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8-3 6 th grade math Solving Proportions Using Cross Products

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Objective To solve proportions using cross products Why? To know how to find the missing number in a proportion- especially when the ratios are not easily ‘convertible.’

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California State Standards NS 1.3 : Use proportions to solve problems … Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. NS 1.2 : Interpret and use ratios in different contexts … to show the relative size of two quantities, using appropriate notations (x/y, x to y, x : y) AF 1.1 : Write and solve one-step linear equations in one variable.

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Vocabulary Cross products – In a proportion, the product of a numerator of one ratio with the denominator of the other ratio. bc (b x c) a = c b d ad (a x d) – This is similar to solving an equation with fractions. a = c b d a (b) = c (b) = bc (b x c) b (a) d (a) = ad (a x d)

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How to Solve Proportions Using Cross Products 1)Multiply the numerator and the denominator of two known numbers 2) Divide by the last used number. 3) Check your answer for reasonableness. You could also recheck the final proportion by dividing the fractions. 7 = n 1.2 3 7 x 3 = 21 21 ÷ 1.2 = 17.5 7 = 17.5 1.2 3 7 ≈ 5.8 1.2 17.5 ≈ 5.8 3

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Try It! 1)6 = 8 9 n 2) 9 = n 15 10 3) 8.5 = n 3.2 8 4) 2.6 = 4 n 4.8 1)n = 12 2)n = 6 3)n = 21.25 4)n = 3.12

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Try Some More! Proportional? 5)4, 6 10 15 6) 6, 9 9 12 7) 6, 9 8 12 8) 6, 9 10 15 5)Yes (60) 6)No (72, 81) 7)Yes (72) 8)Yes (90)

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Objective Review To solve proportions using cross products Why? You now know how to find the missing number in a proportion- especially when the ratios are not easily ‘convertible.’ You can use cross products to solve for the unknown value in a proportion.

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Independent Practice Complete problems 10- 18 Copy original problem first. Show all work! If time, complete Mixed Review: 19-25 If still more time, work on Accelerated Math.

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