Working with Percents

Percent means “for each hundred.” For example 50%, which means 50 for each 100, can also be written as . Recall that fraction bars indicate division, and that dividing a number by 100 is equivalent to moving the decimal point two places to the left. Consequently, . When computing with percents, make a choice between using the decimal notation or a fraction based on the rest of the problem.

Example 1

Find 25% of 200.

Solution 1

Example 2

40 is what percent of 90?

Solution 2

, so by cross-multiplication, 90p = 4000

This results in p = or %

Example 3

Suppose you are buying a house for $145,000 and are asked to pay a 30% down payment, how much do you pay?

Solution 3

We’ll need to find 30% of 145,000. Let’s use the ratio method because 145,000 has enough zeros at the end to cancel out the 100, as follows:

A 30% down payment is $43,500

Example 4

A $955 sofa is on sale for 23% off and there is a 5.5% sales tax. What is the final cost of the sofa, including tax?

Solution 4

We use decimal notation since the numbers are not "nice".
First, find 23% of $955, which is .23 · 955 = 219.65.

The sale price of the sofa is then 955 - 219.65, which is $735.35.

Next, compute 5.5% of 735.35, which is .055 · 735.35 40.44.

Note that we rounded to the nearest penny. The final cost of the sofa is the sale price + the sales tax, $735.35 + $40.44 = $775.79.