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number multiplied by 0 is 0 (people call this trait the
zero property of multiplication
).
Any number multiplied by 1 is that number itself (which is why mathematicians call 1 the
multiplicative identity
— because when you multiply any number by 1, the answer is identical to the number you started with).
Multiplying by 2 is fairly easy; if you can count by 2s — 2, 4, 6, 8, 10, and so forth — you can multiply by 2.
    The rest of the numbers I've gotten rid of are redundant. (And not just redundant, but also repeated, extraneous, and unnecessary!) For example, any way you slice it, 3 × 5 and 5 × 3 are both 15 (you can switch the order of the factors because multiplication is commutative — see Chapter 4 for details). In my condensed table, I've simply removed the clutter.
    So what's left? Just the numbers you need. These numbers include a gray row and a gray diagonal. The gray row is the 5 times table, which you probably know pretty well. (In fact, the 5s may evoke a childhood memory of running to find a hiding place on a warm spring day while one of your friends counted in a loud voice: 5, 10, 15, 20, …)
    The numbers on the gray diagonal are the square numbers. As I discuss in Chapter 1 , when you multiply any number by itself, the result is a square number. You probably know these numbers better than you think.
Getting to know the short multiplication table
    In about an hour, you can make huge strides in memorizing the multiplication table. To start, make a set of flash cards that give a multiplication problem on the front and the answer on the back. They may look like Figure  3-1 .
    Illustration by Wiley, Composition Services Graphics
    Figure 3-1: Both sides of a flash card, with 7 × 6 on the front and 42 on the back.
    Remember, you need to make only 28 flash cards — one for every example in Table  3-2 . Split these 28 into two piles — a “gray” pile with 11 cards and a “white” pile with 17. (You don't have to color the cards gray and white; just keep track of which pile is which, according to the shading in Table  3-2 .) Then begin:
5 minutes: Work with the gray pile, going through it one card at a time. If you get the answer right, put that card on the bottom of the pile. If you get it wrong, put it in the middle so you get another chance at it more quickly.
10 minutes: Switch to the white pile and work with it in the same way.
15 minutes: Repeat Steps 1 and 2.
    Now take a break. Really — the break is important to rest your brain. Come back later in the day and do the same thing.
    When you're done with this exercise, you should find going through all 28 cards with almost no mistakes to be fairly easy. At this point, feel free to make cards for the rest of the standard times table — you know, the cards with all the 0, 1, and 2 times tables on them and the redundant problems — mix all 100 cards together, and amaze your family and friends.
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    To the nines: A slick trick
    Here's a trick to help you remember the 9 times table. To multiply any one-digit number by 9,
Subtract 1 from the number being multiplied by 9 and jot down the answer.
    For example, suppose you want to multiply 7 × 9. Here, 7 – 1 = 6.
Jot down a second number so that, together, the two numbers you wrote add up to 9. You've just written the answer you were looking for.
    Adding, you get 6 + 3 = 9. So 7 × 9 = 63.
    As another example, suppose you want to multiply 8 × 9:
8 – 1 = 7
7 + 2 = 9
    So 8 × 9 = 72.
    This trick works for every one-digit number except 0 (but you already know that 0 × 9 = 0).
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Double digits: Multiplying larger numbers
    The main reason to know the multiplication table is so you can more easily multiply larger numbers. For example, suppose you want to multiply 53 × 7. Start by stacking these numbers on top of one another with a line underneath, and then multiply 3 by 7. Because 3 × 7 = 21, write down the 1 and carry the