Download ADDITION AND SUBTRACTION WITH FRACTIONS

ADDITION AND SUBTRACTION WITH FRACTIONS
Addition and subtraction of fractions is very useful in everyday life. However, addition and
subtraction with fractions can be quite cumbersome. Let’s take a look at an example:
!
!
Add the fractions ! and !.
The first thing that we have to do is find a common denominator (the bottom part of the fraction)
for both fractions. We do that by looking at the common multiples of the denominators (5 and
3).
•
5: 5, 10, 15, 20, 25, 30, 35, 40, …
•
3: 3, 6, 9, 12, 15, 18, 21, 24, 27, …
So the common multiple of 5 and 3 is 15. Now we need to see what we multiplied each number
(5 and 3) by to get 15.
•
5 x 3 = 15
•
3 x 5 = 15
So we have to multiply 5 and 3 by 3 and 5 (respectively) to get the common denominator (the
bottom part of the fraction) of 15. So, now we have to multiply the numerator (or the top of the
!
fraction) by the same thing. Let’s look at the first fraction: !. Since we multiplied 5 by 3 to get
!
15, we must now multiply 1 by 3, giving us 3. That changes the fraction to !".
1
3
= .
5 15
!
Now let’s look at the second fraction: !. Since we multiplied the 3 by 5 to get 15, we must
!"
multiply 2 by 5, giving us 10. That changes the fraction to !".
2 10
=
.
3 15
Now we’re ready to add!
Now that we have changed to fractions and given them “like denominators” (that is, the same
number on the bottom), all we have to do is add the numerators together (the numbers on the
top). 3 + 10 = 13. In fraction form it would look like this:
3 10 13
+
=
15 15 15
Therefore
1 2 13
+ = .
5 3 15
A more general form of this would be
!
!
+
!
!
=
!"!!"
!"
.
*Note: Subtraction would be the same as addition, only instead of adding the top together,
you subtract the top.
For a video on this, please reference http://www.youtube.com/watch?v=OVMceVL_CEQ
MULTIPLYING FRACTIONS
Multiplying fractions is much simpler than adding or subtracting fractions. Let’s take a look at
an example:
!
!
Multiply the two fractions ! and !.
Let’s start by setting up our equation:
1 2
𝑥 =?
5 3
To multiply fractions, all we have to do is multiply the two numerators together (that is, the top
of the fraction) and put it as the numerator and do the same with the denominator (that is, the
bottom of the fraction).
•
1x2=2
•
5 x 3 = 15
We now know that 2 is our numerator (the top part of the fraction) and that 15 is the denominator
(the bottom part of the fraction). Now we put it in the fraction, and we’re done!
1 2
2
𝑥 = .
5 3 15
A more general form of this would be
!
!
!"
× ! = !".
!
For a video on this, please reference http://www.youtube.com/watch?v=CTKMK1ZGLuk
DIVIDING FRACTIONS
Dividing fractions is very similar to multiplying fractions, but with a little “twist”. Let’s look at
an example:
!
!
Divide ! by !.
!
Let’s start by setting up our equation. Since we’re dividing ! into something, that term is our
!
first term in our equation. Since we’re dividing by !, that is our second term.
1 3
÷ =?
2 4
Now, here comes our “twist”. We’re going to keep the first term the same, change the sign, and
flip the second fraction.
1
3
÷ =?
2
4
↓
Same
↓
↓
Change
Flip
↓
↓
↓
1
4
𝑥 =?
2
3
Now all we have to do is multiply our fractions together.
1 4 4 2
𝑥 = =
2 3 6 3
!
!
A more generalized form of this would be ! ÷ ! =
!"
!"
. For a video on this, please reference http://www.youtube.com/watch?v=zQMU-lsMb3U