Ratio and Proportion free essay sample

Hence similar is with the aggregate values. †¢If a number is to be proportionately changed in a given ratio then the antecedent refers to the given number. Hence find the proportionality constant (number / antecedent) and multiply this constant with the consequent to get the answer. If 25 is to be changed in ratio 5:7 then 25 is represented by 5, so constant is 25/5 = 5, hence answer is 57 = 35 †¢In a given ratio a : b †¢If a gt; b then ratio is of greater inequality †¢If a lt; b then ratio is of lesser / less inequality. The inverse ratio is b : a †¢Duplicate ratio is a2 : b2 †¢Triplicate ratio is a3 : b3 †¢Subduplicate ratio is va : vb †¢Subtriplicate ratio is 3va : 3vb †¢Commensurable if a and b are integers †¢Incommensurable if a and b are not integers †¢The compounded ratio of (a1: b1), (a2 : b2) and (a3 : b3) is (a1. a2. a3) : (b1. b2. b3) [ that is product of the antecedents by product of the consequents ] †¢A ratio, multiplied with its inverse produces 1. We will write a custom essay sample on Ratio and Proportion or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page †¢A ratio multiplied with itself produces duplicate ratio Continued ratio or proportion is the proportional relationship between 3 or more items. Proportion brings about a continuous relationship between 3 or more items = relationship between 2 or more ratios †¢Let A : B = 2 : 3 and B : C = 5 : 7 . then A : B : C ? 2 : 3 : 7 or ? 2 : 5 : 7 †¢We need to bring parity at b and LCM of 3 and 5 is 15. So †¢A 2 2 x 5 = 10 †¢B 3 3 x 5 = 15 5 5 x 3 = 15 †¢C 7 7 x 3 = 21 †¢so A : B : C = 10 : 15 : 21 The mean proportion of A and B is X such that †¢A, X and B are in proportion †¢A, X and B are in geometric progression †¢X is the geometric mean †¢(A/X) = (X/B) †¢X2 = AB †¢In A : B : C : D †¢A and D are called extremes / extreme terms †¢B and C are called means / middle terms †¢A, B, C and D are in a geometric progression †¢(A/B) = (B/C) = (C/D) †¢A. D = B. C that is (product of extremes) = (product of means) †¢B2 = AC †¢C2 = BD †¢The third proportion of A and B is X such that †¢A, B and X are in proportion †¢A, B and X are in geometric progression B is the mean proportion of A and X †¢(A/B) = (B/X) †¢B2 = AX.