Basic Math and Pre-Algebra For Dummies (11 page)

Therefore, 386 − 94 = 292.

In some cases, the column directly to the left may not have anything to lend. Suppose, for instance, that you want to subtract 1,002 − 398. Beginning in the ones column, you find that you need to subtract 2 − 8. Because 2 is smaller than 8, you need to borrow from the next column to the left. But the digit in the tens column is a 0, so you can't borrow from there because the cupboard is bare, so to speak:

 When borrowing from the next column isn't an option, you need to borrow from the nearest nonzero column to the left.

In this example, the column you need to borrow from is the thousands column. First, cross out the 1 and replace it with a 0. Then place a 1 in front of the 0 in the hundreds column:

Now cross out the 10 and replace it with a 9. Place a 1 in front of the 0 in the tens column:

Finally, cross out the 10 in the tens column and replace it with a 9. Then place a 1 in front of the 2:

At last, you can begin subtracting in the ones column: 12 − 8 = 4:

Then subtract in the tens column: 9 − 9 = 0:

Then subtract in the hundreds column: 9 − 3 = 9:

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

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

• 4 × 3 means add 4 to itself 3 times: 4 + 4 + 4 = 12
  
• 9 × 6 means add 9 to itself 6 times: 9 + 9 + 9 + 9 + 9 + 9 = 54
  
• 100 × 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).

 When you multiply two numbers, the two numbers that you're multiplying are called
factors,
and the result is the
product.

 In multiplication, the first number is also called the
multiplicand
and the second number is the
multiplier.
But almost nobody ever remembers — or uses — these words.

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

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