3 6 Solve Proportions Using Cross Products Vocabulary

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

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

Example 3 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 4 x = 30 4 4 x = 7. 5 buckets of perlite 10 = x Cross Multiply. Solve: Divide both sides by 4.

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) = 60 p 900 = 60 p 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) = 20 p 1300 = 20 p 20 20 p = 65%

Example 3 What number is 12% of 85? IS % = OF 100 x 85 12 = 100 x(100) = 12(85) 100 x = 1020 100 x = 10. 2

Example 4 75 is 62. 5% of what number? IS % = OF 100 75 x 62. 5 = 100 x(62. 5) = 75(100) 62. 5 x = 7500 62. 5 x = 120

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