Скачать презентацию Ratios and Unit Rates PRE-ALGEBRA LESSON 6 -1 Скачать презентацию Ratios and Unit Rates PRE-ALGEBRA LESSON 6 -1

97e286347b857ad4ad8fb4187c2e6a4a.ppt

  • Количество слайдов: 72

Ratios and Unit Rates PRE-ALGEBRA LESSON 6 -1 4 Write three fractions equivalent to Ratios and Unit Rates PRE-ALGEBRA LESSON 6 -1 4 Write three fractions equivalent to . 12 Sample answers 1 , , 6 2 3 6 18 6 -1

Ratios and Unit Rates PRE-ALGEBRA LESSON 6 -1 (For help, go to Lesson 4 Ratios and Unit Rates PRE-ALGEBRA LESSON 6 -1 (For help, go to Lesson 4 -4. ) Write in simplest form. 1. 30 2. 24 3. 54 4. 12 5. 14 6. 40 35 15 40 60 42 24 Check Skills You’ll Need 6 -1

Ratios and Unit Rates PRE-ALGEBRA LESSON 6 -1 Solutions 30 30 ÷ 5 24 Ratios and Unit Rates PRE-ALGEBRA LESSON 6 -1 Solutions 30 30 ÷ 5 24 24 ÷ 8 1. 35 = 35 ÷ 5 2. = 40 ÷ 8 40 6 = 7 3 = 5 54 54 ÷ 6 3. 60 = 60 ÷ 6 12 9 4 = 10 14 14 ÷ 14 5. 42 = 42 ÷ 14 12 ÷ 3 4. = 15 ÷ 3 15 = 5 40 40 ÷ 8 6. = 24 ÷ 8 24 1 5 = = 1 2 3 = 3 3 6 -1

Ratios and Unit Rates PRE-ALGEBRA LESSON 6 -1 A survey asked students whether they Ratios and Unit Rates PRE-ALGEBRA LESSON 6 -1 A survey asked students whether they had afterschool jobs. Write each ratio as a fraction in simplest form. a. all students surveyed to students without jobs all students surveyed students without jobs = 100 Response 60 5 = 3 Number Have a Job 40 Don’t Have a Job b. all students surveyed to students with jobs all students surveyed students with jobs After-School Jobs 60 Total 100 = 100 40 5 = 2 Quick Check 6 -1

Ratios and Unit Rates PRE-ALGEBRA LESSON 6 -1 The table shows prices for different Ratios and Unit Rates PRE-ALGEBRA LESSON 6 -1 The table shows prices for different packages of index cards. Which size has the lowest unit price? Size (cards) Price 100 $2. 70 50 $1. 30 25 $. 75 100 cards: price number of cards $2. 70 100 cards = $. 027/card 50 cards: price number of cards $1. 30 50 cards Find the = $. 026/card unit prices. 25 cards: price number of cards $0. 75 25 cards = $. 03/card The 50 -card pack has the lowest unit price. 6 -1 Quick Check

Ratios and Unit Rates PRE-ALGEBRA LESSON 6 -1 Convert 30 gal/min to cups/second. 30 Ratios and Unit Rates PRE-ALGEBRA LESSON 6 -1 Convert 30 gal/min to cups/second. 30 gal 16 c 1 min 30 gal/min = • 60 s 1 min 1 gal 130 gal 816 c = • 1 min 1 gal 1 min 260 s 1 8 c Use conversion factors that convert gallons to cups and minutes to seconds. Divide the common factors and units. Simplify. = s 30 gal/min equals 8 c/s. Quick Check 6 -1

Ratios and Unit Rates PRE-ALGEBRA LESSON 6 -1 Write each ratio as a fraction Ratios and Unit Rates PRE-ALGEBRA LESSON 6 -1 Write each ratio as a fraction in simplest form. 1. 4 out of 20 students ride the bus to school. 1 5 2. 8 out of 10 students buy lunch. 4 5 Find each unit rate. 3. You pay $4. 50 for 2 gallons of orange juice. $2. 25/gal 4. You pay $21. 60 for a 20 -lb bag of dog food. $1. 08/lb 5. Convert 15 yd/min to inches/second. 9 in. /s 6 -1

