Learning to Multiply Three-Digit Numbers
Date: 07/03/98 at 10:51:18 From: Jonathan W Subject: Multiplying big numbers Dear Dr. Math, I am going into second grade. My class is only doing multiplication of easy numbers like 2 x 4. I would like to learn how to do multiplication of bigger numbers like 120 x 743. Could you please help me? Thank you, Jonathan
Date: 07/06/98 at 12:43:05 From: Doctor Peterson Subject: Re: Multiplying big numbers Hi, Jonathan. I love to help people who want an extra challenge! I don't know how well I can teach you about this in a short message, but I think I can show you some ways to understand multiplication so that you can work out the rest on your own. The first step is to learn how to multiply a two-digit number by one digit. Here's an example: 24 x 3 ---- 72 Here's how it works: Think of 24 as 20 + 4, and multiply each part by 3: 20 4 x 3 x 3 ---- --- 60 12 If you can see why 20 x 3 is 60, you know enough to figure everything else out. 20 x 3 is just two tens times three, which is two-times- three tens, or six tens, which is 60. Everything else I'll be telling you depends on that kind of thinking. Now we just add the 60 and the 12 together to get 72, which is the answer. I could write it all together like this: 24 x 3 ---- 12 + 60 ---- 72 I could also write it this way, just putting an empty space instead of the zero, so that the 6 goes in the same column as the 2 it comes from: 24 x 3 ---- 12 + 6 ---- 72 What we usually do is to write down the 2 as part of the answer, and the 1 as a carry, just as you do when you add big numbers: 1 24 x 3 ---- 72 Once you've learned to do that, the next step is to multiply two digits by two digits. It's really the same thing, but there's more to keep track of, so we usually write out a bit more: 24 x 13 ---- 72 24 ---- 312 Here I've multiplied the 24 first by 3, as before, and then by 1. But since the 1 really means 10 (since 13 = 10 + 3), I move the 24 left one space as I did with the 6 in an earlier example. Here's a way to see what we are really doing: 10 3 +----+----+ 20 |200 | 60 | +----+----+ 4 | 40 | 12 | +----+----+ This means that 20 + 4 times 10 + 3 is the sum of: 20 x 10 = 200 20 x 3 = 60 4 x 10 = 40 4 x 3 = 12 --- 312 You may be interested in an old method of multiplication called the lattice method, which works just this way. I think that understanding how to do that can help a lot in seeing what you are really doing when you multiply. Here's a place to learn about that: http://mathforum.org/dr.math/problems/susan.8.340.96.html I hope this will help you discover how to multiply. If I've told you more than you can follow yet, just take it one step at a time and ask someone to help you with it. It's really a lot of fun once you get used to it. - Doctor Peterson, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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