"Percent" means divided by 100. Thus 52% means 52/100 = .52 or 52 parts out of 100. A percent is a ratio, that is a fraction whose denominator is always 100. Note: A percent may be called a rate - that is, so many per hundred. % is % use --- = -- 100 of Fill in known values. Solve the resulting proportion by cross multiplying and dividing. :RA % 6 Example: --- = -- 100 24 x 6 --- = -- 100 24 24x = 600 x = 25% Ans. :RA 2 1/3 140 Example: ----- = --- 100 x 2 1/3x = 14000 7 x = 14000/ - 3 x = 6000 Ans. :RA The following is a method to solve most percent problems. % decrease amt. decrease ---------- = ------------- 100 orignal % increase amt. increase ---------- = ------------- 100 orignal % discount amt. discount ---------- = ------------- 100 orignal :RA Example: 2 x .36y --- = ----- 2 100 1y x = 36% Ans. :RA Example: % decrease amt. decrease ---------- = ------------- 100 orignal 20 120,000 - x --- = ----------- 100 x 20x = 12,000,000 - 100x 120x = 12,000,000 x = 100,000 Ans. :RA Note: In converting from fractions to percents and decimals, bear in mind that per cent means "divided by 100". Thus, when you convert to percent (words or symbols) you must multiply the original number by 100 so as not to change the original value. Correspondingly, when you convert from percent to a decimal, you must divide the original number by 100 for the same reason. :RA Examples: 1. 0.0294 = 0.0294 x 100 = 2.94% 2. 0.13% = .13/100 = 0.0013 3. 1 1/2% = 1.5/100 = 0.015 4. 2.78 = 2.78 x 100 = 278% 5. 3/4 = .75 x 100 = 75% 6. .35 = .35 x 100 = 35% :RA Example: If the length of each side of a square is decreased 20%, what is the percent decrease in area? Let y = side of large square 4 -y = side of small square 5 2 original area = y :RA 2 4y 4y 16y new area = -- x -- = ---- 5 5 25 2 2 2 16y 9y decrease = y - ---- = --- 25 25 % decrease in area = 9/25 x 100 = 36% Ans. :RA Note: You should memorize the following: 10% = 1/10 20% = 1/5 30% = 3/10 40% = 2/5 50% = 1/2 60% = 3/5 70% = 7/10 80% = 4/5 90% = 9/10 100% = 1 :RA 33 1/3% = 1/3 66 2/3% = 2/3 25% = 1/4 75% = 3/4 12 1/2% = 1/8 37 1/2% = 3/8 62 1/2% = 5/8 87 1/2% = 7/8 16 2/3% = 1/6 83 1/3% = 5/6 :RA Example: The population of a city is now 120,000. If the census shows a 20% increase over the previous census, what was the previous population? Let 100% = previous population 120% = present population = 120,000 1% = 120,000/120 = 1000 100% = 100,000 Ans. :ET :ET
