Basic Math and Pre-Algebra For Dummies (12 page)

In Parts I through IV of this book, I stick to the tried-and-true symbol × for multiplication. Just be aware that the symbol · exists so that you won't be stumped if your teacher or textbook uses it.

 In math beyond arithmetic, using parentheses without another operator stands for multiplication. The parentheses can enclose the first number, the second number, or both numbers. For example,

This switch makes sense when you stop to consider that the letter
x
, which is often used in algebra, looks a lot like the multiplication sign ×. So in this book, when I start using
x
in Part V, I also stop using × and begin using parentheses without another sign to indicate multiplication.

You may consider yourself among the multiplicationally challenged. That is, you consider being called upon to remember 9 × 7 a tad less appealing than being dropped from an airplane while clutching a parachute purchased from the trunk of some guy's car. If so, then this section is for you.

One glance at the old multiplication table, Table 
3-1
, reveals the problem. If you saw the movie
Amadeus
, you may recall that Mozart was criticized for writing music that had “too many notes.” Well, in my humble opinion, the multiplication table has too many numbers.

I don't like the multiplication table any more than you do. Just looking at it makes my eyes glaze over. With 100 numbers to memorize, no wonder so many folks just give up and carry a calculator.

If the multiplication table from Table 
3-1
were smaller and a little more manageable, I'd like it a lot more. So here's my short multiplication table, in Table 
3-2
.

As you can see, I've gotten rid of a bunch of numbers. In fact, I've reduced the table from 100 numbers to 28. I've also shaded 11 of the numbers I've kept.

Is just slashing and burning the sacred multiplication table wise? Is it even legal? Well, of course it is! After all, the table is just a tool, like a hammer. If a hammer's too heavy to pick up, then you need to buy a lighter one. Similarly, if the multiplication table is too big to work with, you need a smaller one. Besides, I've removed only the numbers you don't need. For example, the condensed table doesn't include rows or columns for 0, 1, or 2. Here's why:

• Any 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.

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
.

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:

1. 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.
   
2. 10 minutes:
   Switch to the white pile and work with it in the same way.
   
3. 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.

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 2: