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Math Math Solving Solving

ProportionsProportions

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Vocabulary Vocabulary

►ProportionProportion—an equation that shows —an equation that shows that two ratios are equivalent.that two ratios are equivalent.

►Cross ProductCross Product—the product of the —the product of the numerator of one ratio and the numerator of one ratio and the denominator of the other ratio.denominator of the other ratio.

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NotesNotes

►11 == 33 1 x 6 is a cross product.1 x 6 is a cross product.

22 66 2 x 3 is a cross product.2 x 3 is a cross product.

►The cross products of a proportion are The cross products of a proportion are equal.equal.

►Two ratios form a proportion if their Two ratios form a proportion if their cross products are equal.cross products are equal.

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Determine whether each pair of Determine whether each pair of ratios form a proportion.ratios form a proportion.

a.a. 8/10 and 4/58/10 and 4/5

b.b. 9/4 and 11/69/4 and 11/6

c.c. 6/14 and 6/14 and 9/219/21

d.d. 15/12 and 9/615/12 and 9/6

e.e. $2.48/4oz and $2.48/4oz and $3.72/6 oz$3.72/6 oz

f.f. 125 mi/5.7 gal 125 mi/5.7 gal and 120 mi/5.6 and 120 mi/5.6 galgal

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ExampleExample

►Before dinner, Mohammed solved 8 Before dinner, Mohammed solved 8 math problems in 12 minutes. After math problems in 12 minutes. After dinner, he solved 2 problems in 3 dinner, he solved 2 problems in 3 minutes. Is the number of problems minutes. Is the number of problems he solve proportional to the time?he solve proportional to the time?

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ExampleExample

►Determine if the quantities $30 for 12 Determine if the quantities $30 for 12 gallons of gasoline and $10 for 4 gallons of gasoline and $10 for 4 gallons are proportional.gallons are proportional.

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NotesNotes

► Solving the proportionSolving the proportion—Process of —Process of using cross products to find a missing using cross products to find a missing term in a proportion. term in a proportion.

►Solving a proportion is similar to Solving a proportion is similar to solving an equation.solving an equation.

ExampleExamplexx = = 449 69 6

x • 6 = 9 • 4 (Cross multiply)x • 6 = 9 • 4 (Cross multiply)

6x = 36 (Solve for the variable)6x = 36 (Solve for the variable)

6x6x = = 3636 (Divide to undo multiplication (Divide to undo multiplication 6 66 6

x = 6x = 6

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ExamplesExamples

a.a. 5/8 = 18/x5/8 = 18/x

b.b. 9/15 = k/189/15 = k/18

c.c. 3.5/14 = 6/n3.5/14 = 6/n

d.d. 4.6/w = 4/54.6/w = 4/5

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Solve each proportion.Solve each proportion.

a.a. 5/15 = 15/w5/15 = 15/w

b.b. 24/13 = a/2624/13 = a/26

c.c. y/7 = 16/28y/7 = 16/28

d.d. 18/x = 3/3618/x = 3/36

e.e. 52/8 = m/952/8 = m/9

f.f. 3/u = 5/153/u = 5/15

g.g. 20/b = 70/2820/b = 70/28

h.h. 650/6.5 = z/5650/6.5 = z/5