Module 6 Percent % Section 6.1 Understanding Percent CQ-6-01. Write 0.19% 19% 1900% 0.0019% 19 as a percent. P. 1 of 54 P. 4 of 54 Denominators of The word percent means per hundred. A percent is another way to describe a part of a whole. 7 7% 7 out of of the rectangles are shaded. 7 percent of the whole is shaded. CQ-6-02. Write 0.059% 0.59% 5.9% 59% 5.9 as a percent. P. 2 of 54 P. 5 of 54 Denominators of 8.3 Write as a percent. 8.3 8.3% 435 Write as a percent. 435 435% Writing Percents as Decimals Percents can be written as fractions and decimals. 27 27% 27 0.27 27% 0.27 Changing a Percent to a Decimal 1. Drop the % symbol. 2. Move the decimal point two places to the left. P. 3 of 54 P. 6 of 54 1 of 9
Writing Percents as Decimals Write 19% as a decimal. 19%. 19. 0.19 Write 2.67% as a decimal. 2.67%. 2.67 0.0267 Write.2% as a decimal..2%.2. 0.002 An extra zero is added to the left of the 2. Two extra zeroes are added to the left of the 2. CQ-6-04. Write 0.001 as a percent. 0.001% 1% 10% 0.1% P. 7 of 54 P. 10 of 54 CQ-6-03. Write 2% to a decimal. 0.02 0.2 200 2 CQ-6-05. Write 2.467 as a percent. 0.02467% 246.7% 24.67% 2467% P. 8 of 54 P. 11 of 54 Writing Decimals as Percents Changing a Decimal to a Percent 1. Move the decimal point two places to the right. 2. Add the % symbol at the end of the number. Write 0.25 as a percent. 0.25 0.25. 25% Write 3.95 as a percent. 3.95 3.95. 395% P. 9 of 54 CQ-6-06. In Minnesota, 0.06 of the state is covered by water, more than any other state. What percent is covered by water? 6% 0.06% 60% 0.6% P. 12 of 54 2 of 9
Section 6.2 Changing Between Percents, Decimals, and Fractions CQ-6-07. Write 135% as a fraction in simplified form. 5 4 13.5 29 20 27 20 P. 13 of 54 P. 16 of 54 Percents to Fractions Any percent can be written as a fraction whose denominator is. The fraction should be simplified if possible. Convert 59.6% into a fraction in simplest form. 59.6% 0.596 Write as a decimal. 596 0 149 250 Write as a fraction. Simplify. P. 14 of 54 Fractions to Percents A convenient way to write a fraction as a percent is to write the fraction in decimal form first and then convert the decimal into a percent. Write 7 8 as a percent. 7 7 8 8 Divide. 0.875 Write as a decimal. 87.5% Write as a percent. P. 17 of 54 Percents to Fractions Convert 65% into a fraction in simplest form. 65% 65 13 20 Write as a fraction. Simplify. CQ-6-08. Write 34% 17.80% 21.25% 42.5% 17 80 as a percent. P. 15 of 54 P. 18 of 54 3 of 9
CQ-6-09. Change 510% 5.1% 51% 0.51% 1 5 10 to a percent. Section 6.3.A Solving Percent Problems Using Equations P. 19 of 54 P. 22 of 54 CQ-6-10. The brain represents of an average person s weight. What percent is this? 1.1. 2.2. 7.5% 3.3. 0.075% 4.4. 13.3% 75% 3 40 P. 20 of 54 Percent Problems into Equations To solve a percent problem, we express it as an equation with an unknown quantity. The following table is helpful when translating from a percent problem to an equation. Word Mathematical Symbol of Multiplication symbol: or ( ) or is what Any letter, for example, n or x find n or x P. 23 of 54 CQ-6-11. LeBron scored a basket 24 times out of 50 shots. What percent of his shots did he score? 42% 50% 48% 24% Percent Problems into Equations Translate into an equation. What is 9% of 65? n 9% 65 Translate into an equation. 24 is what percent of 144? P. 21 of 54 24 n 144 P. 24 of 54 4 of 9
Solving a Percent Problem A percent problem has three different parts. amount percent base Any one of the three quantities may be unknown. 1. When we do not know the amount: n 10% 500 2. When we do not know the base: 50 10% n 3. When we do not know the percent: 50 n 500 P. 25 of 54 Solving a Percent Problem: Base Unknown amount percent base 36 is 6% of what? 36 6% 36 0.06n 36 0.06n 0.06 0.06 600 n 36 is 6% of 600. n P. 28 of 54 Solving a Percent Problem: Amount Unknown amount percent base What is 9% of 65? n 9% 65 n (0.09) (65) n 5.85 5.85 is 9% of 65. P. 26 of 54 CQ-6-13. 17.4 is 25% of what number?. 4.35 52.2 69.6 34.8 P. 29 of 54 CQ-6-12. What is 23% of 256? 58.88 5.89 3. 1113.04 11.13 P. 27 of 54 CQ-6-14. A total of 2,480 students voted in the Student Government elections. This was 32% of the students enrolled. How many students were enrolled? 794 7,440 6,200 7,750 P. 30 of 54 5 of 9