Proportions PRE-ALGEBRA LESSON 6 -2 Evaluate each of the following operations for n = Proportions PRE-ALGEBRA LESSON 6 -2 Evaluate each of the following operations for n = 6. a. Multiply n by 4 and add 6. b. Multiply n by 9 and add 12 30 66 6 -2

Proportions PRE-ALGEBRA LESSON 6 -2 (For help, go to Lesson 2 -6. ) Solve Proportions PRE-ALGEBRA LESSON 6 -2 (For help, go to Lesson 2 -6. ) Solve each equation. 1. 4 x = 52 2. 3 y = 18 3. 5 b = 75 4. 7 k = 21 Check Skills You’ll Need 6 -2

Proportions PRE-ALGEBRA LESSON 6 -2 Solutions 1. 4 x = 52 4 x 4 Proportions PRE-ALGEBRA LESSON 6 -2 Solutions 1. 4 x = 52 4 x 4 = 2. 3 y = 18 52 4 3 y 3 = 18 3 x = 13 y = 6 3. 5 b = 75 4. 7 k = 21 5 b 5 = 75 5 7 k 7 b = 15 = 21 7 k = 3 6 -2

Proportions PRE-ALGEBRA LESSON 6 -2 2 y Solve = . 7 14 Method 1 Proportions PRE-ALGEBRA LESSON 6 -2 2 y Solve = . 7 14 Method 1 2 Multiplication Property of Equality y 7 = 14 2 y • 14 = • 14 7 14 28 = y 7 4 = y 6 -2

Proportions PRE-ALGEBRA LESSON 6 -2 (continued) Method 2 2 Cross products y 7 = Proportions PRE-ALGEBRA LESSON 6 -2 (continued) Method 2 2 Cross products y 7 = 14 2 • 14 = 7 • y 28 = 7 y 28 7 y 7 = 7 4 = y Quick Check 6 -2

Proportions PRE-ALGEBRA LESSON 6 -2 3 5 21 35 Do the ratios and form Proportions PRE-ALGEBRA LESSON 6 -2 3 5 21 35 Do the ratios and form a proportion? Explain. 3 5 21 35 Test by writing as a proportion. 3 • 35 5 • 21 Write cross products. 105 = 105 Simplify. Yes; the ratios do form a proportion. The cross products are equal. Quick Check 6 -2

Proportions PRE-ALGEBRA LESSON 6 -2 One hundred rods is about 275 fathoms. About how Proportions PRE-ALGEBRA LESSON 6 -2 One hundred rods is about 275 fathoms. About how many fathoms is 25 rods? Let d = distance in fathoms. length in rods length in fathoms 100 d = 275(25) d = 275(25) 100 d = 68. 75 100 25 = d 275 distance in rods distance in fathoms Write cross products. Divide each side by 100. Simplify. 25 rods is about 68. 75 fathoms. Quick Check 6 -2

Proportions PRE-ALGEBRA LESSON 6 -2 Solve each proportion. 1. a = 5 12 6 Proportions PRE-ALGEBRA LESSON 6 -2 Solve each proportion. 1. a = 5 12 6 10 2. 3 = 6 8 x 16 Does each pair of ratios form a proportion? Explain. 2 0. 4 3. 9 = 1. 8 Yes; the cross products are equal. 21 14 4. 50 = 25 No; the cross products are not equal. 5. 100 nautical miles equals about 115 statute miles. About how far in ` nautical miles is 50 statute miles? Round to the nearest whole number. about 43 nautical miles 6 -2

Similar Figures and Scale Drawings PRE-ALGEBRA LESSON 6 -3 Find each value of n. Similar Figures and Scale Drawings PRE-ALGEBRA LESSON 6 -3 Find each value of n. 18 n a. b. 1. 5 = n =5 15 4. 5 2. 7 n = 6 n = 0. 9 6 -3

