Paperless Multiplication

Date: 07/23/2002 at 18:11:25
From: Emily Wong
Subject: Two-digit multiplication

Hi,

My name is Emily and I was wondering how I could learn to do 
harder multiplication by heart. I always have to do it on a piece of 
paper. I can solve them, but it takes more time.

 99x99  98x99  15x15  25x25  35x35  45x45  etc.

Do you have any tips?

Emily

Date: 07/24/2002 at 13:33:00
From: Doctor Ian
Subject: Re: Two-digit multiplication

Hi Emily,

If you _really_ want to do them 'by heart', you'll just have to 
memorize them. That seems like a lot of work, though.  

For two-digit multiplications like these, I'll usually use the 
distributive property. For example, 

  15 * 17 = 15 * (10 + 7)

          = 15 * 10 + 15 * 7

          = 150 + (10 + 5) * 7

          = 150 + 70 + 35

          = 150 + 105

          = 255

That still seems like a lot of work, doesn't it?  Well, note that 

  17 = 10 + 7 

     = 20 - 3

so 

  15 * 17 = 15 * (20 - 3)

          = 15*20 - 15*3

          = 300 - 45

          = 255

I can do the same thing with something like 

  98 * 99 = 98 * (100 - 1)

          = 98*100 - 98*1

          = 9800 - 98

          = 9702

The general idea is to use the distributive property to allow you 
to quickly get close to the answer, and then add or subtract a 
small number to get the exact answer. 

It still takes some practice to get good at this, but a lot less 
than it would take to memorize all the possible two-digit 
multiplications!

Does this help? 

The BEATCALC (Beat the Calculator) archive on the Math Forum site has 
some tricks for multiplying by 15, 25, 99, etc.  You might enjoy 
browsing starting at:

   Multiplying a 2-digit number by 99
   http://mathforum.org/k12/mathtips/multiplyby99.html

- Doctors Ian and Sarah, The Math Forum
  http://mathforum.org/dr.math/