© William James Calhoun, 2001

4-4: Percents

OBJECTIVES:You need to be able to solve percent problems.

Two quick questions:1) What does “per” mean?2) What does “cent” mean?

When we say miles per gallon, we are actually saying “miles divided by gallons.”

Per is a math word for divide.Cent comes from early Roman times when there were centurions and times were began to be measured in centuries.

Cent was a Roman word for 100. C was the Roman numeral for 100.C is also for cookie, and that’s good enough for me.

So, percent must mean: divide by 100.If you remember this, you will be fine in this section.

© William James Calhoun, 2001

4-4: Percents

The official book definition of percent:•percent - a ratio that compares a number to 100We use the “%” sign for percent.Percents can also be expressed as fractions or decimals.Examples of how we can write percents:

60% = = 0.60100

60

EXAMPLE 1: Write as a percent.4

3

METHOD 1 METHOD 2Use a proportion.

Three-fourths is how many percents?

3(100) = 4x

300 = 4x 75 = x 75%

Use a calculator.

This is seventy-five one-hundredths, orseventy-five per hundred, which is the same as: 75%

3 x

4 100

30.75

4

means three divided by four.3

4

© William James Calhoun, 2001

4-4: Percents

Remember these quick rules to help you out:(1) To turn a decimal into a percent, move the decimal two places to the right and slap a %-sign on the number.

0.28. 28. 28%(2) To turn a percent into a decimal, rip off the %-sign and move the decimal two places to the left.

38.4% 38.4 .384.(3) To turn a fraction into a decimal, divide the numerator by the denominator.

(4) To turn a fraction into a percent, do (3) then (1).

5

3 3 5 0.6

3 5 0.6 60. 60%5

3

© William James Calhoun, 2001

EXAMPLE 2: Solve.A. 30 is what percent of 50?

Turn this English expression into an algebraic expression using some special variables.

30 is what percent of 50?

30 = % * 50

Notice that I used a “%” as the variable in this example.This is to remind me that at the end of the problem, I need to turn my answer into a percent.

30 = %(50)5050 % = 0.6 % = 60%

B. 20 is what percent of 30?

20 = % * 30

20 = %(30)3030 % = 0.66666666667

30 is 60% of 50.

20 is 66.6% of 30.%

3

266

% = 66.6%or

4-4: Percents

© William James Calhoun, 2001

EXAMPLE 3: Solve.A. 60% of what number is 54?

60% of what number is 54?For this one, I will again use my preferred method.The book’s method does not even work for this type of problem.

0.6Notice I turned the % into a decimal to work the problem.

* n = 540.6n = 54

0.60.6n = 90 60% of 90 is 54.

B. What number is 40% of 37.5?n = 0.4 * 37.5 n = 0.4(37.5) n = 15 15 is 40% of 37.5.

4-4: Percents

© William James Calhoun, 2001

4-4: Percents

HOMEWORK

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