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Math 8

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How do you use proportions to convert measurements, find the unknown side length of polygon or real life objects, and interpret and construct scale models?

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Proportion two ratios that are equivalent Customary system a system of measurement used in the United States Metric system a decimal system of weights and measures

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With the help of a calculator, we can determine if two ratios are proportional. Proportion means two ratios that are equivalent or can be written with an equal sign between them. Example: 7 2 21 and 6 Nonexample: 9 16 12 and 24

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Your turn. Determine if these ratios are proportional or not. 3 2 27 and 18 12 27 15 and 36 1 12 2 and 24

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We know that when two ratios are equal to each other they are called proportional or proportions. We can use the knowledge that two ratios are equal in a proportion to help us find a missing numerator or denominator in one of those ratios.

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In order to find a missing number in a ratio, we use cross products. What does the word product mean when we are talking about math? When you picture a cross, what does it look like?

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Cross products are used in proportions that are equal. You multiply the numerator of one proportion by the denominator of another. Here is an example without any missing numbers. 3 = 9 4 12 3x12 = 4x9 ~~ 36=36

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We can use cross products to determine if two ratios are proportional. Example: 6 ? 4 15 = 10 Nonexample: 5 ? 15 6 = 21

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4 ? 5 12 = 15 3 ? 6 9 = 12 10 ? 20 15 = 30

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2 ? 6 3 = 10 3 ? 6 4 = 8 5 ? 4 9 = 12

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When you do not know one of the 4 numbers in a proportion, set the cross products equal to each other and solve. Here are some examples: 12 = 4 d 14 4d = 12 14 4d = 168 d = 168 4 = 42 r = 9 4 11 11r = 4 9 11 r = 36 r = 3.27

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1 = x 5 12 5x = 1 12 5x = 12 x = 12 5 x = 2.4

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2 = 6 3 y 2y = 6 3 2y = 18 y = 18 2 y = 9

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1 = 9 h 36 9h = 1 36 9h = 36 h = 36 9 h = 4

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4 = 9 8 d 3 = 7 j 9 r = 8 5 12

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4 = 9 8 d 4d = 9 8 4d = 72 d = 72 4 d = 18

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3 = 7 j 9 7j = 3 9 7j = 27 j = 27 7 j = 3.86

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r = 8 5 12 12r = 5 8 12r = 40 r = 40 12 r = 3.33

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