1 / 72

Ratios and Unit Rates

, ,. Sample answers. 4 12. 6 18. 1 3. 2 6. Ratios and Unit Rates. PRE-ALGEBRA LESSON 6-1. Write three fractions equivalent to. 6-1. Ratios and Unit Rates. PRE-ALGEBRA LESSON 6-1. (For help, go to Lesson 4-4.). Write in simplest form. 1. 2. 3. 4. 5. 6. 30 35.

damara
Download Presentation

Ratios and Unit Rates

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

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

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

  4. 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 2 5 3 100 40 100 60 Ratios and Unit Rates PRE-ALGEBRA LESSON 6-1 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 Quick Check 6-1

  5. 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: = $.03/card = $.026/card Find the unit prices. 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? Quick Check The 50-card pack has the lowest unit price. 6-1

  6. 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 PRE-ALGEBRA LESSON 6-1 Convert 30 gal/min to cups/second. 30 gal/min equals 8 c/s. Quick Check 6-1

  7. 1 5 4 5 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. 2. 8 out of 10 students buy lunch. Find each unit rate. 3. You pay $4.50 for 2 gallons of orange juice. 4. You pay $21.60 for a 20-lb bag of dog food. 5. Convert 15 yd/min to inches/second. $2.25/gal $1.08/lb 9 in./s 6-1

  8. 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

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

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

  11. 2 7 y 14 = 2 7 y 14 • 14 = • 14 28 7 = y Proportions PRE-ALGEBRA LESSON 6-2 2 7 y 14 Solve = . Method 1 Multiplication Property of Equality 4 = y 6-2

  12. 28 7 2 7 y 14 7y 7 = = Proportions PRE-ALGEBRA LESSON 6-2 (continued) Method 2 Cross products 2 • 14 = 7 • y 28 = 7y 4 = y Quick Check 6-2

  13. 3 5 21 35 3 5 21 35 Test by writing as a proportion. 3 • 35 5 • 21 Write cross products. Proportions PRE-ALGEBRA LESSON 6-2 Do the ratios and form a proportion? Explain. 105 = 105 Simplify. Yes; the ratios do form a proportion. The cross products are equal. Quick Check 6-2

  14. 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 PRE-ALGEBRA LESSON 6-2 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. Quick Check 6-2

  15. Proportions PRE-ALGEBRA LESSON 6-2 Solve each proportion. 1.2. Does each pair of ratios form a proportion? Explain. 3.4. 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. a 12 5 6 3 8 6 x 10 16 = = 2 9 0.4 1.8 21 50 14 25 = = Yes; the cross products are equal. No; the cross products are not equal. about 43 nautical miles 6-2

  16. 18 15 n 2.7 1.5 4.5 = = n 5 Similar Figures and Scale Drawings PRE-ALGEBRA LESSON 6-3 Find each value of n. a.b. n = 6 n = 0.9 6-3

  17. 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. 1. 2. 3. 4. 2 3 f 21 3 8 50 p = = 9 4 15 p 16 3 19 g = = Check Skills You’ll Need 6-3

  18. 2 3 f 21 3 8 50 p 9 4 15 p 16 3 19 g = = = = 1. 2. 3. 4. 3 • f = 2 • 21 8 • 50 = 3 • p 4 • 15 = 9 • p 3 • 19 = 16 • g 3f = 42 400 = 3p 60 = 9p 57 = 16g 3f 3 42 3 400 3 3p 3 60 9 9p 9 57 16 16g 16 = = = = f = 14 133.3 = p 6.7 = p 3.6 = g Similar Figures and Scale Drawings PRE-ALGEBRA LESSON 6-3 Solutions 6-3

  19. 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 PRE-ALGEBRA LESSON 6-3 Trapezoid ABCD ~ trapezoid EFGH. Find the value of k. Write a proportion for corresponding sides. 6 • 2 = k • 3 Write cross products. Quick Check 4 = kSimplify. 6-3

  20. 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 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? 1.5x = 5 • 3   Write cross products. x = 10   Simplify. The flagpole is 10 ft tall. Quick Check 6-3

  21. 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 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? It is about 72 mi between the two cities. Quick Check 6-3

  22. Similar Figures and Scale Drawings PRE-ALGEBRA LESSON 6-3 Solve. 1. Parallelogram ABCD ~ parallelogram EFGH. Find the value of x. 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? 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? 12 8 ft 300 mi 6-3

  23. 4 5 1 6 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 those who were left, were dropped after the second day. Of those who remained, made the team. How many students made the team? 24 6-4

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

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

  26. 3 6 number of favorable outcomes number of possible outcomes 3 prime-number outcomes (2, 3, 5) 6 possible outcomes = 3 6 1 2 P(rolling a prime number) = , or . Probability PRE-ALGEBRA LESSON 6-4 Find P(rolling a prime number) with one number cube. Quick Check 6-4

  27. 4 1,000 4 1,000 4 1,000 4 1,000 996 1,000 249 250 P(not an identical twin) + = 1  Substitute. P(not an identical twin) + – = 1  – Subtract from each side. 4 1,000 P(not an identical twin) =   Simplify. = 249 250 The probability that a child is not an identical twin is . 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(not an identical twin) + P(identical twin) = 1  Write an equation. Quick Check 6-4

