7 1 Lesson Ratio and Proportion 97 Ratio

7 -1 Lesson Ratio and Proportion #97: Ratio & Proportion Warm Up Simplify the following radicals. 1. 64 8 2. 20 2 5 Solve each equation. x= 4 3. x 2 = 16 4. (x – 5)2 = 81 5. Write Holt Geometry x = 14 or x = – 4 in simplest form.

7 -1 Ratio and Proportion Take out your HW Holt Geometry

7 -1 Ratio and Proportion A ratio compares two numbers by division. Holt Geometry

7 -1 Ratio and Proportion Holt Geometry

7 -1 Ratio and Proportion A ratio can be written in 3 ways. a to b, a: b, or , where b ≠ 0. The ratios 1 to 2, 1: 2, and the same comparison. Holt Geometry all represent

7 -1 Ratio and Proportion Remember! In a ratio, the denominator of the fraction cannot be zero because division by zero is UNDEFINED. Holt Geometry

7 -1 Ratio and Proportion A ratio can involve more than two numbers. For the rectangle, the ratio of the side lengths may be written as 3: 7: 3: 7. 35 15 15 35 Holt Geometry

7 -1 Ratio and Proportion Example : Using Ratios The ratio of the side lengths of a triangle is 4: 7: 5, and its perimeter is 96 cm. What is the length of the shortest side? Let the side lengths be 4 x, 7 x & 5 x. Then 4 x + 7 x + 5 x = 96 16 x = 96 x=6 The length of the shortest side is 4 x = 4(6) = 24 cm. Holt Geometry

7 -1 Ratio and Proportion A proportion states that two ratios are equal. Holt Geometry

7 -1 Ratio and Proportion In the proportion , a & d are the extremes. b & c are the means. Holt Geometry

7 -1 Ratio and Proportion When the proportion is written as a: b = c: d, the extremes are in the first and last positions. The means are in the two middle positions. extremes a: b = c: d means Holt Geometry

7 -1 Ratio and Proportion In Algebra, you learned the Cross Products Property. The product of the extremes ad and the product of the means bc are called the cross products. Holt Geometry

7 -1 Ratio and Proportion Reading Math The Cross Products Property can also be stated as a theorem: “In a proportion, the product of the extremes is equal to the product of the means. ” This will be used in similarity proofs. Holt Geometry

7 -1 Ratio and Proportion Example 2 A: Solving Proportions Solve the proportion. 7(72) = x(56) 504 = 56 x x=9 Holt Geometry Cross Products Property Simplify. Divide both sides by 56.

7 -1 Ratio and Proportion Example 2 B: Solving Proportions Solve the proportion. (z – 4)2 = 5(20) (z – 4)2 = 100 (z – 4) = 10 or (z – 4) = – 10 z = 14 or z = – 6 Holt Geometry

7 -1 Ratio and Proportion If the 2 means in a proportion are equal, they are called the mean proportional or the geometric mean. 2=6 6 18 The mean proportional is 6 The mean proportional is the POSITIVE value of the means. Holt Geometry

7 -1 Ratio and Proportion Find the mean proportional between 9 and 4. 9=x x 36 = x 2 4 9(4) = x 2 36 = x 2 Holt Geometry 6=x

7 -1 Ratio and Proportion Find the mean proportional between 9 and 8 9=x x 72 = x 2 8 9(8) = x 2 36 2 = x 72 = x 2 6 2 = x Holt Geometry

7 -1 Ratio and Proportion Homework #97: Holt Reteach Worksheets 7 r e t p a e h C m o H e k Ta Due ! ay d n Mo 7 -1 (#4 - 9) AND 6 -5 (#5) Th in k Du 2 l thr e ess ou 11 Sun on gh : 5 da s 9 p y m by ! In your notebook! Holt Geometry