Percents

1. Percents

2. After-School Jobs all students surveyed students without jobs Response Number = Have a Job 40 = 60 Don’t Have a Job Total 100 all students surveyed students with jobs = = 5 3 5 2 100 40 100 60 Ratios and Unit Rates A survey asked students whether they had after-school jobs. Write each ratio as a fraction in simplest form. a. all students surveyed to students without jobs b. all students surveyed to students with jobs

3. Size (cards) Price 100 $2.70 50 $1.30 25 $.75 price number of cards price number of cards price number of cards $2.70 100 cards $1.30 50 cards $0.75 25 cards 100 cards: = $.027/card 25 cards: 50 cards: = $.026/card = $.03/card Find the unit prices. Ratios and Unit Rates The table shows prices for different packages of index cards. Which size has the lowest unit price? The 50-card pack has the lowest unit price.

4. Use conversion factors that convert gallons to cups and minutes to seconds. 30 gal 1 min 16 c 1 gal 1 min 60 s 30 gal/min = • • 130 gal 1 min 816 c 1 gal 1 min 1260 s Divide the common factors and units. = • • 8 c s = Simplify. Ratios and Unit Rates Convert 30 gal/min to cups/second. 30 gal/min equals 8 c/s.

5. 2 7 y 14 = 2 7 y 14 • 14 = • 14 28 7 = y Proportions 2 7 y 14 Solve = . Method 1: Multiplication Property of Equality 4 = y

6. 28 7 2 7 y 14 7y 7 = = Proportions (continued) Method 2: Cross products 2 • 14 = 7 • y 28 = 7y 4 = y

7. 3 5 21 35 3 5 21 35 Test by writing as a proportion. 3 • 35 5 • 21 Write cross products. Proportions Do the ratios and form a proportion? Explain. 105 = 105 Simplify. Yes; the ratios do form a proportion. The cross products are equal.

8. 100 275 25 d = d = Divide each side by 100. 275(25) 100 distance in rods distance in fathoms length in rods length in fathoms Proportions One hundred rods is about 275 fathoms. About how many fathoms is 25 rods? Let d = distance in fathoms. 100d = 275(25) Write cross products. d = 68.75 Simplify. 25 rods is about 68.75 fathoms.

9. Side AB corresponds = Side CD corresponds to side EF. to side GH. 6 • 2 3 3k 3 = Divide each side by 3. 6 k 3 2 Similar Figures and Scale Drawings Trapezoid ABCD ~ trapezoid EFGH. Find the value of k. Write a proportion for corresponding sides. 6 • 2 = k • 3 Write cross products. 4 = kSimplify.

10. Corresponding sides of similar triangles are in proportion. 1.5 5 3 x = 1.5x 1.5 5 • 3 1.5 Divide each side by 1.5. = Similar Figures and Scale Drawings A flagpole casts a shadow 5 ft long. At the same time, a yardstick casts a shadow 1.5 ft long. The triangle shown for the flagpole and its shadow is similar to the triangle shown for the yardstick and its shadow. How tall is the flagpole? 1.5x = 5 • 3   Write cross products. x = 10   Simplify. The flagpole is 10 ft tall.

11. map (in.) actual (mi.) 1 24 3 d map (in.) actual (mi.) Write a proportion. = 1 • d = 24 • 3 Write cross products. d = 72 Simplify. Similar Figures and Scale Drawings The scale of a map is 1 in. : 24 mi. About how far is it between two cities that are 3 in. apart on the map? It is about 72 mi between the two cities.

12. 3 4 7 4 30 100 175 100 Write as a fraction with a denominator of 100. 3 10 Simplify. Write as a fraction with a denominator of 100. Simplify. 1 Write as a mixed number. Fractions, Decimals, and Percents Write each percent as a fraction or a mixed number. a. 30% b. 175%

13. 7.3% = Write as a fraction with a denominator of 100. = 007.3   Divide by moving the decimal point two places to the left. You may need to write one or more zeros. 7.3 100 Fractions, Decimals, and Percents Express 7.3% as a decimal. = 0.073

14. 412 1,000 0.412 = 412 ÷ 10 1,000 ÷ 10 = 41.2 100 = 0.412 = 41.2% Fractions, Decimals, and Percents Express 0.412 as a percent. Method 1:Rewrite as a fraction. = 41.2% Method 2: Move the decimal point.

