 Ratio – a ratio is a quotient of two numbers, or a fraction; a comparison of two quantities by division  It represents the rate at which one thing compares to another.  Since it is a fraction, it should always be in simplest form.

 16:4  = 4:1 (4/1 or 4 to 1)  6:9  = 2:3 (2/3 or 2 to 3)  25:75  = 1:3 (1/3 or 1 to 3)

 We can state a ratio of parts within a figure:  ∠ABC:∠ACB =  ∠A:∠AED =  AD:DE =  (AC+BC):AE =

 We can state a ratio of parts within a figure:  ∠ABC:∠ACB = 40:120 = 1:3 (1/3)  ∠A:∠AED = 20:120 = 1:6 (1/6)  AD:DE = 16:6 = 8:3 (8/3)  AC+BC:AE = 5+3:10 = 8:10 = 4:5 (4/5)

 When indicating the ratio between two measurement, we never want a decimal involved:  A sheet of printer paper is 8.5 by 11 inches. What is the ratio of the length to the width?  11:8.5 ⁂ But, we don’t want decimals, so what should we do?  Ratio = _____

 Ratios can be made from more than 2 measures:  A triangle that has angle measures would have a ratio of 1:2:3 among its 3 sides.  A triangles with sides 3, 12, and 9 would have a ratio of 1:4:3.

 If we know that the ratio among the angles of a triangle is 2:3:4, what are the angle measures?

 If we know that the ratio among the angles of a triangle is 1:12:5, what are the angle measures?

 If we know that one angle of a triangle is 45° and the ratio among the other angles of the triangle is 2:1, what are the remaining angle measures?

 Proportions  A proportion is an equation that states two or more ratios are equal  Example: a:b = c:d

 Using that Ratio, we know a few things:  a:b = c:d  a ∙ d = b ∙ c  b and c are called the means  a and d are called the extremes

acbd bdad = bcac aba+b c+d cd b d a = c = e then a = c = e = a+c+e b d f b d fb+d+f

 Applying those properties: 2 =  2:3 = 6:9  2 ∙ 9 = 3 ∙ 6

 That last property allows us to solve proportions:  100n = 3000  n = 30

 That last property allows us to solve proportions:  75n = 1800  n = 24

 7-1worksheet #1-17 all  7-2 worksheet #1-7 and all