CHAPTER 7.1 RATIO AND PROPORTION

RATIO A ratio compares two numbers by division. The ratio of two numbers a and b can be written as a to b; a:b; or a/b, where b ≠ 0. Slope is an example of a ratio.

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

EXAMPLE 1: 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? Since we do not know the side lengths we need use the ratio multiplied by ‘X’ to find them. 4x + 7x + 5x = 96 16x = 96 X = 6 Then we will plug into the smallest side: 4x = 4(6) = 24cm

EXAMPLE 2: The ratio of the angle measures in a triangle is 1:6:13. What is the measure of each angle? We do not know the angle measures but we know they all add to = 180° x + 6x + 13x = x = 180 X = 9 Then we need to substitute into the other 2. 6x = 6(9) = 54° 13x = 13(9) = 117° So the angle measures are 9°, 54°, and 117°

PROPORTION A proportion is an equation stating that two ratios are equal. In the proportion, the values a and d are the extremes. The values b and c are the means. 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.

CROSS MULTIPLY

EXAMPLE 1: Solve this proportion: 7(72) = 56(x) 504 = 56x X = 9

EXAMPLE 2: Solve the proportion: (z – 4)² = 5(20) (z – 4)² = 100 z – 4 = ±10** when taking sq root you have to have ± z – 4 = 10or z – 4 = -10 z = 14 or – 6

EXAMPLE 3: Solve the proportion: (x + 3)² = 4(9) (x + 3)² = 36 x + 3 = ±6 x + 3 = 6orx + 3 = -6 x = 3 or -9

PROPERTIES OF PROPORTIONS

EXAMPLE 1 Given that 18c = 24d, find the ratio of d to c in simplest form. 18c = 24d

EXAMPLE 2 Given that 16s = 20t, find the ratio t:s in simplest form. 16s = 20t

HOMEWORK P ; 17-29