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:

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):

To help you remember:

"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"

 leave change turn

 

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 many1/6in3/6?  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.

Answer = 215

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 number
  • divide by the bottom number
 fraction multiply divide

But for DIVISION we:

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

fraction multiply divide

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