  28. 2 are worth less than ten cents. 3 are not. odds in favor = The odds are , or 2 to 3, in favor of the coin being worth less than ten cents. 2 3 2 3 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? Quick Check 6-4

  29. 1 5 3 2 1 6 5 6 ; 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. 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. When rolling a number cube, what is P(6)? What is P(not 6)? 6-4

  30. 5 8 Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6-5 Samantha needs a -in. bit for her drill. Should she look in the bin marked 62.5 in., 6.25 in., 0.625 in., or 0.063 in.? 0.625 in. 6-5

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

  32. Solutions 5 8 5 6 2 3 9 20 8 11 3 4 1. = 5 ÷ 8 2. = 9 ÷ 20 3. = 3 ÷ 4 = 0.625 = 0.45 = 0.75 4. = 5 ÷ 6 5. = 2 ÷ 3 6. = 8 ÷ 11 = 0.83 = 0.6 = 0.72 Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6-5 6-5

  33. 7 4 3 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 PRE-ALGEBRA LESSON 6-5 Write each percent as a fraction or a mixed number. a. 30% b. 175% Quick Check 6-5

  34. 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 PRE-ALGEBRA LESSON 6-5 Express 7.3% as a decimal. = 0.073 Quick Check 6-5

  35. 412 1,000 0.412 = 412 ÷ 10 1,000 ÷ 10 = 41.2 100 = 0.412 = 41.2% Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6-5 Express 0.412 as a percent. Method 1Rewrite as a fraction. = 41.2% Method 2 Move the decimal point. Quick Check 6-5

  36. 4 7 Write a fraction. 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? 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

  37. 13 4 1 4 11 1,000 , or 3 ; 3.25 ; or 0.011 3 5 Fractions, Decimals, and Percents PRE-ALGEBRA LESSON 6-5 Write each percent as a fraction or mixed number, and as a decimal. 1. 325% 2. 1.1% Write each as a percent. 3. 2.01 4. 5. Six out of fifteen students own skateboards. What percent of students own skateboards? 201% 60% 40% 6-5

  38. 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

  39. Proportions and Percents PRE-ALGEBRA LESSON 6-6 (For help, go to Lesson 6-2.) Solve each proportion. 1. = 2. = 3. = 4. = x 28 25 100 98.9 x 43 100 13 x 27 150 52 100 x 100 Check Skills You’ll Need 6-6

  40. 25 100 98.9 x 43 100 x 28 13 x 100x 100 700 100 43x 43 9890 43 27 150 x 100 52 100 1300 52 52x 52 2700 150 150x 150 Proportions and Percents PRE-ALGEBRA LESSON 6-6 Solutions 1. = 2. = 100 • x = 25 • 28 43 • x = 98.9 • 100 100x = 700 43x = 9890 = = x = 7 x = 230 3. = 4. = 13 • 100 = 52 • x 100 • 27 = x • 150 1300 = 52x 2700 = 150x = = 25 = x 18 = x 6-6

  41. 100n 100 = Write a proportion. 23(158) 100 =    Divide each side by 100. 23 100 n 158 Proportions and Percents PRE-ALGEBRA LESSON 6-6 Find 23% of 158. 23(158) = 100nWrite cross products. 36.34 = nSimplify. 23% of 158 is 36.34. Quick Check 6-6

  42. = Write a proportion. =    Divide each side by 34. 100(28) 34 n 100 34n 34 82.4 Round. 28 34 Proportions and Percents PRE-ALGEBRA LESSON 6-6 What percent of 34 is 28? Round to the nearest tenth of a percent. 34n = 100(28) Write cross products. n = 82.35... Simplify. Quick Check 28 is approximately 82.4% of 34. 6-6

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

  44. = Write a proportion. 100(90) 15 =    Divide each side by 15. 15 100 15x 15 90 x 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? 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. Quick Check 6-6

  45. Proportions and Percents PRE-ALGEBRA LESSON 6-6 Solve. 1. Find 47% of 2,400. 2. What percent of 700 is 1,498? 3. 6 is 3% of what number? 4. Water covers about 361,736,000 km2, or about 70.8% of Earth’s surface. What is the approximate surface area of Earth? 1,128 214% 200 about 511,000,000 km2 6-6

  46. 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

  47. 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% 3. 23.8% 4. 72.25% 5. 136% 6. 178.5% Check Skills You’ll Need 6-7

  48. Solutions 48 100 5 100 1. 48%= 2. 5%= = 0.48 = 0.05 3. 23.8% = 4. 72.25%= = 0.238 = 0.7225 5. 136% = 6. 178.5% = = 1.36 = 1.785 23.8 100 72.25 100 178.5 100 136 100 Percents and Equations PRE-ALGEBRA LESSON 6-7 6-7

  49. 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

  50. = Divide each side by 26. 26n 26 65 26 Percents and Equations PRE-ALGEBRA LESSON 6-7 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. Quick Check 6-7

More Related