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):

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"

 

 

A Trick that May Help

Try to rewrite the question the other way around ...

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

So you can also rewrite 1/2 divided by 1/6 into "how many 1/6s in 1/2" (=3)

 

Further Explanation ...

When you divide, you are cutting something into equal shares.

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 1/6 in 3/6 ?   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.

Answer =   2
15

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

 

Remember the "Trick to Help You" ...

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.