PROPORTIONS Write ratios Use properties of proportions Circle

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PROPORTIONS • Write ratios • Use properties of proportions “Circle Limit IV (Heaven and

PROPORTIONS • Write ratios • Use properties of proportions “Circle Limit IV (Heaven and Hell)” M. C. Escher, 1960

Example 1 – Write a Ratio In 17 seasons as a major-league baseball player,

Example 1 – Write a Ratio In 17 seasons as a major-league baseball player, Chipper Jones of the Atlanta Braves made 2490 hits in 8142 times at bat. What is his overall majorleague batting average? number of hits Batting average = number of times at bat or about 0. 306

Example 2 – Extended Ratios in Triangles In a triangle, the ratios of the

Example 2 – Extended Ratios in Triangles In a triangle, the ratios of the measures of the three sides is 4: 6: 9, and its perimeter is 190 inches. Find the lengths of the sides of the triangle.

Example 2 – Extended Ratios in Triangles cont. Recall that equivalent fractions can be

Example 2 – Extended Ratios in Triangles cont. Recall that equivalent fractions can be found by multiplying the numerator and denominator by the same number. Thus: We can rewrite 4: 6: 9 as 4 x: 6 x: 9 x and use those measures for the sides of the triangle. 9 x 4 x 6 x

Example 2 – Extended Ratios in Triangles cont. Write an equation to represent the

Example 2 – Extended Ratios in Triangles cont. Write an equation to represent the perimeter of the triangle as the sum of the measures of its sides. 9 x 4 x 6 x

Example 2 – Extended Ratios in Triangles cont. 9 x 4 x 6 x

Example 2 – Extended Ratios in Triangles cont. 9 x 4 x 6 x Use the value of x to find the measures of the sides of the triangle. 4 x = 4(10) or 40 inches 6 x = 6(10) or 60 inches 9 x = 9(10) or 90 inches

USE PROPERTIES OF PROPORTIONS An equation stating that two ratios are equal is called

USE PROPERTIES OF PROPORTIONS An equation stating that two ratios are equal is called a proportion. Every proportion has two cross products.

Example 3 – Solve Proportions by Using Cross Products Solve the proportion Original problem

Example 3 – Solve Proportions by Using Cross Products Solve the proportion Original problem Cross products Simplify Divide each side by 35

Example 4 – Solve Proportions by Using Cross Products Original problem Cross products Simplify

Example 4 – Solve Proportions by Using Cross Products Original problem Cross products Simplify Add 10 to each side Divide each side by 6

Example 5 – Solve Problems Using Proportions The Gulfstream V business jet has a

Example 5 – Solve Problems Using Proportions The Gulfstream V business jet has a length of 96 feet and a wingspan of 94 feet. A toy model is made in proportion to the real airplane. If the wingspan of the toy is 36 cm, find the length of the toy.

Example 5 – Solve Problems Using Proportions cont.

Example 5 – Solve Problems Using Proportions cont.