ALGEBRA 1 LESSON 4 1 Ratios and Proportion

ALGEBRA 1 LESSON 4 -1 Ratios and Proportion (For help, go to Skills Handbook pages 724 and 727. ) Write each fraction in simplest form. 1. 49 84 24 2. 42 135 3. 180 Simplify each product. 4. 35 25 40 14 5. 99 144 96 88 6. 7 -1 21 81 108 56

ALGEBRA 1 LESSON 4 -1 Ratios and Proportion Solutions 49 7 • 7 7 1. 84 = 7 • 12 = 12 2. 24 = 6 • 4 = 4 3. 4. 5. 42 6 • 7 7 135 45 • 3 3 = = 180 45 • 4 4 35 40 5 • 7 5 • 8 5 • 7 • 5 • 8 8 = =4 25 14 5 • 5 7 • 2 5 • 7 • 2 2 99 96 = 9 • 11 8 • 12 = 9 • 11 • 8 • 12 = 9 = 3 144 88 12 • 12 8 • 11 12 • 8 • 11 12 4 6. 21 108 = 3 • 7 81 56 3 • 3 • 4 34 • 7 • 4 = 4 7 • 8 3 • 7 • 8 7 -1 = 4 = 1 8 2

ALGEBRA 1 LESSON 4 -1 Ratios and Proportion Another brand of apple juice costs $1. 56 for 48 oz. Find the unit rate. cost ounces $1. 56 = $. 0325/oz 48 oz The unit rate is 3. 25¢/oz. 7 -1

ALGEBRA 1 LESSON 4 -1 Ratios and Proportion The fastest recorded speed for an eastern gray kangaroo is 40 mi per hour. What is the kangaroo’s speed in feet per second? 40 mi 5280 ft 1 h 1 min • • • 1 h 1 mi 60 min 60 s Use appropriate conversion factors. 40 mi 5280 ft 1 h 1 min • • • 1 h 1 mi 60 min 60 s Divide the common units. = 58. 6 ft/s Simplify. The kangaroo’s speed is about 58. 7 ft/s. 7 -1

ALGEBRA 1 LESSON 4 -1 Ratios and Proportion Solve y 3 • 12 = • 12 3 4 y 3 =. 3 4 Multiply each side by the least common multiple of 3 and 4, which is 12. 4 y = 9 Simplify. 4 y 9 = 4 4 Divide each side by 4. y = 2. 25 Simplify. 7 -2

ALGEBRA 1 LESSON 4 -1 Ratios and Proportion w 6 Use cross products to solve the proportion 4. 5 = – 5. w 6 =– 4. 5 5 w(5) = (4. 5)(– 6) Write cross products. 5 w = �– 27 Simplify. 5 w – 27 = 5 5 Divide each side by 5. w = �– 5. 4 Simplify. 7 -2

ALGEBRA 1 LESSON 4 -1 Ratios and Proportion In 2000, Lance Armstrong completed the 3630 -km Tour de France course in 92. 5 hours. Traveling at his average speed, how long would it take Lance Armstrong to ride 295 km? Define: Let t = time needed to ride 295 km. Relate: Tour de France average speed 3630 Write: 92. 5 3630 295 = 92. 5 t 3630 t = 92. 5(295) t= 92. 5(295) 3630 equals 295 -km trip average speed 295 t = kilometers hours Write cross products. Divide each side by 3630. t 7. 5 Simplify. Round to the nearest tenth. Traveling at his average speed, it would take Lance approximately 7. 5 hours to cycle 295 km. 7 -2

ALGEBRA 1 LESSON 4 -1 Ratios and Proportion Solve the proportion z+3 z– 4 =. 4 6 z+3 z– 4 = 4 6 (z + 3)(6) = 4(z – 4) Write cross products. 6 z + 18 = 4 z – 16 Use the Distributive Property. 2 z + 18 = – 16 Subtract 4 z from each side. 2 z = – 34 Subtract 18 from each side. 2 z – 34 = 2 2 Divide each side by 2. z = – 17 Simplify. 7 -2

