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). |
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| Step 2. Multiply the first fraction by that reciprocal Step 3. Simplify the fraction (if needed) |
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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:
| 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):
A Trick to Help You
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 |  |
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 |
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" ♫
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: | ||
|
 |
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.