Adding Fractions
It is easy to add fractions with the same denominator (same bottom number):
/4
(One-Quarter)
/4
(One-Quarter)
/4
(Two-Quarters)
/2
(One-Half)
Another example:
/8
/8
/8
Adding Fractions with Different Denominators
But what about when the denominators (the bottom numbers) are not the same?
3
/8
/4
We must somehow make the denominators the same.
/4
In this case it is easy, because we know that
3
/8
/8
/4 is the same as 2/8 :
/8
But when it is hard to make the denominators the same, use one of these methods
(they both work, use the one you prefer):
Least Common Denominator, or
Common Denominator
There are 3 simple steps to subtract fractions
Step 1. Make sure the bottom numbers (the denominators) are the same
Step 2. Subtract the top numbers (the numerators). Put the answer over the same
denominator.
Step 3. Simplify the fraction (if needed).
Example 1:
34 14
Step 1. The bottom numbers are already the same. Go straight to step 2.
Step 2. Subtract the top numbers and put the answer over the same denominator:
34 14 = 3 14 = 24
Step 3. Simplify the fraction:
24 = 12
(If you are unsure of the last step see Equivalent Fractions .)
Example 2:
12 16
Step 1. The bottom numbers are different. See how the slices are different sizes? We need
to make them the same before we can continue, because we can't subtract them like this:
12
16
To make the bottom numbers the same, multiply the top and bottom of the first fraction
(1/2) by 3 like this:
12
36
3
And now our question looks like this:
36
16
The bottom numbers (the denominators) are the same, so we can go to step 2.
Step 2. Subtract the top numbers and put the answer over the same denominator:
36 16 = 3 16 = 26
In picture form it looks like this:
36
16
26
Step 3. Simplify the fraction:
26 = 13
With Pen and Paper
And here is how to do it with a pen and paper (press the play button):
Subtracting Mixed Fractions
I have a special page on Adding and Subtracting Mixed Fractions .
Making the Denominators the Same
In the previous example it was easy to make the denominators the same, but it can be
harder ... so you may need to use either the
Common Denominator Method, or the
Least Common Denominator Method
They both work, use which one you prefer!
Example: Cupcakes
You want to sell cupcakes at a market:
You get paid 25 of total sales
But you have to pay 14 of total sales for the stall
How much do you get?
We need to subtract 14 from 25
25 14 = ??
First make the bottom numbers (the denominators) the same.
Multiply top and bottom of 2/5 by 4:
2 45 4 14 = ??
And multiply top and bottom of 1/4 by 5:
2 45 4 1 54 5 = ??
Now do the calculations:
820 520 = 8 520 = 320
Answer: you get to keep 320 of total sales.
There are 3 simple steps to multiply fractions
1. Multiply the top numbers (the numerators).
2. Multiply the bottom numbers (the denominators).
3. Simplify the fraction if needed.
Example:
12 25
Step 1. Multiply the top numbers:
12 25 = 1 2
= 2
Step 2. Multiply the bottom numbers:
12 25 = 1 22 5 = 210
Step 3. Simplify the fraction :
210 = 15
With Pizza
Here you can see it with pizza ...
... and do you see how two-tenths is simpler as one-fifth?
With Pen and Paper
And here is how to do it with a pen and paper (press the play button):
Another Example
13 916
Step 1. Multiply the top numbers:
13 916 = 1 9
= 9
Step 2. Multiply the bottom numbers:
13 916 = 1 93 16 = 948
Step 3. Simplify the fraction:
948 = 316
(This time we simplified by dividing both top and bottom by 3)
The Rhyme
"Multiplying fractions: no big problem,
Top times top over bottom times bottom.
"And don't forget to simplify,
Before it's time to say goodbye"
Fractions and Whole Numbers
What about multiplying 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
Now just go ahead as normal.
Multiply tops and bottoms:
23 51 = 2 53 1 = 103
The fraction is already as simple as it can be.
Answer = 103
Or you can just think of the whole number as being a "top" number:
Example:
3 29
Multiply tops and bottoms:
3 29 = 3 29 = 69
Simplify:
69 = 23
Mixed Fractions
You can also read how to multiply mixed fractions
here 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:
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
So now you can see why 12 16 = 3
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
Answer: 3
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 " into "how many s 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.
