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how do you simplfy fractions

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Hi Anna, 1. Make a list of the factor pairs for your numerator and your denominator. 2. Find the BIGGEST factor that is on both of your lists (this is called the Greatest Common Factor, or GCF). I tell my students to circle this number. 3. Divide both the numerator and the denominator by the factor you circled. For example: If your fraction is 9/24 Step 1 is list the factors: 9 = 1 X 9, 3 x 3 24 = 1 x 24, 2 x 12, 3 x 8, 4 x 6 Step 2 is find the BIGGEST factor they each have in common. In this case, the factor is 3. Step 3 is divide both the numerator and denominator by this factor. So, 9 divided by 3 = 3 24 divided by 3 = 8 That means your simplified fraction is 3/8. Hope this helps.

If you have a fraction - there are various ways of reducing it to its simplest form.

Well know method is : Divide the Num and Den of the fraction by the GCD of Num and Den. 


Most often students try the random method to see if Num and Den can be divided by either 2, 3, 5, 7, 

11, 13, 17 , 19 etc ............

 

I always found it easiest to simplify fractions by setting up both the numerator and denominator by way of a factor tree.  Sounds kind of rudimentary, but, most any student knows how to do a factor tree for prime factorization (they also work real well when trying to find square roots).

For example, let's say we have the fraction 120/200.  By creating a factor tree, we see that we get 2*2*2*3*5 for the numerator and 2*2*2*5*5 for the denominator.  We can then eliminate the factors we have in common, which leaves us with 3 for the numerator and 5 for the denominator, or 3/5.  It takes a lot of the guesswork out of the problem, as well, so, instead of trying to guess what goes into both, you already have the prime factorization in front of you and you can actually see what you can eliminate.

I like to think of simplifying fractions as looking at a cut-up pie and trying to make smaller equal size pieces. Let's start with a small pie to start. Draw your circle for a pie. Now, to cut it into 4 equal size pieces you will need to draw a straight line down the middle of the pie and a straight line across the middle of the pie. Suppose you and your best friend eat some pie. You eat 1 piece, and your friend eats 2 pieces. Color in the piece you eat with a red crayon. Color 2 pieces side by side to show that your best friend eats with a blue crayon. Wow! It should look like your friend ate more than you. In fact, it should look like your friend ate 1/2 (one half) of the pie!

So, we know that 1/2 of your pie is blue. But there is another way to right this, a way that you can find by looking at how many pieces of pie you first cut and how many pieces you each ate.

The original pie was cut into 4 pieces. When setting up a fraction, the number of pieces you cut the pie into will be on the bottom of the fraction. This number is the denominator.

Your friend ate 2 pieces of the pie. The number of pieces your friend ate goes on the top of the fraction. This number is called the numerator.

So, to set up the fraction you would right 2/4.

When looking at a fraction, the most important thing to remember is the little saying 'is over of.' This means that the top number 'is' the number your friend ate. The bottom number is the number 'of' pieces there were to start.

So now we have our fraction 2/4. Let's take a look at that pie again. When you colored the 2 pieces of pie side by side, it looked like your friend ate 1/2 of the pie. The truth is, your friend did eat half! This may be confusing because we just said your friend ate 2 OF the 4 pieces, or 2/4.

1/2 and 2/4

They are actually the same. 1/2 is a simply version of 2/4. Math books say that you simplify 2/4 to 1/2. The reason is that if you divide 2 by 2 and 4 by 2, you will get 1 and 2. It is like smashing the 4 pieces of pie back into 2 pieces of pie. The numbers are different, but they represent the same amount of pie.

I hope this gets you going in the right direction. Good luck!

In order to simplify a fraction, you must take it to it's lowest terms. To do so, find a number that you can divide both the numerator and the denominator by. It must be the same number. Dividing the numerator and denominator by the largest possible number will get you to the lowest terms fastest, but if you have difficulty with division, you can start with dividing by 2, 3 or 5 and keep going until you can't divide anymore.

For example: If you want to simplify 6/10, you first know that you can divide 6 and 10 by 2. Divide 6 by 2 and put the answer in the numerator position. Then divide 10 by 2 and put the answer in the denominator position.

6÷2 = 3 and 10÷2 = 5

So 6/10 ÷ 2/2 = 3/5

3/5 is the simplified fraction.

Here is another example:

Simplify 8/12. I know I can divide both 8 and 12 by 4, so

8÷4 = 2 and 12÷4 = 3

8/12 ÷ 4/4 = 2/3   2/3 is the simplified fraction.

I hope this helps!

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