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Use cross products to decide whether the ratios form a proportion.

Use cross products to decide whether the ratios form a proportion. ?. ?. =. =. 3 ∙ 18. 5 ∙ 12. ≠. 54. 60. EXAMPLE 1. Checking a Proportion. 3. 12. a. 5. 18. The cross products are not equal, so the ratios do not form a proportion.

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Use cross products to decide whether the ratios form a proportion.

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  1. Use cross products to decide whether the ratios form a proportion. ? ? = = 3∙18 5∙12 ≠ 54 60 EXAMPLE 1 Checking a Proportion 3 12 a. 5 18 The cross products are not equal, so the ratios do not form a proportion.

  2. Use cross products to decide whether the ratios form a proportion. ? ? = = 825 1020 ● ● 200 200 = EXAMPLE 1 Checking a Proportion 8 20 b. 10 25 The cross products are equal, so the ratios form a proportion.

  3. 4 5 4 20 = x 12 12 5 12 5 = 60, so x = 60. The solution is 60. ANSWER EXAMPLE 2 Solving Using Mental Math 4 20 . = Solve the proportion x 12 METHOD 1 Use equivalent ratios.

  4. 4 20 = x 12 4x = 240 The solution is 60. ANSWER EXAMPLE 2 Solving Using Mental Math 4 20 . = Solve the proportion x 12 METHOD 2 Use cross products. x = 60

  5. EXAMPLE 3 Solving Using a Verbal Model Boating You are on a riverboat trip. You travel 5 miles in 3 hours. At that same rate, how long will it take you to travel 20 miles? SOLUTION Use a proportion. Let trepresent the total time, in hours, of the 20 mile trip. Distance traveled Total distance Write a verbal model. = Time traveled Total time 20 mi 5 mi Substitutevalues. = t h 3 h

  6. 20 5 = t 3 5t = 60 ANSWER It will take you 12 hours to travel 20 miles. EXAMPLE 3 Solving Using a Verbal Model Write the cross products. They are equal. t = 12 Solve using mental math.

  7. ? ? = = 12 25 3 5 32 36 8 6 GUIDED PRACTICE for Examples 1, 2, and 3 1. Does form a proportion? ANSWER yes 2. Does form a proportion? ANSWER no

  8. n 6 25 5 4. 3. = = 24 4 10 k ANSWER ANSWER n = 1 k = 2 s 10 30 6 6. 5. = = 11 4 12 x ANSWER ANSWER s = 30 x = 55 GUIDED PRACTICE for Examples 1, 2, and 3 Solve the proportion using mental math.

  9. ANSWER 10 hours GUIDED PRACTICE for Examples 1, 2, and 3 7. What If? In Example 3, suppose you travel 4 miles in 2 hours. At that same rate, how long will it take you to travel 20 miles?

  10. 2.1 x = 3 1.4 6.3 1.4 = x ANSWER The solution is 4.5. EXAMPLE 4 Solving Using a Related Equation 2.1 x . = Solve the proportion 3 1.4 SOLUTION Write the cross products. 6.3 =1.4x They are equal. Write the related division equation. 4.5 = x Divide.

  11. 22.5 30 a 50 9. 8. = = 6 60 6 y ANSWER ANSWER 1800 135 y a = = 50 6 a= 22.5 y= 36 GUIDED PRACTICE for Example 4 Write the related equation. Use it to solve the proportion.

  12. 1.1 13.2 11. = m 3.5 ANSWER ANSWER 1.5 46.2 x m = = 0.6 1.1 x= 2.5 m= 42 GUIDED PRACTICE for Example 4 Write the related equation. Use it to solve the proportion. x 1 10. = 0.6 1.5

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