Ratio and Proportion

Ratio
A ratio is the comparison of two or more quantities of same kind using division or we can define ratio of two quantities a and b of the same kind in the same units as a fraction which is written generally as a : b (read as ‘a’ is to ‘b’). In the ratio a : b, ‘a’ is called the first term or antecedent and ‘b’ is called the second term or consequent.

RATIO IN SIMPLEST FORM OR LOWEST TERM
A ratio is said to be in its simplest form or lowest terms when its terms do not have common factor except 1.
Note :
1.    Ratio only exists between quantities of same kind :
(i)     There exists no ratio between the height of a child and the weights of a child.
(ii)     We cannot write a ratio between the age of a student and the marks obtained by the student.
2.    To find a ratio between the quantities of same kind, quantities should be expressed in same units.
3.    Ratio has no unit.

(I)    Comparison of Ratio:      Two ratios can be compared by converting them to like fractions. If the two fractions are equal, we say that two given ratios are equivalent.

Illustration 1
Express the ratio 36 : 81 in the simplest form.
Solution
H.C.F. of 36 and 81 is 9  