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Lesson 7-1 Ratios and Proportions Ratio: comparison of two quantities using division • Can be expressed as: • a to b • a:b • 𝑎𝑏 𝑤ℎ𝑒𝑟𝑒 𝑏≠0 Extended ratios: comparison of three or more quantities. a:b:c Example: • A video game store has 60 games to choose from, including 40 sports games. What is the ratio of sports games to video games? 𝑔𝑎𝑚𝑒𝑠 • We are comparing 𝑠𝑝𝑜𝑟𝑡𝑠 = 𝑡𝑜𝑡𝑎𝑙 𝑔𝑎𝑚𝑒𝑠 40 60 = 23 • In 2015, David Ortiz had 37 homeruns and was at bat 528. What is his ratio of homeruns to at bats? • We are comparing ℎ𝑜𝑚𝑟𝑢𝑛𝑠 = 𝑎𝑡 𝑏𝑎𝑡𝑠 37 528 or about 0.07 Extended Ratio problem: • In a triangle, the ratio of the measures of the sides is 3:3:8 and the perimeter is 392 inches. Find the length of the largest side. • First set up the equation: 3x + 3x + 8x = 392 14x = 392 x = 28 Now we need to plug in x for the longest side 8x = 8(28) So the longest side is 224 inches. Cross Product: Example for solving proportions using Cross Product. 𝑤 1 • = 6.4 2 • 2𝑤 = 6.4(1) • 2w = 6.4 • 2𝑤 2 = 6.4 2 • W=3.2 4𝑥 56 = 24 112 (4x)(112)=(24)(56) 448x = 1344 x=3 3𝑥 − 6 4𝑥 − 2 = 2 4 (3x-6)(4) = (2)(4x-2) 12x-24 = 8x-4 4x-24 = -4 4x = 20 X=5