Similar Figures and Scale Drawings PRE-ALGEBRA LESSON 6 -3 (For help, go to Lesson Similar Figures and Scale Drawings PRE-ALGEBRA LESSON 6 -3 (For help, go to Lesson 6 -2. ) Solve each proportion. Round to the nearest tenth where necessary. 2 f 3 50 1. 3 = 21 2. 8 = p 9 15 3. 4 = p 16 19 4. 3 = g Check Skills You’ll Need 6 -3

Similar Figures and Scale Drawings PRE-ALGEBRA LESSON 6 -3 Solutions 1. 2 f = Similar Figures and Scale Drawings PRE-ALGEBRA LESSON 6 -3 Solutions 1. 2 f = 21 3 2. 3 50 = p 8 3. 9 15 = p 4 4. 16 19 = g 3 3 • f = 2 • 21 8 • 50 = 3 • p 4 • 15 = 9 • p 3 • 19 = 16 • g 3 f = 42 400 = 3 p 60 = 9 p 57 = 16 g 3 f 42 = 3 3 400 3 p = 3 3 60 9 p = 9 9 57 16 g = 16 16 6. 7 = p 3. 6 = g f = 14 133. 3 = p 6 -3

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

Similar Figures and Scale Drawings PRE-ALGEBRA LESSON 6 -3 A flagpole casts a shadow Similar Figures and Scale Drawings PRE-ALGEBRA LESSON 6 -3 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. 5 3 = 5 x Corresponding sides of similar triangles are in proportion. 1. 5 x = 5 • 3 Write cross products. 1. 5 x 5 • 3 = 1. 5 Divide each side by 1. 5. x = 10 Simplify. The flagpole is 10 ft tall. Quick Check 6 -3

Similar Figures and Scale Drawings PRE-ALGEBRA LESSON 6 -3 The scale of a map Similar Figures and Scale Drawings PRE-ALGEBRA LESSON 6 -3 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? map (in. ) actual (mi. ) 1 3 = d 24 map (in. ) actual (mi. ) 1 • d = 24 • 3 d = 72 Write a proportion. Write cross products. Simplify. It is about 72 mi between the two cities. Quick Check 6 -3

Similar Figures and Scale Drawings PRE-ALGEBRA LESSON 6 -3 Solve. 1. Parallelogram ABCD ~ Similar Figures and Scale Drawings PRE-ALGEBRA LESSON 6 -3 Solve. 1. Parallelogram ABCD ~ parallelogram EFGH. Find the value of x. 12 2. A girl who is 4 feet tall casts a shadow that is 6 feet long. The tree next to her casts a shadow that is 12 feet long. How tall is the tree? 8 ft 3. The scale on a map is 3 in. : 100 mi. What is the actual distance between two towns that are 9 in. apart on the map? 300 mi 6 -3

Probability PRE-ALGEBRA LESSON 6 -4 Forty-three boys and five girls tried out for the Probability PRE-ALGEBRA LESSON 6 -4 Forty-three boys and five girls tried out for the middle school football team. One-fourth of the students were dropped after the first day. Of 1 those who were left, were dropped after the second day. Of those 6 4 who remained, made the team. How many students made 5 the team? 24 6 -4

Probability PRE-ALGEBRA LESSON 6 -4 (For help, go to Lesson 5 -3. ) Simplify. Probability PRE-ALGEBRA LESSON 6 -4 (For help, go to Lesson 5 -3. ) Simplify. 3 1. 1 – 8 3. 1 – 6 11 17 2. 1 – 20 1 4. 1 – 12 Check Skills You’ll Need 6 -4

Probability PRE-ALGEBRA LESSON 6 -4 Solutions 1. 1 – 3 2. 1 – 17 Probability PRE-ALGEBRA LESSON 6 -4 Solutions 1. 1 – 3 2. 1 – 17 8 8 3 8 – 3 – = 8 8 8 5 = 8 6 11 11 6 11 – 6 – = 11 11 11 5 = 11 20 20 – 17 20 17 – = 20 20 20 3 = 20 4. 1 – 1 3. 1 – 6 -4 12 12 1 12 – 1 – = 12 12 12 11 = 12

