Meaning of Multiplying FractionsDate: 12/09/1999 at 20:10:51 From: Mary Subject: What does it mean to multiply a fraction by a fraction? I am doing an essay assignment, and I got stuck on this question: What does it mean to multiply a fraction by a fraction? My sister and I think multiplying a fraction by a fraction just means to multiply a fraction by a fraction! Please help. Date: 12/09/1999 at 23:28:20 From: Doctor Peterson Subject: Re: What does it mean to multiply a fraction by a fraction? Hi, Mary. Well, what does it mean to multiply a whole number by a whole number? Two times three means the total of two groups of three things; here are two groups of three squares: +-------+-------+-------+ | | | | | | | | | | | | +-------+-------+-------+ | | | | | | | | | | | | +-------+-------+-------+ So 2 times 3 is 6. Now what does it mean to multiply a fraction times a whole number? One half times six means half a group of six; here's half a group of three squares: +-------+-------+-------+ | | | | +-------+-------+-------+ : : : : :.......:.......:.......: 1/2 times 3 is 3/2, because I've cut the squares into six halves, of which I'm keeping three. We do the same thing to multiply a fraction times a fraction; here's half a group of 2/3 of a square: +-----+..: | : | : +-----+..: : : : : :..:..:..: 1/2 times 2/3 is 2/6, because by cutting the square into two slices one way and three the other way, I have six pieces, of which I'm keeping only two. So a fraction times anything is just that fraction OF that amount; break it into as many pieces as the denominator says, and keep as many of them as the numerator says. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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