### Ratio and Proportion

Coming Soon

1) Ratio → A ratio is simply a fraction that is expressed as "x : y" and read as "ratio of x is to y".

• The first is called "antecedent" while second is called "Consequent".
• A ratio provides a convenient way to compare two quantities of same units. We can not compare the two quantities of different units with the help of ratio.

2) Proportion → The equality of two ratios on fractions is called proportion.

Expression ⇒ a : b : : c : d or a : b = c : d

Which implied (b × c) = (a × d)

2.1) Fourth proportional → If a : b : : c : d then d is called fourth proportion calculated as d =

2.2) Third proportional → If a : b : : b : c then c is called third proportional.

2.3) Mean proportional → If a : b : : b : c then b is called mean proportional.

2.4) Compounded ratio → If three ratios are given as (a : b) (c : d) (e : f).

The compound ratio is ⇒ (ace : bdf)

2.5) Table for various ratios

2.6) Variations → If 'x' is directly proportional to 'y' then x = ky.

Where is constant.

2.7) If sides of any two figure are in the ratio a : b then,

ratio of their areas = a2 : b2

ratio of their volumes = a3 : b3

Coming Soon