Probability PRE-ALGEBRA LESSON 6 -4 Find P(rolling a prime number) with one number cube. Probability PRE-ALGEBRA LESSON 6 -4 Find P(rolling a prime number) with one number cube. 3 number of favorable outcomes = 6 number of possible outcomes 3 3 prime-number outcomes (2, 3, 5) 6 possible outcomes 1 P(rolling a prime number) = , or . 6 2 Quick Check 6 -4

Probability PRE-ALGEBRA LESSON 6 -4 The probability that a child is an identical twin Probability PRE-ALGEBRA LESSON 6 -4 The probability that a child is an identical twin is 4 in 1, 000. Find P(not an identical twin) + P(identical twin) = 1 Write an equation. 4 P(not an identical twin) + 1, 000 = 1 P(not an identical twin) + Substitute. 4 – 4 = 1 – 4 1, 000 996 P(not an identical twin) = 1, 000 = Subtract 4 from 1, 000 each side. Simplify. 249 250 The probability that a child is not an identical twin is 249 . 250 6 -4 Quick Check

Probability PRE-ALGEBRA LESSON 6 -4 You have five different coins in your pocket: a Probability PRE-ALGEBRA LESSON 6 -4 You have five different coins in your pocket: a penny, a nickel, a dime, a quarter, and a half-dollar. You pull out one coin at random. What are the odds in favor of the coin being worth less than ten cents? 2 odds in favor = 3 2 are worth less than ten cents. 3 are not. 2 3 The odds are , or 2 to 3, in favor of the coin being worth less than ten cents. Quick Check 6 -4

Probability PRE-ALGEBRA LESSON 6 -4 Find each probability. 1. A letter is selected at Probability PRE-ALGEBRA LESSON 6 -4 Find each probability. 1. A letter is selected at random from the letters A, E, I, O, and U. Find the probability that the letter is an A. 1 5 2. In one class, Ms. Lang has 8 boys and 12 girls. She needs to choose one student to help pass out papers. What are the odds that a girl is chosen? 3 2 3. When rolling a number cube, what is P(6)? What is P(not 6)? 1; 5 6 6 6 -4

Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6 -5 5 Samantha needs a -in. bit Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6 -5 5 Samantha needs a -in. bit for her drill. Should she look in the bin 8 marked 62. 5 in. , 6. 25 in. , 0. 625 in. , or 0. 063 in. ? 0. 625 in. 6 -5

Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6 -5 (For help, go to Lesson 5 Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6 -5 (For help, go to Lesson 5 -2. ) Write each fraction as a decimal. 5 1. 8 4. 5 6 9 2. 20 3. 3 4 2 3 6. 8 11 5. Check Skills You’ll Need 6 -5

Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6 -5 Solutions 5 8 9 20 1. Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6 -5 Solutions 5 8 9 20 1. = 5 ÷ 8 2. = 9 ÷ 20 = 0. 625 = 0. 45 5 4. = 5 ÷ 6 6 = 0. 83 2 5. = 2 ÷ 3 3 = 0. 6 6 -5 3 4 3. = 3 ÷ 4 = 0. 75 8 6. = 8 ÷ 11 11 = 0. 72

Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6 -5 Write each percent as a fraction Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6 -5 Write each percent as a fraction or a mixed number. a. 30% 30 100 3 10 Write as a fraction with a denominator of 100. Simplify. b. 175% 175 100 Write as a fraction with a denominator of 100. 7 4 Simplify. 13 4 Write as a mixed number. 6 -5 Quick Check

Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6 -5 Express 7. 3% as a decimal. Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6 -5 Express 7. 3% as a decimal. 7. 3% = 7. 3 100 = 007. 3 Write as a fraction with a denominator of 100. Divide by moving the decimal point two places to the left. You may need to write one or more zeros. = 0. 073 Quick Check 6 -5

Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6 -5 Express 0. 412 as a percent. Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6 -5 Express 0. 412 as a percent. Method 1 0. 412 = Rewrite as a fraction. 412 1, 000 = 412 ÷ 10 1, 000 ÷ 10 = 41. 2 100 = 41. 2% Method 2 Move the decimal point. 0. 412 = 41. 2% Quick Check 6 -5

Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6 -5 Four out of seven members of Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6 -5 Four out of seven members of the chess club are boys. What percent of the chess club members are boys? 4 7 Write a fraction. 0. 5714 Divide the numerator by the denominator. 57. 14% Write as a percent. About 57% of the chess club members are boys. Quick Check 6 -5

Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6 -5 Write each percent as a fraction Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6 -5 Write each percent as a fraction or mixed number, and as a decimal. 1. 325% 13 , or 3 ; 3. 25 1 4 4 2. 1. 1% 11 ; or 0. 011 1, 000 Write each as a percent. 3. 2. 01 201% 3 4. 5 60% 5. Six out of fifteen students own skateboards. What percent of students own skateboards? 40% 6 -5

Proportions and Percents PRE-ALGEBRA LESSON 6 -6 A painter uses 3 cans of paint Proportions and Percents PRE-ALGEBRA LESSON 6 -6 A painter uses 3 cans of paint to paint four sets of shelves. How many cans of paint does he need to buy to paint nine sets of shelves? 7 cans 6 -6

Proportions and Percents PRE-ALGEBRA LESSON 6 -6 (For help, go to Lesson 6 -2. Proportions and Percents PRE-ALGEBRA LESSON 6 -6 (For help, go to Lesson 6 -2. ) Solve each proportion. x 25 1. 100 28 = 52 98. 9 43 x 100 27 2. = 100 x 13 3. = x 100 4. = 150 Check Skills You’ll Need 6 -6

Proportions and Percents PRE-ALGEBRA LESSON 6 -6 Solutions 1. 25 x 100 = 28 Proportions and Percents PRE-ALGEBRA LESSON 6 -6 Solutions 1. 25 x 100 = 28 2. 98. 9 43 x = 100 • x = 25 • 28 43 • x = 98. 9 • 100 100 x = 700 43 x = 9890 100 x 700 = 100 43 x 9890 43 = 43 x = 7 52 x = 230 13 x 1300 52 = 27 2700 150 3. = x 100 13 • 100 = 52 • x 1300 = 52 x 150 4. = 150 100 • 27 = x • 150 2700 = 150 x 52 = 25 = x 18 = x 6 -6

Proportions and Percents PRE-ALGEBRA LESSON 6 -6 Find 23% of 158. 23 n = Proportions and Percents PRE-ALGEBRA LESSON 6 -6 Find 23% of 158. 23 n = 158 100 Write a proportion. 23(158) = 100 n Write cross products. 100 n 23(158) = 100 Divide each side by 100. 36. 34 = n Simplify. 23% of 158 is 36. 34. Quick Check 6 -6

Proportions and Percents PRE-ALGEBRA LESSON 6 -6 What percent of 34 is 28? Round Proportions and Percents PRE-ALGEBRA LESSON 6 -6 What percent of 34 is 28? Round to the nearest tenth of a percent. n 28 = 34 100 Write a proportion. 34 n = 100(28) Write cross products. 100(28) 34 n = 34 34 Divide each side by 34. n = 82. 35. . . 82. 4 Simplify. Round. 28 is approximately 82. 4% of 34. 6 -6 Quick Check

Proportions and Percents PRE-ALGEBRA LESSON 6 -6 216 is 72% of what number? 72 Proportions and Percents PRE-ALGEBRA LESSON 6 -6 216 is 72% of what number? 72 216 = n 100 Write a proportion. 72 n = 100(216) Write cross products. 72 n 100(216) = 72 72 Divide each side by 72. n = 300 Simplify. 216 is 72% of 300. Quick Check 6 -6

Proportions and Percents PRE-ALGEBRA LESSON 6 -6 A tile floor has 90 blue tiles, Proportions and Percents PRE-ALGEBRA LESSON 6 -6 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? 90 15 = x 100 Write a proportion. 15 x = 100(90) Write cross products. 100(90) 15 x = 15 15 Divide each side by 15. 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. Quick Check 6 -6

Proportions and Percents PRE-ALGEBRA LESSON 6 -6 Solve. 1. Find 47% of 2, 400. Proportions and Percents PRE-ALGEBRA LESSON 6 -6 Solve. 1. Find 47% of 2, 400. 1, 128 2. What percent of 700 is 1, 498? 214% 3. 6 is 3% of what number? 200 4. Water covers about 361, 736, 000 km 2, or about 70. 8% of Earth’s surface. What is the approximate surface area of Earth? about 511, 000 km 2 6 -6

