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).
Example:
Example:
12 ÷ 16
Step 1. Turn the second fraction upside down (it becomes a reciprocal):
16 becomes 61
Step 2. Multiply the first fraction by that reciprocal:
(multiply tops ...)
12×61 = 1 × 62 × 1 = 62
(... multiply bottoms)
Step 3. Simplify the fraction:
62 = 3
With Pen and Paper
And here is how to do it with a pen and paper (press the play button):
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?
20 divided by 5 is asking "how many 5s in 20?" (=4) and so:
12 ÷ 16 is really asking:
how many 16s in 12 ?
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 12 ÷ 16 = 3
In other words "I have half a pizza, if I divide it into one-sixth slices, how many slices is that?"
Another Example:
18 ÷ 14
Step 1. Turn the second fraction upside down (the reciprocal):
14 becomes 41
Step 2. Multiply the first fraction by that reciprocal:
18 × 41 = 1 × 48 × 1 = 48
Step 3. Simplify the fraction:
48 = 12
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 51
Then continue as before.
Example:
23 ÷ 5
Make 5 into 51 :
23 ÷ 51
Then continue as before.
Step 1. Turn the second fraction upside down (the reciprocal):
51 becomes 15
Step 2. Multiply the first fraction by that reciprocal:
23 × 15 = 2 × 13 × 5 = 215
Step 3. Simplify the fraction:
The fraction is already as simple as it can be.
Answer = 215
Example:
3 ÷ 14
Make 3 into 31 :
31 ÷ 14
Then continue as before.
Step 1. Turn the second fraction upside down (the reciprocal):
14 becomes 41
Step 2. Multiply the first fraction by that reciprocal:
31 × 41 = 3 × 41 × 1 = 121
Step 3. Simplify the fraction:
121 = 12
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: | ||
|  |
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.
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