Alright- last time, I told you that I'd put up a post on how to simplify fractions, so here it is:
To start with, you have to have a fraction that isn't simplified (you may also hear it called 'a fraction not in simplest form') all the way. Now, a fraction that isn't simplified all the way is just a fraction with common factors in the top and the bottom (technically called the numerator and denominator, respectively). For example, 8/12 (8 is the top and 12 is the bottom, just FYI). 8 and 12 have many common factors; the first and typically most obvious one is 2. If you multiply 2 and 4, you will get 8 (therefore, 2 and 4 are considered factors of 8) and if you multiply 2 and 6 you'll get 12 (so 2 and 6 are also factors of 12. If you list all the numbers that you can multiply to get a couple of numbers and you see some of the same numbers in each list, you have common factors). Since you can multiply 2 by something to get both 8 and 12, 2 is one of their common factors; you can use this to simplify the fraction 8/12.
Now, you're first going to write the fraction on your paper (it would probably benefit you to write it out if this is your first time, because you'll be able to understand it a little better) straight up and down: write the 8 then a little horizontal line right below it then a 12 below that. Now, know that your 8 is called your numerator and your 12 is called your denominator. Now, take your common factor and write it as a straight up and down fraction, like this: write a 2 then the little horizontal bar right below it then another 2 right below that. Write this right next to your 8/12 with a division sign in between them. You should have:
8/12 <division sign> 2/2 (only straight up and down)
Your 8 and your top 2 should line up and your 12 and your bottom 2 should also line up.
Now, this is the easy part: divide straight across. Take 8 (the top of your 8/12) and divide by 2 (the top in your 2/2). You should get 4; now, take 12 (the bottom of your 8/12) and divide by 2 (the bottom in your 2/2). You should get 6. Now write your new fraction with the numbers you got just now, remember- keep the top division answer (the quotient) on the top of our new fraction and the bottom division answer on the bottom of your new fraction. You should have:
4/6
As with most fractions that you simplify, you will have to do what I just taught above more than once. In this case, you can divide again by 2/2 again, and you will have your final answer.
NOTE 1: (You know you have a fully simplified fraction when there are no more common factors between the top and the bottom)
NOTE 2: (Dividing by a number over itself, in this case 2/2, is the same as dividing by 1 and therefore, your note actually changing the fraction, you're just rewriting it using smaller numbers)
NOTE 3: (You could have worked this problem by dividing the original fraction by 4/4, basically, you would just be using the common factor of 4 instead of 2. [4x2=8 4x3=12, so they have 4 in common as a factor. Working the problem this way would have given you
8/12 <division sign> 4/4= 2/3 which is a simplified fraction because 2 and 3 have no common factors).
Now, since 4 and 6 have the common factor of 2 (2x2=4 and 2x3=6), divide 4/6 (the fraction you have now) by 2/2 (the common factor of 4 and 6). You should get:
4/6 <division sign> 2/2 (4 divided by 2 = 2 and 6 divided by 2 = 3)
2/3
This is a completely simplified fraction because 2 and 3 have no common factors.
This wasn't the best post that I've ever done so if you need some more help on common factors or on simplifying fractions, just go to www.khanacademy.org and you'll get a bunch of videos that can probably explain it a lot better than I can.
:) Bye for now
-Meredith
