Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 2: Arithmetic 23

CHECK POINT

Subtract by adding back.

16. 100 – 62


17. 250 – 183


18. 500 – 29

19. 400 – 285

20. 850 – 319

Multiplication and Division

There’s a lot of talk about the four operations of arithmetic: addition, subtraction, multiplication,

and division. In a way, they all boil down to addition. As we’ve seen, subtraction is the inverse,

or opposite, of addition. Multiplication is actually just a shortcut for adding the same number

several times, and division is the inverse of multiplication. While each operation has its place, it’s

good to remember that they’re all connected.

Multiplication

Multiplication originated as a shorter way to express repeated addition. Suppose you pay $40

every month for your phone. How much is that per year? You could say that you pay $40 in each

of the 12 months of the year and write an addition problem 40 + 40 + 40 + 40 + 40 + 40 + 40 +

40 + 40 + 40 + 40 + 40. It’s long, but it would do the job. Multiplication lets you say the same

thing as 40 v 12. (Or 12 v 40, thanks to the commutative property.) In this example, 40 and 12

are both called factors. When you multiply 40 by 12, you get 480, which is called the product.

DEFINITION

Each number in a multiplication problem is a factor. The result of the multiplication is

the product. In the equation 5 v 3 = 15, 5 and 3 are factors, and 15 is the product.

Although it’s nice to have a shorter way to write the problem, multiplication isn’t much use to

us unless it also gives us a simpler way to do the problem. And it will, but you need to do the

memory work to learn the basic multiplication facts, or what most people call the times tables.

In the following chart, each column is one table or family of facts. The first column is the ones

table, or what you’d get if you added one 1, two 1s, three 1s, and so on. The last column is the

nines table. One 9 is 9, two 9s are 18, three 9s are 27, and on down to nine 9s are 81. (You’ll see

some tables that include 10 and sometimes even larger numbers, and the more tables you can

learn, the faster at multiplication you’ll be.)