## RATIO

If general, the ratio of a number x to a number y is defined as the quotient of the number x & y.

The numbers that form the ratio are called the terms of the ratio. The numerator of the ratio is called the antecedent & the denominator is called the consequent of the ratio.

Some important properties of ratios:

1. If

$$\frac { a }{ b } =\frac { c }{ d } =\frac { e }{ f } =\frac { g }{ h } =k\quad$$

, then

$$\frac { a }{ b } =\frac { c }{ d } =\frac { e }{ f } =\frac { g }{ h } =k=\frac { (a\quad +\quad c\quad +\quad e\quad +\quad g) }{ (b\quad +\quad d\quad +\quad f\quad +\quad h) }$$

2. If  $$\frac { { a }_{ 1 } }{ { b }_{ 1 } } ,\frac { { a }_{ 2 } }{ { b }_{ 2 } } ,\frac { { a }_{ 3 } }{ { b }_{ 3 } } ——-\frac { { a }_{ n } }{ { b }_{ n } }$$ are unequal fractions.

Then the ratio:

$$\frac { { a }_{ 1 }\quad +\quad { a }_{ 2 }\quad +\quad { a }_{ 3 }\quad ——-{ a }_{ n } }{ { b }_{ 1 }\quad +\quad { b }_{ 2 }\quad +\quad { b }_{ 3 }——–{ b }_{ n } }$$

lies between the lowest & highest of these percentage.

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