Renaming FractionsDate: 05/22/2000 at 11:24:53 From: Alyssa Bombard Subject: Fractions I don't understand how you rename fractions. Can you help me? Thank you. Alyssa Date: 05/22/2000 at 12:52:31 From: Doctor Peterson Subject: Re: Fractions Hi, Alyssa. Let's start with a simple fraction, 1/2. That means we've taken something, say a block, and cut it into two (the denominator) equal pieces, and then taken one (the numerator) of them: +---------+---------+ |XXXXXXXXX| | |XXXXXXXXX| | |XXXXXXXXX| | |XXXXXXXXX| | |XXXXXXXXX| | |XXXXXXXXX| | +---------+---------+ Now, if I cut each of those pieces in half, I'll have a total of 4 pieces, of which I've taken 2: +---------+---------+ |XXXXXXXXX| | |XXXXXXXXX| | |XXXXXXXXX| | +---------+---------+ |XXXXXXXXX| | |XXXXXXXXX| | |XXXXXXXXX| | +---------+---------+ In other words, the fraction 1/2 is the same as 2/4; they are two names for the same amount. We call these equivalent fractions. Do you see how I changed 1/2 to 2/4? I just had to multiply both the numerator and the denominator by 2, since there are twice as many pieces in all, and I took twice as many of them. I could just as well have divided the pieces in thirds, to make a different fraction: +---------+---------+ |XXXXXXXXX| | |XXXXXXXXX| | +---------+---------+ |XXXXXXXXX| | |XXXXXXXXX| | +---------+---------+ |XXXXXXXXX| | |XXXXXXXXX| | +---------+---------+ Now I've rewritten 1/2 as 3/6, by multiplying numerator and denominator by 3, so that I have 3 out of 6 pieces. Here's a list of equivalent fractions: 1 2 3 4 5 6 7 8 --- = --- = --- = --- = --- = --- = --- = --- = ... 2 4 6 8 10 12 14 16 Now, we can also rename fractions in the opposite direction. If I DIVIDE both the numerator and the denominator of a fraction by the same number, then I get another name for the same fraction. For example, if you gave me the fraction 3/6, I would see that I could divide both 3 and 6 by 3, giving 1/2. By doing this, I have SIMPLIFIED (or REDUCED) the fraction; the smaller numbers are easier to work with, so this is a good thing to be able to do. You can always make the numbers bigger by multiplying them by something; but you can't always make them smaller, since two numbers are not always divisible by the same thing. If I can't divide them by anything, we say the fraction is "in lowest terms" - that is, we can't make the numerator and denominator any smaller. Our original 1/2 is in lowest terms, but 2/4 is not. You can find more help with this process by going to the Dr. Math search page at http://mathforum.org/mathgrepform.html and entering words like reduce fractions or lowest terms - be sure to select the button for "that exact phrase." - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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