RWM101 Study Guide

Unit 7: Percentages

7a. Identify the components of a percent problem

  • What does percent mean?

Percent has a literal meaning where "per" means "out of" and "cent" means 100. Think of the words century or centipede, where "cent" also means 100. When we say percent, it literally means "out of 100". For example, 35%, means 35 out of 100.

To review, see The Meaning of Percents.

7b. Convert between percent, decimal, and/or fraction notation

  • How do you convert a percentage to a fraction?
  • How do you convert a percentage to a decimal?
  • How do you convert a decimal to a percentage?
  • How do you convert a fraction to a percentage?

Since percentages are basically just fractions, converting them to fractions or decimals is quite easy.

When converting a percentage to a decimal, simply rewrite the percentage as a fraction with a denominator of 100. Then simplify as necessary. For example, 63% is 63/100 in fractional form.

Converting a percentage to a decimal is just as easy. First, convert the percentage to a fraction, then divide the fraction to get a decimal. Since the denominator of the fraction is always 100, you can simply move the decimal point in the numerator two places to the left. Continuing from our previous example, 63% is 63/100, which is .63 as a decimal.

To convert a decimal to a percentage is even easier. Simply multiply the decimal by 100 (or move the decimal point two places to the right) and you are done. For example, the decimal .635 is equal to 63.5%.

To convert a fraction to a percentage, simply convert the fraction to a decimal, then multiply by 100, as we just saw. For example, to convert ⅗ to a percentage, first convert ⅗ to .6, then convert to 60%.

To review, see Converting Percent to Decimal and Fraction.

7c. Use proportional relationships to solve multi-step percent problems

  • How do you calculate a percentage?

Calculating a percentage is all about correctly identifying the "part" and the "whole" in the situation, then dividing the part by the whole, and finally multiplying by 100, to convert the decimal you found to a percentage.

For example, say a tour company is giving 1 hour tours. Out of 225 tours, they found that 37 were over 1 hour, and the rest were exactly 1 hour. What percent of the tours finished on time? In order to solve this problem, first we need to find out how many tours ended on time. Since there were 225 total tours and 37 went over time, 225 - 37 = 188 tours finished on time. Now that we have the correct values for our problem, we can calculate the percentage. 188 tours out of 225 finished on time, so the percentage is  \frac{188}{225} \times 100=83.6 \% .

To review, see Solving Basic Percent Problems.

7d. Apply percent concepts in practical application

  • How do you calculate percent increase/decrease?
  • How do you calculate sales tax or commission?

To calculate percent of change (increase or decrease), divide the amount of the change by the original price/value. For example, if a pair of pants were originally $80, but are on sale for $60, divide the difference in price ($80-$20= $20) by the original price ($80). Since  \frac{20}{80}=.25 , convert the decimal to a percentage, and you will find the percent decrease of 25%.

To calculate tax (percent of increase) or commission (percent of what is sold), first you must convert the tax or commission percentage to a decimal, by dividing by 100. Then, multiply the decimal times the price to find the tax or commission. For example, if you buy some clothes for $150 plus 7% tax, first convert 7% to .07, then multiply .07 × 150 to find the tax is $10.50.

To review, see Calculating Sales Tax and Commission.

Unit 7 Vocabulary

This vocabulary list includes terms listed above that students need to know to successfully complete the final exam for the course.

  • commission
  • decrease
  • increase
  • percent
  • tax