PERCENTS

Percent (%) means one part per hundred. 1% means one part per hundred and can be expressed as or 0.01. 35% means 35 parts per hundred and can be expressed as or 0.35.

Changing Percents to Equivalent Fractions

To change a percent to an equivalent fraction:

(1) Replace the percent sign with and multiply

(2) Reduce the resulting fraction to simplest form

Examples:

(a)

(b)

(c)

(d)

Changing Percents to Equivalent Decimals

To change a percent to an equivalent decimal:

(1) Replace the percent sign with 0.01 and multiply

Examples:

(a)

(b)

(c)

(d)

Observe: You can also change a percent to an equivalent decimal by

(1) dropping the percent sign and (2) moving the decimal point two

places to the left.

(e)

Changing Fractions to Percents

To change a fraction to an equivalent percent, multiply the fraction by 100%

Examples:

(a)

(b)

(c)

Changing Decimals to Percents

To change a decimal to an equivalent percent: move the decimal point two places to

the right and add the percent sign.

Examples:

(a)

(b)

(c)

(d)

Problems

(1) Convert each percent to a fraction

(a) 32% (b) 78% (c) 64% (d) 150% (e) (f)

(2) Convert each percent to a decimal

(a) 55% (b) 72% (c) 8.5% (d) 3% (e) 125% (f)

(3) Convert each fraction to a percent

(a) (b) (c) (d) (e) (f)

(4) Convert each decimal to a percent

(a) 0.08 (b) 0.56 (c) 0.825 (d) 0.063 (e) 1.82 (f) 3

Answers

(1) (a) (b) (c) (d) (e) (f)

(2) (a) 0.55 (b) 0.72 (c) 0.085 (d) 0.03 (e) 1.25 (f) 0.065

(3) (a) 70% (b) 40% (c) (d) 175% (e) (f) 225%

(4) (a) 8% (b) 56% (c) 82.5% (d) 6.3% (e) 182% (f) 300%

Solving Percent Problems

Amount is the part of the base

Percent is the part of the base in hundredths (always contains the percent sign)

Base is the number we are taking the percent of (always follows the word of)

Three types of problems

(1) 20% of 120 is what number or Find 20% of 120

(2) 15% of what number is 30 or 30 is 15% of what number

(3) What percent of 20 is 10 or 10 is what percent of 20

Problems

(1) 35% of 120 is what number

(2) What is of 72

(3) 15% of what number is 24

(4) 28 is 40% of what number

(5) What percent of 60 is 15

(6) 12 is what percent of 96

(7) 50 is what percent of 40

(8) A meal costs $18.80. A diner wants to leave a 15% tip. How much is the tip?

(9) A student answers 96 questions correctly on a 120 question multiple-choice exam. What percent of the questions were answered correctly?

(10) A person buying a home made a down payment of 20% of the purchase price.

The down payment was $36,000. What was the purchase price of the home?

Answers

(1) 42 (9) 80%

(2) 9 (10) $180,000

(3) 160

(4) 70

(5) 25

(6)

(7) 125%

(8) $2.82