Basic Math and Pre-Algebra For Dummies (13 page)

Next, multiply 7 by 5. This time, 5 × 7 = 35. But you also need to add the 2 that you carried over, which makes the result 37. Because 5 and 7 are the last numbers to multiply, you don't have to carry, so write down the 37 — you find that 53 × 7 = 371:

When multiplying larger numbers, the idea is similar. For example, suppose you want to multiply 53 by 47. (The first few steps — multiplying by the 7 in 47 — are the same, so I pick up with the next step.) Now you're ready to multiply by the 4 in 47. But remember that this 4 is in the tens column, so it really means 40. So to begin, put a 0 directly under the 1 in 371:

This 0 acts as a placeholder so that this row is arranged properly. (See Chapter
1
for more about placeholding zeros.)

 When multiplying by larger numbers with two digits or more, use one placeholding zero when multiplying by the tens digit, two placeholding zeros when multiplying the hundreds digit, three zeros when multiplying by the thousands digit, and so forth.

Now you multiply 3 × 4 to get 12, so write down the 2 and carry the 1:

Continuing, multiply 5 × 4 to get 20, and then add the 1 that you carried over, giving a result of 21:

To finish, add the two products (the multiplication results):

So 53 × 47 = 2,491.

The last of the Big Four operations is division. Division literally means splitting things up. For example, suppose you're a parent on a picnic with your three children. You've brought along 12 pretzel sticks as snacks, and want to split them fairly so that each child gets the same number (don't want to cause a fight, right?).

Each child gets four pretzel sticks. This problem tells you that

As with multiplication, division also has more than one sign: the division sign (÷) and the fraction slash (/) or fraction bar (—). So some other ways to write the same information are

12/3 = 4  and  

Whichever way you write it, the idea is the same: When you divide 12 pretzel sticks equally among three people, each person gets 4 of them.

 When you divide one number by another, the first number is called the
dividend,
the second is called the
divisor,
and the result is the
quotient
. For example, in the division from the earlier example, the dividend is 12, the divisor is 3, and the quotient is 4.

In the olden days, knowing how to divide large numbers — for example, 62,997 ÷ 843 — was important. People used
long division,
an organized method for dividing a large number by another number. The process involved dividing, multiplying, subtracting, and dropping numbers down.

But face it — one of the main reasons the pocket calculator was invented was to save 21st-century humans from ever having to do long division again.

Having said that, I need to add that your teacher and math-crazy friends may not agree. Perhaps they just want to make sure you're not completely helpless if your calculator disappears somewhere into your backpack or your desk drawer or the Bermuda Triangle. But if do you get stuck doing page after page of long division against your will, you have my deepest sympathy.

I will go this far, however: Understanding how to do long division with some not-too-horrible numbers is a good idea. In this section, I give you a good start with long division, telling you how to do a division problem that has a one-digit divisor.