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 !!".

15 =

315.

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 !"!".

23 =

1015 .

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:

315+

1015 =

1315

Therefore

15+

23 =

1315.

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:

15 𝑥

23 =?

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).

• 1 x 2 = 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!

15 𝑥

23 =

215.

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.

12÷

34 =?

Now, here comes our “twist”. We’re going to keep the first term the same, change the sign, and

flip the second fraction.

12                  ÷                   

34 =?

↓ ↓ ↓

Same Change Flip

↓ ↓ ↓

12                   𝑥                  

43 =?

Now all we have to do is multiply our fractions together.

12 𝑥

43 =

46 =

23

A more generalized form of this would be !!÷ !

!= !"

!".  

For a video on this, please reference http://www.youtube.com/watch?v=zQMU-lsMb3U