Ratio of two quantities of the same kind P and Q is written as P/Q or P:Q.RatioP/Q is known as fractional form whereas P:Q is known as linear form. In a ratio first term is known as the antecedent and the second term is known as the consequent.Ratio does not has any units. As ratio is just a number so multiplying both the antecedent and the consequent by the same number does not change the fraction.
Proportion is the equality of two ratios. If A, B, C, D are in a proportion then ProportionA:B :: C:D.A:B :: C:D can even be written as A:B = C:D.A and D are known as extremes terms whereas B and C are mean terms.A:B = C:D and AD = BC i.e. Product of extremes = Product of means
D is the fourth proportional of A, B, C if A:B = C:D.Fourth ProportionalExample: Find the 4th proportional to 3, 7 and 9.Solution: 3:7::9:x 3/7 = 9/x x = 21
C is the third proportional of two numbers A, B if A:B = B:C.Third ProportionalExample: Find the 3rd proportional to 16 and 32.Solution: 16:32::32:x 16/32 = 32/x x = 64 ## Download: Practice Questions on Ratio Proportion
C is the mean proportion of two numbers A, B if CMean Proportion^{2} = AB.Example: Find the mean proportional to 4 and 25.Solution: 4:x::x:25 x ^{2} = 100x = 10 If P is directly proportional to Q then P = KQ where K is a constant of proportionality.Direct Proportion: If P is inversely proportional to Q then PQ = K where K is a constant of proportionality.Inverse Proportion:If a/b = c/d then1)Invertendo, b/a = d/c2)Alternendo, a/c = b/d3)Componendo, (a + b)/b = (c + d)/d 4)Dividendo, (a - b)/b = (c - d)/d 5)Componendo, (a + b)/b = (c + d)/d 6)Componendo and Dividendo, (a + b)/(a - b) = (c + d)/(c - d)7)If a/b = c/d = e/f = ... = k, then (a + c + e +...)/(b + d + f +...) = k(Pa + Qc + Re +...)/(Pb + Qd + Rf +...) = k where P, Q, R,... are constants. |