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
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:
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 |
 |
in |
 |
? |
|
Answer: 3 |
| So now you can see that |
|
1 |
÷ |
1 |
= 3 |
|
really does makes sense! |
|
|
| 2 |
6 |
Example 2
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:
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.
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