Associated Topics || Dr. Math Home || Search Dr. Math

### 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/
```
Associated Topics:
Elementary Multiplication

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search