Percents and Equations PRE-ALGEBRA LESSON 6 -7 Match each expression in Column 1 with Percents and Equations PRE-ALGEBRA LESSON 6 -7 Match each expression in Column 1 with an equivalent expression in Column 2. Column 1 Column 2 1. 50% of 250 a. 250 2. 100% of 250 b. 2. 5 3. 1% of 250 c. 25 4. 10% of 250 d. 125 1. d 2. a 3. b 4. c 6 -7

Percents and Equations PRE-ALGEBRA LESSON 6 -7 (For help, go to Lesson 6 -5. Percents and Equations PRE-ALGEBRA LESSON 6 -7 (For help, go to Lesson 6 -5. ) Write each percent as a decimal. 1. 48% 2. 5% 4. 72. 25% 5. 136% 3. 23. 8% 6. 178. 5% Check Skills You’ll Need 6 -7

Percents and Equations PRE-ALGEBRA LESSON 6 -7 Solutions 48 5 1. 48% = 100 Percents and Equations PRE-ALGEBRA LESSON 6 -7 Solutions 48 5 1. 48% = 100 2. 5% = 100 = 0. 48 = 0. 05 23. 8 72. 25 3. 23. 8% = 100 = 0. 238 4. 72. 25% = 100 = 0. 7225 178. 5 136 5. 136% = 100 6. 178. 5% = 100 = 1. 785 = 1. 36 6 -7

Percents and Equations PRE-ALGEBRA LESSON 6 -7 What is 35% of 84? n = Percents and Equations PRE-ALGEBRA LESSON 6 -7 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. Quick Check 6 -7

Percents and Equations PRE-ALGEBRA LESSON 6 -7 What percent of 26 is 65? n Percents and Equations PRE-ALGEBRA LESSON 6 -7 What percent of 26 is 65? n • 26 = 65 26 n 65 = 26 26 n = 2. 5 = 250% Write an equation. Divide each side by 26. Simplify. Change the decimal to a percent. 65 is 250% of 26. Quick Check 6 -7

Percents and Equations PRE-ALGEBRA LESSON 6 -7 A car salesman makes a 6. 5% Percents and Equations PRE-ALGEBRA LESSON 6 -7 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 commission is 6. 5% of $35, 000 • $35, 000 Let c = amount of commission. Equation c = 0. 065 • 35, 000 = 2, 275 The salesman’s commission is $2, 275. 6 -7 Quick Check

Percents and Equations PRE-ALGEBRA LESSON 6 -7 During a telephone survey, 414 people, or Percents and Equations PRE-ALGEBRA LESSON 6 -7 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? Words 414 is 46% of people called Let n = number of people called. Equation 414 = 0. 46 • n 0. 46 n = 414 0. 46 n 414 = 0. 46 n = 900 Quick Check 900 people were called. 6 -7

Percents and Equations PRE-ALGEBRA LESSON 6 -7 Solve 1. What is 9% of 30? Percents and Equations PRE-ALGEBRA LESSON 6 -7 Solve 1. What is 9% of 30? 2. 7 2. What is 25% of 312? 3. What percent of 9 is 3? 1 33 % 3 4. What percent of 3 is 9? 78 300% 5. A car dealer makes an 8% commission on each car she sells. How much does she make on a $40, 000 sale? $3, 200 6. During a telephone survey, 320 people, or 25% of those called, said they were listening to the same station at the time of the call. How many people were called? 1, 280 people 6 -7

Percent of Change PRE-ALGEBRA LESSON 6 -8 Write these fractions to the nearest tenth Percent of Change PRE-ALGEBRA LESSON 6 -8 Write these fractions to the nearest tenth of a percent. 65 a. b. 42 255 52 25. 5% 80. 8% 6 -8

Percent of Change PRE-ALGEBRA LESSON 6 -8 (For help, go to Lesson 6 -5. Percent of Change PRE-ALGEBRA LESSON 6 -8 (For help, go to Lesson 6 -5. ) Write each decimal as a percent. 1. 0. 46 2. 2. 47 3. 0. 03 4. 5. 236 Check Skills You’ll Need 6 -8

