RatioRatio of two quantities of the same kind P and Q is written as P/Q or P:Q.P/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. ProportionProportion is the equality of two ratios. If A, B, C, D are in a proportion then A: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 Fourth ProportionalD is the fourth proportional of A, B, C if A:B = C:D.Example: Find the 4th proportional to 3, 7 and 9. Solution: 3:7::9:x 3/7 = 9/x x = 21 Third ProportionalC is the third proportional of two numbers A, B if A:B = B:C.Example: Find the 3rd proportional to 16 and 32. Solution: 16:32::32:x 16/32 = 32/x x = 64 Download: Practice Questions on Ratio ProportionMean ProportionC is the mean proportion of two numbers A, B if C2 = AB.Example: Find the mean proportional to 4 and 25. Solution: 4:x::x:25 x2 = 100 x = 10 Direct Proportion:If P is directly proportional to Q then P = KQ where K is a constant of proportionality.Inverse Proportion:If P is inversely proportional to Q then PQ = K where K is a constant of proportionality.If a/b = c/d then 1)Invertendo, b/a = d/c 2)Alternendo, a/c = b/d 3)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. |