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Lesson 6-2 Using Proportions Pgs. 270-274 What you will learn: Solve proportions Use proportions to solve real- world problems

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Vocabulary & Key Concept Proportion (270): a statement of equality of two ratios Cross Products (270): From the example, ad & cb are the cross products of the proportion Proportion: A proportion is an equation stating that two ratios are equal Symbol: a = c b d Example: 2 = 6 3 9

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Consider this proportion: a = c b d a bd = c bd b d 1 1 1 1 ad = cb Simplified to cross products 12 = 24 84 168 12(168) 84(24) 2016 = 2016 The cross products are equal.

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Key Concept (271): Property of Proportions Words: The cross products of a proportion are equal. Symbols: If a = c, then ad=bc. If ad=bc, then a = c b d b d

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Example 1: Identify Proportions Determine whether each pair of ratios forms a proportion. 1, 4 4 16 Write a proportion: 1 = 4 4 16 Cross Products: 1 16 = 4 4 Simplify: 16 = 16 1 = 4 Yes these are 4 16 proportions 2.1, 3 3.5 7 Write a proportion: 2.1 = 3 3.5 7 2.1 3 Cross Products: 2.1 7 = 3.5 3 3.5 7 Simplify: 14.7 10.5

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Example 2: Solve Proportions Solve each proportion. k = 3 35 7 k = 3 35 7 Cross Products: k 7 = 35 3 Multiply: 7k = 105 Divide: 7k = 105 7 7 Solve: k = 15 The solution is 15 3 = 18 t 24 3 = 18 t 24 Cross Products: 3 24 = t 18 Multiply: 72 = 18t Divide: 72 = 18t 18 18 Solve: t = 4 The solution is 4

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Example 3: Use a Proportion to Solve a Problem: A 3” x 5” photo is enlarged so that the length of the new photo Is 7 inches. Find the width of the new photo. Explore: You know the photo is 3”x 5” and you know that the length of the new photo is 7”. You need to find the width of the new photo. Plan: Write and solve a proportion using ratios that compare the lengths and widths of the photos. Let w represent the width of the new photo. Solve: length of the old photo = length of the new photo width of the old photo width of the new photo

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Draw a diagram of the photo, if needed. 3” 5” 7” 5 = 7 3 w 5 w = 3 7 5w = 21 5w = 21w= 4.2 or 4 5 5 w 1515

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Example 4: Convert Measurements Louisville, Ky is home to the world’s largest baseball glove. The glove is 4 feet high, 10 feet long, 9 feet wide, and weighs 15 tons. Find the height of the glove in centimeters if 1ft = 30.48cm. Let h = the height in centimeters Set up a proportion: 1ft = 4ft 30.48cm h cm 1 h = 30.48 4 h = 121.92 The height of the glove is 121.92 cm.

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YOU PRACTICE! Determine whether each pair of ratios forms a proportion. A.4, 16 2 5 B.18, 15 2.4 2 Solve the proportion. C.W = 14 11 22 D. 2 = c 15 72 Write a proportion that could be used to solve for the variable. Then solve. E.Y dollars for 5.4 gallons 14 dollars for 3 gallons 20 32, not a proportion 36 = 36, yes a proportion W = 7 C = 9.6 y = 14 5.4 3 y= $25.20

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Now here is a brain tickler. Think logically thru this! Solve the proportion. 3 = 15 14 m-3 3(m-3) = 14(15) Distributive Property! 3m - 9 = 210 The equation to work with 3m + (-9) = 210 Rewrite the problem so you don’t get confused! 3m + (-9) +9 = 210 Additive Inverse Property (-9) + 9 = 0 3m = 210 + 9 3m = 219 3 3 m = 73 Check: 3 = 15 14 73-3 3 = 15 14 70 3 70 = 14 15 210 = 210

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Extra Practice Sheets Are by the door on your Way out!!

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