Session 9, Part B:
Decimals and Percents (45 minutes)

In This Part: Percent as Proportion | Percents as Fractions and Decimals | Percent Models

The word "percent" means "out of 100." Note 6 For example, 49% means 49 out of 100. Percents can also be expressed as fractions or decimals, since they too can be used to imply some part of a whole. So 49% can also be written as 49/100 or 0.49.

A percent implies a ratio: It is some part "per 100." Ratios enable us to set up a relationship between two numbers. For example, in a water molecule, there is always one oxygen atom for every two hydrogen atoms, which means that the ratio of oxygen to hydrogen is 1:2. In a percent, the second number in the ratio is always 100. Such ratios always express a number of parts per 100 parts.

You can approach any kind of percent problem if you think of it as a proportion that equates two ratios: a data ratio and a percent ratio. In other words:

Since the percent whole is always 100, we can substitute 100 for "percent whole" in this formula:

Notice that there are three different unknowns in this equation. If you know any two of them, you can easily find the third.

For example, if you want to know how much 30% of \$150 is, you'd write the proportion as follows:

From here, you can easily calculate the value you're looking for, which in this case is \$45.

Problem B1

 a. You bought a new television set at a 20% discount and saved \$80. What was the original price of the set? b. How much did you pay for the set?

 Problem B2 Jane bought a dress on a 25%-off sale for a total of \$39. What was the original pre-sale price of the dress?

 "Percent Part" for this problem should not be 25%. Why?   Close Tip "Percent Part" for this problem should not be 25%. Why?

 Problem B3 The bookstore reduced all items by 20% for the spring sale. After the sale, it increased the prices to 20% above the sale price. Were these prices the same as the original prices? Explain.

 Try starting with an original price of \$100. Note that when working with these types of percent problems, using 100 as a starting point can greatly simplify your calculations.   Close Tip Try starting with an original price of \$100. Note that when working with these types of percent problems, using 100 as a starting point can greatly simplify your calculations.

 Session 9: Index | Notes | Solutions | Video