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Solve Proportions Using Cross Products

This lesson presentation provides a warm-up activity, examples, and a quiz to help students practice solving proportions using cross products. It covers various scenarios, such as finding the number of tomatillos needed to make a certain amount of enchilada sauce or estimating distances using maps.

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Solve Proportions Using Cross Products

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  1. Solve Proportions Using Cross Products Warm Up Lesson Presentation Lesson Quiz

  2. 21 28 7 3.= 1.= n 32 16 t 32 4 11 4. = 2. = 18 b p 12 24 12 Warm-Up Solve the proportion. 9 14 ANSWER ANSWER 24 ANSWER 33 ANSWER

  3. Warm-Up 5. It takes 30 tomatillos to make 8 ounces of enchilada sauce. How many tomatillos does it take to make 12 ounces of enchilada sauce? 45 tomatillos ANSWER

  4. Solve the proportion = . 8 6 8 6 15 x x 15 = 8 15 = x 6 ANSWER The solution is 20. Check by substituting 20 forxin the original proportion. Example 1 Write original proportion. Cross products property 120 = 6x Simplify. 20=x Divide each side by 6.

  5. 8 6 = 20 15 ? ? 8 15=20 6 120 = 120 Example 1 CHECK Substitute 20 for x. Cross products property Simplify. Solution checks.

  6. 8 What is the value of x in the proportion =? x – 3 ANSWER 3 – 6 – 3 The value ofx is –3. The correct answer is B. 6 A B C D B 4 4 8 = A x x x – 3 D C 4(x – 3) =x8 Example 2 SOLUTION Write originalproportion. Cross products property 4x – 12 = 8x Simplify. –12 = 4x Subtract 4xfrom each side. –3 = x Divide each side by 4.

  7. m – 6 3. 2. 4 = 4 a 24 1. = 30 ANSWER ANSWER 18 18 ANSWER 5 m 3 2 = 5 x x – 6 Guided Practice Solve the proportion. Check your solution.

  8. Seals Each day, the seals at an aquarium are each fed 8 pounds of food for every 100 pounds of their body weight. A seal at the aquarium weighs 280 pounds. How much food should the seal be fed per day? SOLUTION STEP 1 Write a proportion involving two ratios that compare the amount of food with the weight of the seal. x 280 8 amount of food = weight of seal 100 Example 3

  9. = 8 280 = 100 x x ANSWER 8 280 100 A 280 pound seal should be fed 22.4 pounds of food per day. Example 3 STEP 2 Solve the proportion. Write proportion. Cross products property 2240 = 100x Simplify. 22.4 = x Divide each side by 100.

  10. 4. WHAT IF? In Example 3, suppose the seal weighs 260 pounds. How much food should the seal be fed per day? ANSWER 20.8 Guided Practice

  11. Maps Use a metric ruler and the map of Ohio to estimate the distance between Cleveland and Cincinnati. SOLUTION From the map’s scale, 1 centimeter represents 85 kilometers. On the map, the distance between Cleveland and Cincinnati is about 4.2 centimeters. Example 4

  12. 1 centimeters = 85 kilometers 1 d = 85 4.2 ANSWER 4.2 The actual distance between Cleveland and Cincinnati is about 357 kilometers. d Example 4 Write and solve a proportion to find the distance d between the cities. Cross products property d = 357 Simplify.

  13. 5. Use a metric ruler and the map in Example 4 to estimate the distance (in kilometers) between Columbus and Cleveland. 6. The ship model kits sold at a hobby store have a scale of 1 ft : 600 ft. A completed model of the Queen Elizabeth II is 1.6 feet long. Estimate the actual length of the Queen Elizabeth II. ANSWER about 212.5 km ANSWER about 960 ft Guided Practice Model ships

  14. y 4. 1. = 35 42 h 2 16 6 ANSWER ANSWER ANSWER ANSWER 12 22.5 8 9 = 2. 10 5r 15 26 13 = = 9 d + 3 6 17 3. Lesson Quiz Solve the proportion.

  15. A figurine of a ballerina is based on a scale of 0.5 in:4 in. If the real ballerina used as a model for the figurine is 68 inches tall, what is the height of the figurine? 5. ANSWER 8.5 in. Lesson Quiz

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