Percent of Change PRE-ALGEBRA LESSON 6 -8 Solutions 1. Move the decimal 2 places Percent of Change PRE-ALGEBRA LESSON 6 -8 Solutions 1. Move the decimal 2 places to the right. 0. 46 = 46% 2. 2. 47 = 247% 3. 0. 03 = 3% 4. 5. 236 = 523. 6% 6 -8

Percent of Change PRE-ALGEBRA LESSON 6 -8 Find the percent of increase from 8 Percent of Change PRE-ALGEBRA LESSON 6 -8 Find the percent of increase from 8 to 9. 6. amount of increase = 9. 6 – 8 = 1. 6 percent of increase = amount of increase original amount 1. 6 = 8 = 0. 2 = 20% The percent of increase from 8 to 9. 6 is 20%. Quick Check 6 -8

Percent of Change PRE-ALGEBRA LESSON 6 -8 In a given year, Hillsboro had a Percent of Change PRE-ALGEBRA LESSON 6 -8 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 percent of increase = amount of increase original amount 15 = 7. 5 = 200% The percent of increase from March 1 to July 1 was 200%. 6 -8 Quick Check

Percent of Change PRE-ALGEBRA LESSON 6 -8 Find the percent of decrease from 1, Percent of Change PRE-ALGEBRA LESSON 6 -8 Find the percent of decrease from 1, 250 to 1, 120. amount of decrease = 1, 250 – 1, 120 = 130 percent of decrease = = amount of decrease original amount 130 1, 250 = 0. 104 = 10. 4% Quick Check 6 -8

Percent of Change PRE-ALGEBRA LESSON 6 -8 Solve. 1. Find the percent of increase Percent of Change PRE-ALGEBRA LESSON 6 -8 Solve. 1. Find the percent of increase from 22 to 63. 186. 4% 2. Find the percent of decrease from 6. 3 to 2. 2. 65. 1% 3. A surgeon performed 62 operations in 1991. He performed 342 in 2001. Find the percent of increase. 451. 6% 6 -8

Markup and Discount PRE-ALGEBRA LESSON 6 -9 Without computing, explain why 40% of 22 Markup and Discount PRE-ALGEBRA LESSON 6 -9 Without computing, explain why 40% of 22 is less than 11. 11 is half, or 50%, of 22, so 40% of 22 is less than 11. 6 -9

Markup and Discount PRE-ALGEBRA LESSON 6 -9 (For help, go to Lesson 6 -7. Markup and Discount PRE-ALGEBRA LESSON 6 -9 (For help, go to Lesson 6 -7. ) Write an equation and solve. Round to hundredths as needed. 1. What is 75% of $82? 2. What is 42% of $170? 3. What is 5. 5% of $24? 4. What is 80% of $15. 99? Check Skills You’ll Need 6 -9

Markup and Discount PRE-ALGEBRA LESSON 6 -9 Solutions 1. What is 75% of $82? Markup and Discount PRE-ALGEBRA LESSON 6 -9 Solutions 1. What is 75% of $82? n = 0. 75 • 82 n = 61. 5 75% of $82 is $61. 50. 2. What is 42% of $170? n = 0. 42 • 170 n = 71. 4 42% of $170 is $71. 40. 3. What is 5. 5% of $24? n = 0. 055 • 24 n = 1. 32 5. 5% of $24 is $1. 32. 4. What is 80% of $15. 99? n = 0. 80 • 15. 99 n = 12. 79 80% of $15. 99 is $12. 79. 6 -9

Markup and Discount PRE-ALGEBRA LESSON 6 -9 A grocery store has a 20% markup Markup and Discount PRE-ALGEBRA LESSON 6 -9 A grocery store has a 20% markup on a can of soup. The can of soup costs the store $1. 25. Find the markup = percent of markup • store’s cost = 0. 2 • 1. 25 = 0. 25 Simplify. The markup is $. 25. Quick Check 6 -9

