In the Real World Sports A person burned about 150 calories while skateboarding for 30 minutes. About how many calories would the person burn while skateboarding.

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Presentation transcript:

In the Real World Sports A person burned about 150 calories while skateboarding for 30 minutes. About how many calories would the person burn while skateboarding for 60 minutes? In Example 1, you will use a proportion to answer this question. Writing and Solving Proportions 8 4.

NOTE BOOK Words Numbers Algebra Proportions = The proportion is read “ 3 is to 5 as 6 is to 10.” abab = cdcd, where b and d are nonzero numbers. A proportion is an equation that states that two ratios are equivalent. Writing and Solving Proportions 8 4.

Writing and Solving Proportions 8 4. Using Equivalent Ratios When one of the numbers in a proportion is unknown, you can find the number by solving the proportion. One way to solve a proportion is to use mental math to find an equivalent ratio.

Writing and Solving Proportions Using Equivalent Ratios EXAMPLE 1 1 Ask yourself: What number can you multiply 30 by to get 60 ? C 60 =  ? ? To find the number C of calories the person would burn while skateboarding for 60 minutes, solve the proportion C 60 = 8 4. Using Equivalent Ratios When one of the numbers in a proportion is unknown, you can find the number by solving the proportion. One way to solve a proportion is to use mental math to find an equivalent ratio.

Writing and Solving Proportions Using Equivalent Ratios EXAMPLE 1 1 Ask yourself: What number can you multiply 30 by to get 60 ? 2 Because 30  2 = 60, multiply the numerator by 2 to find C C 60 =  ? ? C 60 =  2 ANSWER Because 150  2 = 300, C = 300. So the person would burn about 300 Calories while skateboarding for 60 minutes. To find the number C of calories the person would burn while skateboarding for 60 minutes, solve the proportion C 60 = 8 4. Using Equivalent Ratios When one of the numbers in a proportion is unknown, you can find the number by solving the proportion. One way to solve a proportion is to use mental math to find an equivalent ratio.

Writing and Solving Proportions Solving Proportions Using Algebra EXAMPLE 2 Solve the proportion = x 25 Multiply each side by 25. Simplify. Simplify fraction = x = x 15 = x ANSWER The solution is Using Algebra The same method you used to solve division equations can also be used to solve proportions that have the variable in the numerator = x 25 Write original proportion.

Writing and Solving Proportions Yesterday you bought 8 bagels for $4. Today you want only 5 bagels. How much will 5 bagels cost? The information is arranged in the two tables below, in which x represents the cost of 5 bagels. YesterdayToday Cost Bagels 4 85 x Proportion: 4848 x5x5 = 8 4. Setting up a Proportion There are different ways to set up a proportion. Consider the following problem.

Writing and Solving Proportions Yesterday you bought 8 bagels for $4. Today you want only 5 bagels. How much will 5 bagels cost? The information is arranged in the two tables below, in which x represents the cost of 5 bagels. YesterdayToday Cost Bagels Cost Today Yesterday 4 85 x5 84 x Proportion: 4848 x5x5 = 5858 x4x4 = 8 4. Setting up a Proportion There are different ways to set up a proportion. Consider the following problem.

Writing and Solving Proportions Writing and Solving a Proportion EXAMPLE 3 Empire State Building At maximum speed, the elevators in the Empire State Building can pass 80 floors in 45 seconds. Follow the steps below to find the number of floors that the elevators can pass in 9 seconds. 1 Write a proportion. Let x represent the floors passed in 9 seconds = 9 x seconds floors 2 Solve the proportion x9x9 = Multiply each side by 9. Simplify. Simplify fraction = x9x = x 16 = x ANSWER The elevators can pass 16 floors in 9 seconds. 8 4.