2. Express in sim he ratio a : b when a = 6 in., b = 8 in.; a = 15 in., b = 3 ft.; a = 2 2 in., b = 6% in.; a = 8m, b = 12 m. 3. Cut a line 4 g in. long into two parts in the ratio 3 : 10. /4. Determine x if each of the following is to be a proportion: (a) 12 (b) 7 : 10 = x : 5 (c) 6 : (5 - x) = 7:3 I-A (d) ( x - 0 = 4 5 ( e) m : n = (s -x) :r ( ) (x - 2) x 2 = 3x - 3 /5. In each of the following determine whether the four quantities, taken in the order given, form a proportion:79. If x is the mean proportional between 11. If x is the third proportional to each of each of the following pairs of numbers, the following pairs of numbers, write write the proportions and find x: the proportion in each case and find x: ( d ) r, s (a) 5, 20 (e) 8, 18 (a) 3, 6 ( b ) 8 , 6 ( f ) a , b ( b ) 12, 8 (e) 8, 12 (c) 20, 5 (g) 18, 8 ( c) 6, 3 ( f) s, r (d) 6, 8 (h) b, a 12. In exercise 11, can the quantities be /10. Is the mean proportional between two taken in either order? given quantities the same irrespective of the order in which they are taken? 4.2 Fundamental Properties of Proportions Property 1 In any proportion the product of the means equals the product the extremes. Given: b = d Prove: ad = bc Proof. Develop in class. Remember that any axiom applicab used? to equations is applicable to proportions. What axion Property 1 may be called the fundamental n