ALGEBRA 1 LESSON 4 -1 Ratios and Proportion Solve. 1. Find the unit rate of a 12 -oz bottle of orange juice that sells for $1. 29. 10. 75¢/oz. 2. If you are driving 65 mi/h, how many feet per second are you driving? about 95. 3 ft/s Solve each proportion. 3. c 4. 12 = 6 15 4. 8 21 7 = 12 y 4 5. 3+x 6. = 4 7 8 1 2 2 + x 25 = x – 4 35 – 17 7 -2

ALGEBRA 1 LESSON 4 -2 Proportions and Similar Figures (For help, go to Skills Handbook and Lesson 4 -1. ) Simplify 1. 36 42 2. 81 108 3. 26 52 y 8 = 12 45 6. w 12 = 15 27 9. n+1 n = 24 9 Solve each proportion. 4. x 7 = 12 30 5. 7. 9 81 = a 10 8. 25 = z 75 30 7 -2

ALGEBRA 1 LESSON 4 -2 Proportions and Similar Figures Solutions 36 6 • 6 6 1. 42 = 6 • 7 = 7 2. 3. 4. 81 = 108 26 = 52 27 • 3 3 = 27 • 4 4 26 • 1 1 = 26 • 2 2 x 7 = 12 30 30 x = 12(7) 30 x = 84 84 x = 30 4 x = 25 y 8 9 81 n n+1 5. 12 = 45 45 y = 12(8) 7. a = 10 81 a = 9(10) 9. 9 = 24 24 n = 9(n + 1) 45 y = 96 81 a = 90 24 n = 9 n + 9 96 90 y = 45 a = 81 2 y = 215 1 a = 19 6. w = 12 15 8. 25 = z 27 75 27 w = 15(12) 27 w = 180 w = 27 2 w=63 7 -2 30 75 z = 25(30) 75 z = 750 z = 75 z = 10 15 n = 9 9 n = 15 3 n= 5

ALGEBRA 1 LESSON 4 -2 Proportions and Similar Figures In the figure below, Relate: EF DE = BC AB ABC ~ DEF. Find AB. Write a proportion comparing the lengths of the corresponding sides. Define: Let x = AB. Write: 6 8 = 9 x 6 x = 9(8) 6 x 72 = 6 6 x = 12 AB is 12 mm. Substitute 6 for EF, 9 for BC, 8 for DE, and x for AB. Write cross products. Divide each side by 6. Simplify. 7 -2

ALGEBRA 1 LESSON 4 -2 Proportions and Similar Figures A flagpole casts a shadow 102 feet long. A 6 ft tall man casts a shadow 17 feet long. How tall is the flagpole? 102 x = 17 6 Write a proportion. 17 x = 102 • 6 Write cross products. 17 x = 612 Simplify. 17 x 612 = 17 17 Divide each side by 17. x = 36 Simplify. The flagpole is 36 ft tall. 7 -2

ALGEBRA 1 LESSON 4 -2 Proportions and Similar Figures The scale of a map is 1 inch : 10 miles. The map distance from Valkaria to Gifford is 2. 25 inches. Approximately how far is the actual distance? map actual 1 2. 25 = 10 x map actual 1 • x = 10 • 2. 25 Write a proportion. Write cross products. x = 22. 5 Simplify. The actual distance from Valkaria to Gifford is approximately 22. 5 mi. 7 -2

ALGEBRA 1 LESSON 4 -2 Proportions and Similar Figures 1. In the figure below, ABC ~ DEF. Find DF. About 19. 7 cm 2. A boy who is 5. 5 feet tall casts a shadow that is 8. 25 feet long. The tree next to him casts a shadow that is 18 feet long. How tall is the tree? 12 ft 3. The scale on a map is 1 in. : 20 mi. What is the actual distance between two towns that are 3. 5 inches apart on the map? 70 mi 7 -2