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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 (the reciprocal):

1 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 becomes 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 1/6 in 3/6 ?   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 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

Why Turn the Fraction Upside Down?

Because division is the inverse (opposite) of multiplying.

  • Multiplying by 5 makes something 5 times bigger.
  • Dividing by 5 makes something 5 times smaller.

A fraction has both multiply and divide in it ...you multiply by the top number and divide by the bottom number:

Example: 3/4

That means to cut into 4 pieces, and then take 3 of those.

So you divide by 4 then multiply by 3.

Now, if you have to DIVIDE by a fraction, you are asked to do the opposite of multiply ... so

  • multiply becomes divide, and
  • divide becomes multiply.

Let us see if it works ...

Multiply and divide are opposites, right? It works with simple numbers:

Example: 10 × 5 = 50 can be reversed by 50 / 5 = 10

So will the same work with fractions? Let us try:

Example: Start with 100 and multiply by 3/4

So you divide by 4 then multiply by 3.

So 100 × 3/4 is 100 divided by 4 (=25) then multiplied by 3 (=75).

Answer: 100 × 3/4 = 75

Can we reverse that by dividing by 3/4 ?

Example: 75 / (3/4) is also 75 × (4/3),

which is 75 divided by 3 (=25) then multiplied by 4 (=100)

Answer: 75 / (3/4) = 100

Yes! We ended up back at 100.

So it all makes sense.