Objectives

Find equivalent fractions, decimals, and percents.

Solve problems involving percent.

Page 171 – Percent Problems

Glossary Terms

Percent – a ratio that compares a number with 10025% of 40 is 10

percent rate – 25 is the percent ratethe calculated percentage of the base

base (of a percentage) – 40 is the basenumber of which a percentage is calculated

Percentage – 10 is the percentageamount obtained by multiplying a base by a percent rate

Meteorology Application

Relative humidity is a common example of percent. At 30ºC, 1 cubic meter of air can hold no more than 26

grams of water. At this amount, the relative humidity is 100%. At other amounts, ratios are used to determine the

relative humidity. If 1 cubic meter of air at 30ºC contains 6.5 g of water,

the relative humidity is 25% because 6.5/26 = ¼ or 25%.

Converting between fractions, decimals and percents.

Fractions to decimals – divide the numerator by the denominator

Decimals to percents – move the decimal point 2 places to the right

Fractions to percents – change the fraction to a decimal and the decimal to a percent

Percents to decimals – move the decimal point 2 places to the left

Decimals to fractions – write the decimal as a fraction and simplify

Write each percent as a decimal and as a fraction .

75% = 75100 = 0.75

110% = 110100

= 1.10

4.4% =

75100

= 34

110100

= 1110

= 1 110

4.4100

= 44 .

1000= 0.044 44 .

1000= 11 .

250

The Equation Method

The equation method is a method for finding an unknown part of a percent by setting up an equation

25% of 40 is what number (the percentage is unknown)

.25(40) = x 25% of what number is 10 (the base is unknown)

.25x = 10 What percent of 40 is 10 (the percent rate is unknown)

P · 40 = 10 or 40P = 10

The sophomore class is sponsoring a trip to see a play. Student tickets normally cost $8. If at least 20 people buy tickets, there is a 30% discount. How much will each ticket cost at the discounted price.

If there is a 30% discount, that means the discounted price is 70% of the full price, which is $8.

So, 70% of $8 is what number?

.70(8) = x

5.60 = x

So, the discounted price of the tickets is $5.60.

Examples

What percent of 80 is 15?

P · 80 = 15

80P = 15

P = 1580

P = .1875

18.75%

Find 115% of 200

What is 115% of 200

x = 1.15(200)

x = 230

45 is 40% of what number?

45 = .4x45.4

= x

112.5 = x

A VCR with a sale price of $239.40 is advertised as 40% off. What was the original price?

Since the price was 40% off, that means the $239.40 is 60% of the original price.

So, 239.40 is 60% of what number?239.40 = .6x

239.40 .6

= x

399 = x

So the original price was $399.

More Applications

Many types of problems involve finding a percent of increase or percent of decrease.

It’s important to remember in these types of problems that the original amount is always used as the base.

Percent of increase or decrease:

amount of change

original amount= percent of change

A family is adding additional rooms to their house. The house originally had 1500 sq ft of floor space. After the additions, the house will have 1800 sq ft. Find the percent of increase.

percent of increase = amount of change original amount

Amount of change is 1800 – 1500 = 300original amount is 1500

300 .

1500= 0.2 = 20%

So the percent of increase in floor space is 20%.

The price of a car that originally sold for $17,000 has been reduced to $14,450. Find the percent of decrease in the price of the car.

percent of decrease = amount of change original amount

Amount of change is 17000 – 14450 = 2550

2550 .

17000= 0.15 = 15%

So the percent of decrease was 15%.