Solving a Percent Problem: Percent Unknown 24 amount percent base 24 is what percent of 120? n 120 24 120n 24/120 120n/120 0.2 n 20% n 24 is 20% of 120. P. 31 of 54 The Parts of a Percent Proportion Proportions are another way to solve a percent problem. amount percent number base IS OF To use this proportion, we need to find the amount, base, and percent number in a word problem. % P. 34 of 54 CQ-6-15. What percent of 85 is 72? 18% 84.71% 118% 91.46% The Parts of a Percent Proportion amount percent number IS % base OF p is the percent number. 10% of 500 is 50. The base, b, is the entire quantity. 50 10 500 The amount, a, is the part compared to the whole. P. 32 of 54 P. 35 of 54 Section 6.3.B Solving Percent Problems Using Proportions P. 33 of 54 The Parts of a Percent Proportion Identify the amount, base, and percent number. The amount, a, is unknown. a the amount (unknown) The amount is 24. a 24 What is 9% of 65? The value of p is 9. p 9 24 is what percent of 144? The value of p is unknown. p the percent (unknown) The base usually follows the word of. b 65 The base usually follows the word of. b 144 P. 36 of 54 6 of 9
Solving a Percent Problem: Amount Unknown amount percent number base What is 9% of 65? a b p a 9 65 a 585 a 585 a 5.85 a b p 9 a unknown b 65 5.85 is 9% of 65. p Cross multiply. Divide both sides by. Simplify. IS % OF P. 37 of 54 CQ-6-17. 15% of what number is 75? 475 11.25 500 375 P. 40 of 54 CQ-6-16. What is 23% of 256? 58.88 3. 1113.04 11.13 5.89 P. 38 of 54 Solving a Percent Problem: Percent Unknown amount percent number a p base b 24 is what percent of 144? a p b 24 p 144 144 p 2400 p unknown a 24 b 144 Cross multiply. IS % OF 144p 2400 Divide both sides by 144. 144 144 2 b 0.16 16 % Simplify. 3 2 24 is 16 % of 144. 3 P. 41 of 54 Solving a Percent Problem: Base Unknown amount percent number a p base b 36 is 6% of what? a p b 36 6 b 6 b 3600 6b 3600 6 6 b 600 p 6 a 36 b unknown 36 is 6% of 600. Cross multiply. Divide both sides by 6. Simplify. IS % OF P. 39 of 54 CQ-6-18. What percent of 85 is 72? 18% 84.71% 118% 91.46% P. 42 of 54 7 of 9
Section 6.4 Solving Applied Percent Problems CQ-6-19. An inspector found that 4 out of 116 parts were defective. What percent of the parts were defective? 29% 3.45% 26.1% 3.03% P. 43 of 54 P. 46 of 54 Solving General Percent Problems Mary received a raise of 8% of her monthly salary. The amount of her raise was $48.16 per month. What was her monthly salary before her raise? This problem can be solved using either the equation method or the proportion method. Solving Discount Problems The amount of a discount is the product of the discount rate and the list price. SALE! 25% off a p 48.16 is 8% of n b The unknown quantity is the base. IS OF 48.16 8 b % P. 44 of 54 The discount rate is 25%. Discount discount rate list price P. 47 of 54 Solving General Percent Problems Mary received a raise of 8% of her monthly salary. The amount of her raise was $48.16 per month. What was her monthly salary before her raise? Equation method Proportion method 48.16 is 8% of n 48.16 8 48.16 0.08n b 48.16 0.08n 8 b 4816 0.08 0.08 8b 4816 48.16 n 8 8 0.08 602 n b 602 Mary s monthly salary before the raise was $602. P. 45 of 54 Solving Discount Problems Julie bought a leather sofa that was on sale for 35% off the original price of $1200. What was the discount? How much did Julie pay for the sofa? Discount discount rate list price 35% 1200 420 The discount was $420. Amount paid list price discount 1200 420 780 Julie paid $780 for the sofa. P. 48 of 54 8 of 9
Section 6.5 Solving Commission, Percent of Increase, and Percent of Decrease P. 49 of 54 Solving Increase Problems We sometimes need to find the percent by which a number increases or decreases. amount of increase Percent of increase original amount The cost of a certain car increased from $16,000 last year to $17,280 this year. What was the percent of increase? Amount of increase original amount new amount 17,280 16,000 1280 amount of increase Percent of increase original amount 1280 16000 0.08 The car s cost increased by 8%. P. 52 of 54 Solving Commission Problems The amount of money a person makes that is a percentage of the value of sales is called a commission. It is calculated by multiplying the percentage (called the commission rate) by the value of the sales. Commission commission rate value of sales A salesperson has a commission rate of 18.5%. He sells $43,250 worth of goods. What is his commission? Commission commission rate value of sales 18.5% $43,250 0.18.5 43,250 8001.25 His commission is $8,001.25. P. 50 of 54 Solving Decrease Problems amount of decrease Percent of decrease original amount Patrick weighed 285 pounds two years ago. After dieting, he reduced his weight to 171 pounds. What was the percent of decrease in his weight? Amount of decrease original amount new amount 285 171 114 amount of decrease Percent of decrease original amount 114 0.4 285 Patrick s weight decreased by 40%. P. 53 of 54 CQ-6-20. A real estate agent sells a house for $87,000. She gets a commission of 6% on the sale. What is her commission? $1,458.33 $5,220.00 $4,395.00 $14,583.33 CQ-6-21. The price of a laptop was $400 last summer. If the price of the same laptop is now $320, what is the percent of decrease? 80% 20% 25% % P. 51 of 54 P. 54 of 54 9 of 9