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4<br />

Secrets <strong>of</strong> Mental Math<br />

Absolutely. For instance, for the problem 314 11, the<br />

answer still begins with 3 and ends with 4. Since 3 1 4 <br />

, and<br />

1 4 5 <br />

, the answer is 34 <br />

5 <br />

4. But we’ll save larger problems<br />

like this for later.<br />

More practically, you are probably saying to yourself,<br />

“Well, this is fine for multiplying by elevens, but what about<br />

larger numbers? How do I multiply numbers by twelve, or<br />

thirteen, or thirty-six?”<br />

My answer to that is, Patience! That’s what the rest <strong>of</strong> the<br />

book is all about. In Chapters 2, 3, 6, and 8, you will learn methods<br />

for multiplying together just about any two numbers. Better<br />

still, you don’t have to memorize special rules for every number.<br />

Just a handful <strong>of</strong> techniques is all that it takes to multiply numbers<br />

in your head, quickly and easily.<br />

SQUARING AND MORE<br />

Here is another quick trick.<br />

As you probably know, the square <strong>of</strong> a number is a number<br />

multiplied by itself. For example, the square <strong>of</strong> 7 is 7 7 49.<br />

Later, I will teach you a simple method that will enable you to<br />

easily calculate the square <strong>of</strong> any two-digit or three-digit (or<br />

higher) number. That method is especially simple when the<br />

number ends in 5, so let’s do that trick now.<br />

To square a two-digit number that ends in 5, you need to<br />

remember only two things.<br />

1. The answer begins by multiplying the first digit by the next higher<br />

digit.<br />

2. The answer ends in 25.

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