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6.1 – Ratios, Proportions, and the Geometric Mean Ratio: The relationship between 2 numbers, has no units a:b a b Always simplify them!!! a to b Find the ratio of the width to the length of the rectangle. Then simplify the ratio. 4 cm 1 12 cm 3 Find the ratio of the width to the length of the rectangle. Then simplify the ratio. 6in 3 10in 5 Find the ratio of the width to the length of the rectangle. Then simplify the ratio. 12in 2 18in 3 Use the number line to find the ratio of the distances. AB AC 2 1 6 3 Use the number line to find the ratio of the distances. AB CD 2 3 Use the number line to find the ratio of the distances. AE BC 14 7 4 2 Use the number line to find the ratio of the distances. AE AB 14 7 2 1 Proportion: An equation that states two ratios are equal a c b To solve: d Cross multiply! ad = bc Solve the proportion. 3 x 4 12 4x = 36 4 4 x=9 3 x 4 12 1 3 x=9 Solve the proportion. 1 3 3 y y = 9 1 3 3 y y=9 Solve the proportion. 2 4 x 2 10 1 1 2 2 4 x 2 10 5 4(x + 2) = 20 4x + 8 = 20 4x = 12 x=3 x+2=5 x=3 Solve the proportion. 3 6 x x8 3(x + 8) = 6x 3x + 24 = 6x 24 = 3x 8=x 1 2 3 6 x x8 2x = x + 8 x=8 Solve the proportion. x x 12 24 8 x x 12 24 8 3 24(x – 12) = 8x 24x – 288 = 8x –288 = –16x 18 = x 1 3x – 36 = x 2x – 36 = 0 2x = 36 x = 18 Solve the proportion. 2 4 y 1 y 4 4(y + 1) = 2(y + 4) 4y + 4 = 2y + 8 2y + 4 = 8 2y = 4 y=2 1 2 2 4 y 1 y 4 2y + 2 = y + 4 y+2=4 y=2 The ratio of two side lengths for the triangle is given. Solve for the variable. AC:AB is 2:3. 2 x 3 12 3x = 24 3 3 x=8 2 x 3 12 1 4 x=8 The ratio of two side lengths for the triangle is given. Solve for the variable. 1 1 8 2 16 x AB:CB is 2:1. 2 16 x 1 24 16x = 48 16 16 x=3 1 24 3 x=3 The ratio of two side lengths for the triangle is given. Solve for the variable. 1 3 7 AC:BC is 7:4. 21 7 21 4 2x 4 4 7(2x + 4) = 84 14x + 28 = 84 14x = 56 x=4 2x 4 2x + 4 = 12 2x = 8 x=4 Sally received a 64% on a 150 point test. How many points did she earn on the test? 32 64 x 100 150 64 x 100 150 1 100x = 9600 100 100 x = 96 2 3 x = 96 If Taylor has a batting average of 0.275 and has had 640 at bats, how many hits has he made? x 0.275 640 1 x = 176 Geometric Mean: The square root of the product of two numbers a x x b x2 = ab x ab Find the geometric mean. 1 and 4 x ab x 1 4 x 4 x2 Find the geometric mean. 2 and 50 x ab x 2 50 x 100 x 10 Find the geometric mean. 3 and 15 x ab x 3 15 x 45 x3 5 Find the geometric mean. 7 and 14 x ab x 7 14 x 98 x7 2 HW Problem 6.1 360-362 11-19 odd, 23-35 odd, 39-43 odd, 49, 51, 79, 80 # 19 2 x 9 36 Ans: AB = 8 BC = 28