Transcript General School Presentation

Adding & Subtracting
Fractions
Adding Fractions
If we were adding apples,
1 apple + 1 apple = 2 apples
Same with fractions:
1 1 2
 
3 3 3
You just add the tops and copy the
bottom.
Adding Fractions
1 1

6 12
Oops!
What if we can’t just “copy the bottom” because
the bottoms are different?
Adding Fractions
1 1

6 12
We need a common denominator.
It’s much easier to understand common
denominators if you understand what
common multiples are.
Multiples of a Number
A multiple of a number is a number that
you can get by multiplying your original
number by a whole number.
For example, the multiples of 6 would be
6, 12, 18, 24, 30, 36, 42, 48, . . .
Common Multiples
If you had two numbers like 6 and 12, a
common multiple would be a number that is a
multiple of each of them.
Multiples of 6
6, 12, 18, 24, . . .
Multiples of 12
12, 24, 36, 48, . . .
12 and 24 are two of the many common
multiples of 6 and 12.
Least Common Multiples
Even though 6 and 12 have many common
multiples, we usually work with the smallest,
or least common multiple.
Multiples of 6
6, 12, 18, 24, . . .
Multiples of 12
12, 24, 36, 48, . . .
12 is the least common multiple of 6 and 12.
Common Denominator
In order to add or subtract fractions, you
need to have a common denominator.
The fractions must have the same
number on the bottom.
Common Denominators
Finding common denominators is the same as
finding common multiples.
The denominator is the number on the bottom
of a fraction.
1 1
Finding a common denominator for

6 12
is the same as finding the common multiples of
6 and 12.
Least Common Denominator
Although you can add fractions using any
common denominator, most people like
to work with smaller numbers so they
use the least common denominator.
It’s abbreviated L.C.D.
Adding Fractions
1 1

6 12
To add these fractions, we must first transform
them into equivalent fractions that have the
same number on the bottom.
Adding Fractions
1 1

6 12
We’ve already decided that the least common
multiple of 6 and 12 is 12.
Therefore the L.C.D. of our fractions is 12.
Adding Fractions
1 1

6 12
We only have to change the first fraction so that it has a
12 on the bottom.
We have to be careful not to change the value of the
fraction when we change what it looks like!
Changing Fractions
2 1 2 1 2
 

2 6 2  6 12
An easy way to change a 6 into a 12 is to multiply it by
2.
If we multiply the bottom by 2, we must also multiply the
top by 2.
Changing Fractions
2 1 2 1 2
 

2 6 2  6 12
Why aren’t we changing the value when we
multiply by 2 on the top and bottom?
2
 1 and multiplying by 1 doesn't change the value!
2
Adding Fractions
2 1
3
 
12 12 12
Now our problem is easy!
ARF!
3
3 1 1


12 3  4 4
We aren’t finished until we reduce the answer.
ALWAYS REDUCE FRACTIONS!
Subtracting fractions
7 4 3
 
8 8 8
Good news!
Subtracting fractions is just like adding except
that you subtract the tops and copy the
bottom!
Remember:
To add or subtract you
need the bottoms of the
fractions to be the same.
If they aren’t the same, find a common denominator.
L.C.D. is the least common denominator.
Change the fraction by multiplying the top and the bottom by the
same number.
Add or subtract the tops and copy the bottom.