Authors: Mark Zegarelli

hundreds column: 9 â 3 = 9:

Because nothing is left in the thousands column, you don't need to subtract anything else. Therefore, 1,002 â 398 = 604.

Multiplying

Multiplication is often described as a sort of shorthand for repeated addition. For example,

4 Ã 3 means add 4 to itself 3 times: 4 + 4 + 4 = 12

9 Ã 6 means add 9 to itself 6 times: 9 + 9 + 9 + 9 + 9 + 9 = 54

100 Ã 2 means add 100 to itself 2 times: 100 + 100 = 200

Although multiplication isn't as warm and fuzzy as addition, it's a great timesaver. For example, suppose you coach a Little League baseball team, and you've just won a game against the toughest team in the league. As a reward, you promised to buy three hot dogs for each of the nine players on the team. To find out how many hot dogs you need, you can add 3 together 9 times. Or you can save time by multiplying 3 times 9, which gives you 27. Therefore, you need 27 hot dogs (plus a whole lot of mustard and sauerkraut).

Â When you multiply two numbers, the two numbers that you're multiplying are called

factors,

and the result is the

product.

Â In multiplication, the first number is also called the

multiplicand

and the second number is the

multiplier.

But almost nobody ever remembers â or uses â these words.

Signs of the times

When you're first introduced to multiplication, you use the times sign (Ã). As you move onward and upward on your math journey, you need to be aware of the conventions I discuss in the following sections.

Â The symbol Â· is sometimes used to replace the symbol Ã. For example,

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

Â 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 Ã. So in this book, when I start using

x

in Part V, I also stop using Ã and begin using parentheses without another sign to indicate multiplication.

Memorizing the multiplication table

You may consider yourself among the multiplicationally challenged. That is, you consider being called upon to remember 9 Ã 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.

Looking at the old multiplication table

One glance at the old multiplication table, TableÂ 3-1 , reveals the problem. If you saw the movie

Amadeus

, you may recall that Mozart was criticized for writing music that had âtoo many notes.â 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.

Introducing the short multiplication table

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

Because nothing is left in the thousands column, you don't need to subtract anything else. Therefore, 1,002 â 398 = 604.

Multiplying

Multiplication is often described as a sort of shorthand for repeated addition. For example,

4 Ã 3 means add 4 to itself 3 times: 4 + 4 + 4 = 12

9 Ã 6 means add 9 to itself 6 times: 9 + 9 + 9 + 9 + 9 + 9 = 54

100 Ã 2 means add 100 to itself 2 times: 100 + 100 = 200

Although multiplication isn't as warm and fuzzy as addition, it's a great timesaver. For example, suppose you coach a Little League baseball team, and you've just won a game against the toughest team in the league. As a reward, you promised to buy three hot dogs for each of the nine players on the team. To find out how many hot dogs you need, you can add 3 together 9 times. Or you can save time by multiplying 3 times 9, which gives you 27. Therefore, you need 27 hot dogs (plus a whole lot of mustard and sauerkraut).

Â When you multiply two numbers, the two numbers that you're multiplying are called

factors,

and the result is the

product.

Â In multiplication, the first number is also called the

multiplicand

and the second number is the

multiplier.

But almost nobody ever remembers â or uses â these words.

Signs of the times

When you're first introduced to multiplication, you use the times sign (Ã). As you move onward and upward on your math journey, you need to be aware of the conventions I discuss in the following sections.

Â The symbol Â· is sometimes used to replace the symbol Ã. For example,

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

Â 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 Ã. So in this book, when I start using

x

in Part V, I also stop using Ã and begin using parentheses without another sign to indicate multiplication.

Memorizing the multiplication table

You may consider yourself among the multiplicationally challenged. That is, you consider being called upon to remember 9 Ã 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.

Looking at the old multiplication table

One glance at the old multiplication table, TableÂ 3-1 , reveals the problem. If you saw the movie

Amadeus

, you may recall that Mozart was criticized for writing music that had âtoo many notes.â 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.

Introducing the short multiplication table

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

Vivian Wood

Mark Walden

Rachel van Dyken

Robin Bielman

John Dalmas

David Drake

Jack Campbell

Cheryl Howe

Nancy Frederick