Simplifying FractionsDate: 12/08/2002 at 21:01:13 From: Lillian Subject: Simplifying Fractions How do I simplify a fraction? Date: 12/08/2002 at 22:05:45 From: Doctor Ian Subject: Re: Simplifying Fractions Hi Lillian, It depends on the fraction, but the general idea is this. Suppose you have a fraction, bibbity ------- bobbity and it turns out that both the numerator and denominator share a common factor, e.g., bibbity bibble * itty ------- = ------------- bobbity bobble * itty then you can eliminate the common factor: bibbity bibble * itty ------- = ------------- bobbity bobble * itty bibble itty = ------ * ---- bobble itty bibble = ------ * 1 bobble bibble = ------ bobble In practice, it might look like this: 12 6 * 2 6 -- = ----- = - 18 9 * 2 9 Of course, there can be more than one common factor! 12 6 * 2 6 2 * 3 2 -- = ----- = - = ----- = - 18 9 * 2 9 3 * 3 3 So the easiest way to deal with numbers is to find all the prime factors right away, and kill them off in pairs: / / 12 2 * 2 * 3 2 -- = ------------- = - 18 2 * 3 * 3 3 / / It might be too soon for you to be thinking about 'variables', but when you get to algebra you'll want to use the same rule: / / / / 21 x^3 y^2 3 * 7 * x * x * x * y * y ---------- = ------------------------------------- 35 x y^5 5 * 7 * x * y * y * y * y * y / / / / 3 x^2 = ----- y^3 I'm just telling you this now because it's not uncommon for students who have no trouble reducing fractions with numbers to freeze up when they have to do the same thing to a fraction with variables, because they don't realize that it _is_ the same thing. The important point is not to get confused or intimidated when the numbers get big, or you have lots of variables, or whatever. The main idea is _always_ the same: If you have a bunch of stuff multiplied together ------------------------------------------ another bunch of stuff multiplied together then if you can identify common factors, you can kill them off (cancel them) in pairs. What is tricky is that sometimes it's hard to remember that something like 12 actually _is_ a bunch of stuff multiplied together. 12 a bunch of stuff multiplied together -- = ------------------------------------------ 18 another bunch of stuff multiplied together 2 * 2 * 3 = --------- 2 * 3 * 3 And one of the secrets to happiness in math is to get into the habit of looking at every integer you see this way. For example, as soon as you _see_ a number like 72, you should already be thinking 72 = 8 * 9 = (2 * 2 * 2) * (3 * 3) It's kind of like what Superman does when he uses his x-ray vision to look through people's clothes so he can see if they're hiding things. It takes a little work to get into this habit (learning the most common divisibility rules, Divisibility Rules - Dr. Math FAQ http://mathforum.org/dr.math/faq/faq.divisibility.html can help a lot - especially the rules for 2, 3, 5, 9, and 10), but you wouldn't believe how much work it can save you down the road. I hope this helps. Write back if you'd like to talk more about this, or anything else. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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