Markup and Discount PRE-ALGEBRA LESSON 6 -9 A bookstore pays $4. 50 for a Markup and Discount PRE-ALGEBRA LESSON 6 -9 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. Quick Check 6 -9

Markup and Discount PRE-ALGEBRA LESSON 6 -9 A camera that regularly sells for $210 Markup and Discount PRE-ALGEBRA LESSON 6 -9 A camera that regularly sells for $210 is on sale for 30% off. Find the discount = percent of discount • regular price = 0. 30 • 210 = 63 The discount is $63. Quick Check 6 -9

Markup and Discount PRE-ALGEBRA LESSON 6 -9 Solve. 1. The school store has a Markup and Discount PRE-ALGEBRA LESSON 6 -9 Solve. 1. The school store has a 65% markup on each stapler. Each stapler costs the store $2. 10. Find the markup. $1. 37 2. A clothes store pays $40 for a skirt. The percent of markup is 25%. Find the skirt’s selling price. $50 3. A pair of shoes that regularly sells for $94. 99 is on sale for 30% off. What is the sale price? $66. 49 6 -9

Problem Solving Strategy: Make a Table PRE-ALGEBRA LESSON 6 -10 A theater has 25 Problem Solving Strategy: Make a Table PRE-ALGEBRA LESSON 6 -10 A theater has 25 seats in the first row. Each of the following rows has two more seats than the row before it. How many seats are in the 15 -row theater? 585 6 -10

Problem Solving Strategy: Make a Table PRE-ALGEBRA LESSON 6 -10 (For help, go to Problem Solving Strategy: Make a Table PRE-ALGEBRA LESSON 6 -10 (For help, go to Lesson 1 -8. ) Solve. 1. For two weeks, you double the amount of money you save each day. You save $. 01 the first day. How much money will you have at the end of the two weeks? Check Skills You’ll Need 6 -10

Problem Solving Strategy: Make a Table PRE-ALGEBRA LESSON 6 -10 Solutions Day 1 2 Problem Solving Strategy: Make a Table PRE-ALGEBRA LESSON 6 -10 Solutions Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Amount of new money saved $. 01 $. 02 $. 04 $. 08 $. 16 $. 32 $. 64 $1. 28 $2. 56 $5. 12 $10. 24 $20. 48 $40. 96 $81. 92 Total amount saved $. 01 1 + 2 = $. 03 3 + 4 = $. 07 7 + 8 = $. 15 15 + 16 = $. 31 31 + 32 = $. 63 63 + 64 = $1. 27 + 1. 28 = $2. 55 + 2. 56 = $5. 11 + 5. 12 = $10. 23 + 10. 24 = $20. 47 + 20. 48 = $40. 95 + 40. 96 = $81. 91 + 81. 92 = $163. 83 After 2 weeks, $163. 83 will have been saved. 6 -10

Problem Solving Strategy: Make a Table PRE-ALGEBRA LESSON 6 -10 Martin had 100 trees Problem Solving Strategy: Make a Table PRE-ALGEBRA LESSON 6 -10 Martin had 100 trees in his orchard the first year. Each year after that he increased the number of trees in his orchard by 10%, rounded to the nearest whole number. How many trees did he have in his orchard in the sixth year? Year 1 2 3 4 5 6 Tree Count at Rate of Beginning of Increase Year (10%) 100 0. 1 110 0. 1 121 0. 1 133 0. 1 146 0. 1 161 Increase in Tree Count at End of Year 10 11 12 13 15 110 121 133 146 161 Martin had 161 trees in the sixth year. 6 -10 Quick Check

Problem Solving Strategy: Make a Table PRE-ALGEBRA LESSON 6 -10 Solve. 1. For an Problem Solving Strategy: Make a Table PRE-ALGEBRA LESSON 6 -10 Solve. 1. For an auction item, the bid starts at $100 and increases 50% every minute. In how many minutes will the bid go over $2, 500? 8 minutes 2. Sharon uses her initials, SLF, for her password. How many different three-letter passwords can she make with these letters? 6 passwords 3. In how many ways can you make 45¢ in change using only nickels, dimes, and quarters? 8 ways 6 -10