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### Alternative to Memorizing Times Tables

```Date: 01/13/2004 at 19:09:56
From: Samantha
Subject: how do you remember 12's in just one day

How do you remember the 12's times table in just one day?  I have to
do a times test tommorow and I only have one minute.

```

```
Date: 01/14/2004 at 10:14:23
From: Doctor Ian
Subject: Re: how do you remember 12's in just one day

Hi Samantha,

In general, you can't memorize that many things in a single day, and
have them stick.  Memorization takes lots of repetition and practice.
It's kind of like digging a hole--you have to do it one shovelful at
a time.

However, you don't always have to memorize every little thing.  For
example, I haven't really memorized my 12's, except for

12 * 12 = 144

because the rest of them are pretty easy to figure out when you need
them.  For the first few, you can just multiply the individual digits:

2 * 12 = 24            Double the 1, double the 2

3 * 12 = 36            Triple the 1, triple the 2

Multiplying 10 by anything is easy--just add a zero at the end:

10 * 12 = 120

So 5 times 12 will be half that:

5 * 12 = half of 10 * 12 = half of 120 = 60

For 6 and 8, we can use doubling:

6 * 12 = twice 3 * 12 = twice 36 = 72

8 * 12 = twice 4 * 12 = twice 48 = 96

That leaves only 7, 9, and 11.  And since each of them is just 12 from
something we know, we don't really have to memorize those, either:

7 * 12 = 6 * 12, plus 12   = 72 plus 12   = 84

9 * 12 = 10 * 12, minus 12 = 120 minus 12 = 108

11 * 12 = 10 * 12, plus 12  = 120 plus 12  = 132

Also, if you're multiplying by a single digit, you can use the
distributive property to turn one hard multiplication into two easy
ones, e.g.,

7 * 12 = 7 * (10 + 2)

= 7*10 + 7*2

= 70 + 14

= 84

This works for _all_ of them, and although it's not as quick, it's a
good backup strategy.  While memorizing them probably gives you the
fastest way to recall them when needed, practicing thinking about them
like I just described is a nice alternative.  It may be easier that
way at first and it will help you not only to understand why the
as you keep practicing.

or anything else.

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Multiplication

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