Dividing Fractions

Turn the second fraction upside down, then just 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	÷	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:

1	×	6	=	1 × 6	=	6

2		1		2 × 1		2

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):

Does it make sense?

Does	1	÷	1	really equal 3 ?

	2		6

You can change a question like "What is 20 divided by 5?" into "How many 5s fit into 20?"

In the same way our fraction question can become:

1	÷	1	How many	1	in	1	?

2		6		6		2

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

How many

Answer: 3

So now you can see that	1	÷	1	= 3	really does makes sense!

	2		6

Example 2

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

And that is all you have to do.

But maybe you want to know why we do it this way ...

Why Turn the Fraction Upside Down?

Well ... what Does a Fraction Do?

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

Example: ³/₄ means to cut into 4 pieces, and then take 3 of those.

So you:

divide by 4
multiply by 3

Example: ³/₄ of 20 is:

20 divided by 4, then times 3 = (20/4) × 3 = 5 × 3 = 15

Or you could multiply before dividing:

20 times 3, then divide by 4 = (20 × 3) / 4 = 60/4 = 15

Either way gets the same result

Dividing

But when you DIVIDE by a fraction, you are asked to do the opposite of multiply ...

So you:

divide by the top number
multiply by the bottom number

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

Because:

Dividing by 5, then Multiplying by 2

is the same as

Multiplying by 2, then Dividing by 5

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