Multiplication Makes It ... Smaller?!Date: 07/21/2012 at 16:13:01 From: Justine Subject: Multiplying with a decimal equals a smaller product Hello! My question is, when you multiply with a decimal that is smaller than 1, why does it give a smaller product? For example: 2 x .5 = 1 And 500 x .25 = 125 Isn't multiplying supposed to give a larger product? My dad says 2 x .5 = 1 is the same as 2/2, which is also 1. Why is multiplying by .5 the same as dividing by 2? He tries to explain it to me, but I just can't seem to get it! Related to my question, I think, is when someone says "25% off of 50." That means you don't have to pay the .25. So you can do 50 x .75 = 37.5 I don't understand why, though. When you get 25% off something, that means you get it for a smaller price ... but yet I multiplied? That is kind of strange to me. Please reply back because this has been bugging me lots. Thanks! Date: 07/21/2012 at 16:38:21 From: Doctor Peterson Subject: Re: Multiplying with a decimal equals a smaller product Hi, Justine. When you multiply a number by 2, you get a bigger result. That's what you're used to until now. When you multiply by 1, what do you get? The same number, right? Multiplying by a number GREATER than 1 makes it bigger; multiplying by 1 leaves it the same; and, continuing the pattern, multiplying by a number LESS than 1 makes it smaller. For example, multiplying a number by 1/2 cuts it in half, making it smaller. Multiplying by 0.5 is the same thing. In general, you can think of multiplication as scaling, which can make something either larger or smaller, scaling up or scaling down. Multiplying by 3 scales up: 0 1 2 3 +-----+-----+-----+ | \ \ \ | \ \ \ | \ \ \ | \ \ \ | \ \ \ | \ \ \ | \ \ \ | \ \ \ | \ \ \ | \ \ \ | \ \ \ +-----------------+-----------------+-----------------+ 0 3 6 9 This enlargement turned 1 into 3. Multiplying by 1/3 scales down: 0 1 2 3 4 5 6 7 8 9 +-----+-----+-----+-----+-----+-----+-----+-----+-----+ | / / / | / / / | / / / | / / / | / / / | / / / | / / / | / / / | / / / | / / / | / / / +-+-+-+-+-+-+-+-+-+ 0 1 2 3 This shrinking turned 1 into 1/3, and 3 into 1. Notice that multiplying by 1/3 undoes a multiplication by 3; it divides by 3. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ Date: 07/21/2012 at 19:21:54 From: Justine Subject: Thank you (Multiplying with a decimal equals a smaller product) Thanks so much! Your answer really cleared up my confusion. So now I won't get bugged by this question anymore. |
Search the Dr. Math Library: |
[Privacy Policy] [Terms of Use]
Ask Dr. Math^{TM}
© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/dr.math/