15. 4 7 Write a fraction. Fractions, Decimals, and Percents Four out of seven members of the chess club are boys. What percent of the chess club members are boys? 0.5714 Divide the numerator by the denominator. 57.14%   Write as a percent. About 57% of the chess club members are boys.

16. 100n 100 = Write a proportion. 23(158) 100 =    Divide each side by 100. 23 100 n 158 Proportions and Percents Find 23% of 158. 23(158) = 100nWrite cross products. 36.34 = nSimplify. 23% of 158 is 36.34.

17. = Write a proportion. =    Divide each side by 34. 100(28) 34 n 100 34n 34 82.4 Round. 28 34 Proportions and Percents What percent of 34 is 28? Round to the nearest tenth of a percent. 34n = 100(28) Write cross products. n = 82.35... Simplify. 28 is approximately 82.4% of 34.

18. = Write a proportion. 100(216) 72 =    Divide each side by 72. 72n 72 72 100 216 n Proportions and Percents 216 is 72% of what number? 72n = 100(216) Write cross products. n = 300 Simplify. 216 is 72% of 300.

19. = Write a proportion. 100(90) 15 =    Divide each side by 15. 15 100 15x 15 90 x Proportions and Percents A tile floor has 90 blue tiles, which is 15% of all the tiles in the floor. How many tiles are in the floor in all? 15x = 100(90) Write cross products. x = 600 Simplify. The floor has 600 tiles in all. Check: Is the answer reasonable? The problem says the number of blue tiles is 15%. 10% of 600 is 60, so 5% of 600 is 30, and 15% is 60 + 30 = 90. The answer is reasonable.

20. Percents and Equations What is 35% of 84? n = 0.35 • 84   Write an equation. Write the percent as a decimal. n = 29.4 Simplify. 35% of 84 is 29.4.

21. = Divide each side by 26. 26n 26 65 26 Percents and Equations What percent of 26 is 65? n • 26 = 65 Write an equation. n = 2.5 Simplify. = 250%   Change the decimal to a percent. 65 is 250% of 26.

22. Percents and Equations A car salesman makes a 6.5% commission on each car he sells. How much does he make on the sale of a car for $35,000? Words amount of commissionis 6.5% of $35,000 Let c = amount of commission. Equationc = 0.065 • $35,000 c = 0.065 • 35,000 = 2,275 The salesman’s commission is $2,275.

23. Words 414 is 46% of people called Let n = number of people called. Equation 414 = 0.46 • n 0.46n 0.46 414 0.46 = Percents and Equations During a telephone survey, 414 people, or 46% of those called, said that they were watching station RFGT at the time of the call. How many people were called? 0.46n = 414 n = 900 900 people were called.

24. amount of increase original amount percent of increase = = 1.6 8 Percent of Change Find the percent of increase from 8 to 9.6. amount of increase = 9.6 – 8 = 1.6 = 0.2 = 20% The percent of increase from 8 to 9.6 is 20%.

25. amount of increase original amount percent of increase = = 15 7.5 Percent of Change In a given year, Hillsboro had a total of 7.5 in. of rain by March 1 and a total of 22.5 in. by July 1. Find the percent of increase from 7.5 to 22.5. amount of increase = 22.5 – 7.5 = 15 = 2 = 200% The percent of increase from March 1 to July 1 was 200%.

26. 130 1,250 amount of decrease original amount percent of decrease = = Percent of Change Find the percent of decrease from 1,250 to 1,120. amount of decrease = 1,250 – 1,120 = 130 = 0.104 = 10.4%

27. Markup and Discount A grocery store has a 20% markup on a can of soup. The can of soup costs the store $1.25. Find the markup. markup = percent of markup • store’s cost = 0.2 • 1.25 = 0.25        Simplify. The markup is $.25.

28. Markup and Discount A bookstore pays $4.50 for a novel. The percent of markup is 45%. Find the novel’s selling price. 0.45 • 4.50 = 2.03 Multiply to find the markup. 4.50 + 2.03 = 6.53   Store’s cost + markup = selling price. The selling price is $6.53.

29. Markup and Discount A camera that regularly sells for $210 is on sale for 30% off. Find the discount. discount = percent of discount • regular price = 0.30 • 210 = 63 The discount is $63.