Reducing FractionsDate: 5/30/96 at 15:44:39 From: Vivian McCraw Subject: Reducing fractions I was placed in ESE from Pre-k through grade 12 and they never had me learn to reduce fractions. What is the easiest method of reducing fractions to lowest terms that you know? Greg Date: 5/31/96 at 16:6:3 From: Doctor Byron Subject: Re: Reducing fractions Hi Greg, In order to reduce a fraction, you need to find the biggest number that divides into both the numerator (the top number) and the denominator (the bottom number). After some practice, you may find that you can do this pretty quickly. At first, though, it is often helpful to list all the factors and simply look to see the biggest one shared by both numbers. Factors, by the way, are simply any number that divides into another number evenly. Let me give you an example: Let's look at the fraction - 48 ------ 32 The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 The factors of 32 are: 1, 2, 4, 8, 16, 32 If you look at both lists you'll see that 16 is the biggest number that is on both lists. So to reduce the fraction, we divide the top and bottom by sixteen. 48/16 3 ------- = ----- 32/16 2 If you find that there are no numbers (other than one) which are shared factors of both, the the fraction is as simple as it can get. Also, you don't have to simply look for the biggest factor right away. If you notice a shared factor quickly, you can go ahead and divide by it right away. You will have to make sure that there aren't any factors left, though. Let's look at the same example again: You may have noticed that both 48 and 32 are even, so it's pretty obvious that they both share two as a factor. So you could start by dividing both by two: 48/2 24 ------ = ---- 32/2 16 Now you might notice that 24 and 16 are both divisible by four, so you can go ahead and divide again: 24/4 6 ------ = --- 16/4 4 Finally, we see that these are even and can be divided by 2 again: 6/2 3 ----- = --- 4/2 2 I hope this has been helpful. I would suggest you find a math book that has some problems with answers given so that you can practice reducing fractions for a while, or maybe you could ask someone who knows how to make some problems for you to practice. Good luck! -Doctor Byron, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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