Sec. 8.3 proportions

3 ? = 5. 10 20 3 6 ANSWER = 10 20 32 8 = 24 6 ? 8 6. = 24 6 ANSWER Copy and complete the statement to write an equivalent ratio.

Learning Target:Students will learn how to write proportions and solve proportions using cross products property.

Proportion: an equation that shows two ratios are equivalent. a : b = c : d

Cross Product Property:- The cross products of a proportion are equal.If , then a d = b c.

? = EXAMPLE 1 Use cross products to decide whether the ratios form a proportion. 3 12 a. 5 18

Answer:3 18 = 5 1254 = 6054 does not equal 60 therefore the ratio is NOT a proportion.

? = EXAMPLE 1 Use cross products to decide whether the ratios form a proportion. 8 20 b. 10 25

Answer:10 20 = 8 25 200 = 200200 does equals 200 therefore the ratio is a proportion.

EXAMPLE 2 4 20 . = Solve the proportion x 12 METHOD 1 Use equivalent ratios.

EXAMPLE 2 4 20 . = Solve the proportion x 12 METHOD 1 Use equivalent ratios. 4 12

EXAMPLE 2 4 20 . = Solve the proportion x 12 METHOD 1 Use equivalent ratios. 4 5 4 20 = x 12

EXAMPLE 2 4 20 . = Solve the proportion x 12 METHOD 1 Use equivalent ratios. 4 5 4 20 = x 12 12 5

EXAMPLE 2 4 20 . = Solve the proportion x 12 METHOD 1 Use equivalent ratios. 4 5 4 20 = x 12 12 5 12 5 = 60, so x = 60.

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

EXAMPLE 2 4 20 . = Solve the proportion x 12 METHOD 2 Use cross products.

EXAMPLE 2 4 20 . = Solve the proportion x 12 METHOD 2 Use cross products. 4 20 = x 12

EXAMPLE 2 4 20 . = Solve the proportion x 12 METHOD 2 Use cross products. 4 20 = x 12 4x = 240

EXAMPLE 2 4 20 . = Solve the proportion x 12 METHOD 2 Use cross products. 4 20 = x 12 4x = 240 x = 60

EXAMPLE 4 2.1 x . = Solve the proportion 3 1.4

EXAMPLE 4 2.1 x . = Solve the proportion 3 1.4 SOLUTION

EXAMPLE 4 2.1 x . = Solve the proportion 3 1.4 SOLUTION 2.1 x = 3 1.4

EXAMPLE 4 2.1 x . = Solve the proportion 3 1.4 SOLUTION 2.1 x Write the cross products. = 3 1.4

EXAMPLE 4 2.1 x . = Solve the proportion 3 1.4 SOLUTION 2.1 x Write the cross products. = 3 1.4 6.3 =1.4x

EXAMPLE 4 2.1 x . = Solve the proportion 3 1.4 SOLUTION 2.1 x Write the cross products. = 3 1.4 They are equal. 6.3 =1.4x

EXAMPLE 4 2.1 x . = Solve the proportion 3 1.4 SOLUTION 2.1 x Write the cross products. = 3 1.4 They are equal. 6.3 =1.4x 6.3 1.4 = x

EXAMPLE 4 2.1 x . = Solve the proportion 3 1.4 SOLUTION 2.1 x Write the cross products. = 3 1.4 They are equal. 6.3 =1.4x 6.3 1.4 = x Write the related division equation.

EXAMPLE 4 2.1 x . = Solve the proportion 3 1.4 SOLUTION 2.1 x Write the cross products. = 3 1.4 They are equal. 6.3 =1.4x 6.3 1.4 = x Write the related division equation. 4.5 = x

EXAMPLE 4 2.1 x . = Solve the proportion 3 1.4 SOLUTION 2.1 x Write the cross products. = 3 1.4 They are equal. 6.3 =1.4x 6.3 1.4 = x Write the related division equation. 4.5 = x Divide.

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

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

EXAMPLE 3 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?

EXAMPLE 3 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 t represent the total time, in hours, of the 20 mile trip.

EXAMPLE 3 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 t represent the total time, in hours, of the 20 mile trip. Write a verbal model.

EXAMPLE 3 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 t represent the total time, in hours, of the 20 mile trip. Distance traveled Total distance Write a verbal model. = Time traveled Total time

EXAMPLE 3 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 t represent the total time, in hours, of the 20 mile trip. Distance traveled Total distance Write a verbal model. = Time traveled Total time Substitutevalues.

EXAMPLE 3 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 t represent 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

EXAMPLE 3 Write the cross products.

EXAMPLE 3 20 5 Write the cross products. = t 3

EXAMPLE 3 20 5 Write the cross products. = t 3 They are equal.

EXAMPLE 3 20 5 Write the cross products. = t 3 5t 60 = They are equal.

EXAMPLE 3 20 5 Write the cross products. = t 3 5t 60 = They are equal. Solve using mental math.

EXAMPLE 3 20 5 Write the cross products. = t 3 5t 60 = They are equal. t = 12 Solve using mental math.

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

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?

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? ANSWER

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? ANSWER 20 mi 4 mi = t h 2 h

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? ANSWER 20 mi 4 mi = t h 2 h 20 4 = t 2

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? ANSWER 20 mi 4 mi = t h 2 h 20 4 = t 2 4t 40 =

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? ANSWER 20 mi 4 mi = t h 2 h 20 4 = t 2 4t 40 = t = 10h

Can you write proportions and solve proportions using cross products property.

Sec. 8.3 proportions

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Sec. 8.3 proportions