Grandma's Secret Ingredient Pie!

We all remember our grandmother's special pie; she only made it once a year *around the holidays of course* and she never told anybody the secret ingredient.  What you didn't know is that all this time you have been adding and subtracting fractions!! Don't believe me? Ok. I'll show you!!

Let's pretend that this does not resemble a basketball, but is instead grandma's cherry pie.  She always cut it into 8 equal slices, as shown.  Now, when she gave you a slice, you were handed 1/8 of the pie.  Easy right?  Well, say you asked for another slice...How much would you have had then?  And what if you couldn't finish the first slice *It was a huge meal!* and so you shared it, how much would you have had??  This is where adding and subtracting fractions comes in.

Adding Fractions
When adding fractions, one things is very important: a common denominator.  What is that??  Well, in a fraction, you have two numbers, the top number and the bottom number.  The numerator is the top number; the denominator is the bottom number.  So basically we want to have the same number on the bottom.  After finding a common denominator, then we can add the numbers straight through:

1  + 3 = 4

8     8     8

In this case, we did not have to change the denominator because it was already common.  Let's try a different one:  

1 + 2 = ??

                                                           4    3
Here we want to find a common denominator.  To do this, we must find a common multiple of the numbers.  Let's list the first few multiples:

3: 3, 6, 9, 12, 15, 18                      4: 4, 8, 12, 16, 20, 24 

Right away I see one common multiple: 12! We want to change the denominator to 12, however without changing the value of the fraction.  This means that we will have to multiply the numerator by the same number that we multiply the denominator.

(1 x 3) + (2 x 4) -->  3 + 8  = 11
(4 x 3)    (3 x 4)      12  12    12

After we add the fractions we want to make sure to simplify the fraction.  In this case, the answer was already simplified. 

Subtracting Fractions
When it comes to subtracting fractions, the first few steps are the same as adding fractions: we want a common denominator.  The only difference is that we are subtracting the numbers instead of adding.  Lets try one:

5 - 2 = (5 x 2) - 2 = 10 - 2 = 8
8  16   (8 x 2)  16   16  16   16

We can further simplify the answer by dividing both the numerator and the denominator by 8.  So the simplified answer is 1
                                            2.

For an interactive fraction addition game, click here. For an interactive fraction subtraction game, click here.