Idiot\'s Guides Basic Math and Pre-Algebra

88 Part 1: The World of Numbers

WORLDLY WISDOM

When you’re cross-multiplying, don’t be in a rush to do the arithmetic, especially if

your numbers are large. Your work may be easier if you write out the multiplication

but don’t actually do it. Then when you divide to find the value of the variable, you

may see a shortcut. Why do the work of multiplying 42 v 35 if, a moment later, you’re

going to divide by 21?^4235

21

235 70

2

1

3 55. Leave the multiplication in factored form,

and the division may be easier.

CHECK POINT

Solve the proportion to find the value of the variable.

6.^2
515

x

7.^3
7

24

x



8. x
   63

15

27

=

9.^351

x 68



10.^3
510

x

Percent as a Standard Ratio

The word percent means “out of 100.” If you shoot 100 free throws at basketball practice and you

sink 60 of them, you made 60 out of 100 shots, or 60 percent. But what if you shot 75 and made

40? What percentage is that? Is that better or worse than 60 percent? You can use proportions to

convert any ratio to a percentage.

DEFINITION

A percentage is a ratio that compares numbers to 100. 42 percent means 42 out of

100, or 42:100. Percentages are sometimes written using the percent symbol, %.

Ratios can be hard to compare if they are “out of ” different numbers. Which is larger: 4 out of 9

or 5 out of 12? If you compare them as fractions,^49 and^5

12

, it might help to change to a common

denominator. You could use 36 as the common denominator so^49 ^1636 and 125 ^1536 , and you can

see that^4

9

is larger.