RATIO AND PROPORTION

INTRODUCTION• Ratio is strictly a mathematical term to compare two similar

quantities expressed in the same units• The ratio of two terms ‘x’ and ‘y’ is denoted by x:y• In general, the ratio of a number x to a number y is defined as the

quotient of the numbers x and y• The numerator of the ratio is called the antecedent(x) and the

denominator is called the consequent (y) of the ratio.

COMPARISON OF TWO OR MORE RATIOS

• Two or more ratios may be compared by reducing the equivalent fraction to a common denominator and then comparing the magnitude of their numerator. Thus , suppose 2:5:4:3 and 4:5 are three ratios to be compared then the fractions 2/5, 4/3, and 4/5 are reduced to equivalent fractions with a common denominator.

REMEMBER• The two quantities must be of the same kind and in same unit.

• The ratio is pure number, i.e. , without any unit of measurement.

• The ratio would stay unaltered even if both the antecedent and the consequent are multiplied or divided by the same number.

REMEMBER• If four quantities are in proportion, the proportion of the extremes is equal to the product of the

means.

• Let a, b, c, d b in proportion, then

• a/b=c/d ad=bc .

• If three quantities a, b and c are in continued proportion, then a:b=b:c i.e. ac=

• B is called mean proportional.

• If three quantities are proportional, the first is to the third is the duplicate ratio of the first is to the second.

• If a:b::b:c then a:c=:

To find mean proportional• Example Find the mean proportional between 3 and 75.Solution:Let x be the required mean proportional. Then,

3:x::x:75Therefore,x=

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