Chapter 6: Percents

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42430_Cleaves_ch06 4/12/04 1:22 PM Page 191 Chapter 6 Summary Learning Outcomes Section 6-1 1 Write 2 Write Section 6-2 1 Identify 2 Use a whole number, fraction, or decimal as a percent. (p. 174) a percent as a whole number, fraction, or decimal. (p. 176) the rate, base, and portion in percent problems. (p. 178) the percentage formula to find the unknown value when two values are known. (p. 179) What to Remember with Examples 1. Multiply the number by 1 in the form of 100%. 2. The product has a % symbol. 20 3 3 100 6 = 6 × 100% = 600% = × 5 5 1 % = 60% 0.075 = 0.075 × 100% = 7.5% 1 1 1. Divide by 1 in the form of 100% or multiply by . 2. The quotient does not have a % symbol. 100% 48% = 48% ÷ 100% = 0.48 20% = 20% ÷ 100% = 20 = 100 157% = 157% ÷ 100% = 1.57 33 1 3 % = 331 3 % ÷ 100% = 0.33 1 3 1. Rate is usually written as a percent, but may be a decimal or fraction. 2. Base is the total or original amount. 3. Portion is the part, or amount of increase or decrease. It is also called the percentage. Identify the rate, base, and portion. 42% of 18 is what number? 42% is the rate. 18 is the base. The missing number is the portion. 1. Identify and classify the two known values and the one missing value. 2. Choose the appropriate percentage formula for finding the missing value. 3. Substitute the known values into the formula. For the rate, use the decimal or fractional equivalent of the percent. 4. Perform the calculation indicated by the formula. 5. Interpret the result. If finding the rate, convert decimal or fractional equivalents of the rate to a percent. 1 5 1 5 or 0.33 Find P if B 20 and R 15%. Find B if P 36 and R 9% P = R × B P = 15% ( 20) = 0. 15( 20) P = 3 P B = R 36 B = = 9% B = 400 36 0.09 Percents 191
42430_Cleaves_ch06 4/12/04 1:22 PM Page 192 Section 6-3 1 Find the amount of increase or decrease in percent problems. (p. 184) 2 Find 3 Find the new amount directly in percent problems. (p. 186) the rate or the base in increase or decrease problems. (p. 187) 1. To find the amount of increase: Amount of increase new amount beginning amount 2. To find the amount of decrease: Amount of decrease beginning amount new amount. A truck odometer increased from 37,580.3 to 42,719.6. What was the increase? 42,719.6 37,580.3 5,139.3 A truck carrying 62,980 pounds of food delivered 36,520 pounds. What was the amount of food (pounds) remaining on the truck? 62,980 36,520 26,460 pounds 1. Find the rate of the new amount. For increase: 100% rate of increase For decrease: 100% rate of decrease 2. Find the new amount. P RB New amount rate of new amount original amount Emily Denly works 30 hours a week but plans to increase her work hours by 20%. How many hours will she be working after the increase? For increase: 100% 20% 120% P P = = = = RB 120%( 30 hours) 120 . ( 30) 36 hours 1. Identify or find the amount of increase or decrease. P 2. To find the rate of increase or decrease, use the percentage formula R = . B amount of change R = original amount P 3. To find the base or original amount, use the percentage formula B = . R amount of change B = rate of change Tancia Brown made a profit of $5,896 in June and a profit of $6,265 in July. What is the percent of increase? Round to tenths of a percent. Amount of increase = $ 6, 265 − $ 5, 896 = $ 369 amount of change R = original amount $ 369 = $, 5 896 = 0. 06258 × 100% = 63 .% 192 Chapter 6
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Chapter 6: Percents

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