How to: Divide Fractions

(To divide any number by a fraction:

1. Multiply the number by the reciprocal of the fraction.
2. Simplify the resulting fraction if possible.
3. Check your answer: Multiply the result you got by the divisor and be sure it equals the original dividend.

You can only divide by non-zero fractions.)

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:

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

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"

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.

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

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

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. (Source:  https://www.mathsisfun.com/)