© William James Calhoun, : 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, : Percents The official book definition of percent: percent - a ratio that compares a number to 100 We use the “%” sign for percent. Percents can also be expressed as fractions or decimals. Examples of how we can write percents: 60% == 0.60 EXAMPLE 1: Write as a percent. METHOD 1METHOD 2 Use 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, or seventy-five per hundred, which is the same as: 75% means three divided by four.

© William James Calhoun, : 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 % (2) To turn a percent into a decimal, rip off the %-sign and move the decimal two places to the left. 38.4% (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). 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) 50 % = 0.6% = 60% B. 20 is what percent of 30? 20 = % * = %(30) 30 % = is 60% of is 66.6% of 30. % = 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. 0.6 Notice I turned the % into a decimal to work the problem. * n =54 0.6n = n = 9060% of 90 is 54. B. What number is 40% of 37.5? n = 0.4 * 37.5 n = 0.4(37.5) n = is 40% of : Percents

© William James Calhoun, : Percents HOMEWORK Page 218 # odd