3-6 Solve Proportions Using Cross Products

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Presentation transcript:

3-6 Solve Proportions Using Cross Products

Vocabulary Cross Product: The product of the numerator of one ratio and the denominator of a second ratio. The cross products of a proportion are equal. Example: 3 = 6 4 8 3 (8) = 6 (4) 24 = 24

Example 1 4 (24) = 12(2x) 96 = 24x 24 24 x = 4 Solve the proportion: 4 = 12 2x 24 Cross Multiply. 4 (24) = 12(2x) Solve the Equation. 96 = 24x 24 24 x = 4

Example 2 3(x - 4) = 9x 3x – 12 = 9x -3x -3x -12 = 6x 6 6 x = -2 What is the value of x in the proportion? Put ( ) around the expression part first 3 = 9 x x-4 ( ) Cross Multiply. 3(x - 4) = 9x Simplify by Distributing. 3x – 12 = 9x Solve for x. -3x -3x Subtract 3x from both sides. Divide both sides by 6. -12 = 6x 6 6 x = -2

Example 3 = peat moss perlite 4 3 10 x x = 7.5 buckets of perlite Georgia is making her own potting soil. For every 4 buckets of peat moss, she mixes in 3 buckets of perlite. If she uses 10 buckets of peat moss, how many buckets of perlite should she use? Write and solve a proportion to find the answer. peat moss perlite 4 3 10 x = 4x = 30 Cross Multiply. 4 4 Solve: Divide both sides by 4. x = 7.5 buckets of perlite

Homework Section 3-6 Page 171-173 4 - 10, 24 – 27 33 - 39

3-7 Solve Percent Problems

Vocabulary Percent: Means “divided by 100”. “a is p percent of b” using a proportion: a = p b 100 In General for 3.7:

Example 1 Find a percent using a proportion. What percent of 60 is 9? IS OF % 100 = 9 60 p 100 9(100) = 60p = 900 = 60p 60 60 p = 15%

Example 2 Find a percent using a proportion. 13 is what percent of 20? IS OF % 100 = 13 20 p 100 13(100) = 20p = 1300 = 20p 20 20 p = 65%

Example 3 = = What number is 12% of 85? IS OF % 100 x 85 12 100 100 100 x = 10.2

Example 4 75 is 62.5% of what number? = = IS OF % 100 75 x 62.5 100 62.5 62.5 x = 120

Homework Section 3-7 Page 179 – 181 3 – 18 all, 26 – 29 all, 33, 34