Make 3 into 31 :

31  ÷  14

Then continue as before.

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

14 becomes 41

Step 2. Multiply the first fraction by that reciprocal:

31 × 41 = 3 × 41 × 1 = 121

Step 3. Simplify the fraction:

121 = 12

### And Remember ...

You can rewrite a question like "20 divided by 5" into "how many 5s in 20"

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 numberdivide 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.