RATIO : The ratio of two quantities a and b in the same units, is the fraction ^{a}/_{b}
and we write it as a : b.
In the ratio a: b, we call a as the first term or antecedent and b, the second term
or consequent. Ex. The ratio 5 : 9 represents ^{5}/_{9} with antecedent = 5, consequent = 9. Rule : The multiplication or division of each term of a ratio by the same non-zero
number does not affect the ratio.
Ex. 4 : 5 = 8 : 10 = 12 : 15 etc. Also, 4 : 6 = 2 : 3.
PROPORTION : The equality of two ratios is called proportion.
Ifa:b=c:d, we write, a: b:: c: d and we say that a, b, c, d are in proportion.
Here a and d are called extremes, while b and c are called mean terms. Product of means = Producut of extremes.
Thus, a : b :: c : d <=> ( b x c ) = ( a x d ).
Fourth Proportional : If a : b = c : d, then d is called the fourth proportional
to a, b, c.
Third Proportional : If a : b = b : c, then c is called the third proportional to
a and b.
Mean Proportional : Mean proportional between a and b is √ab
COMPARISON OF RATIOS: We say that (a : b) > (c : d) <=> ^{a}/_{b} > ^{c}/_{d}
COMPOUNDED RATIO: The compounded ratio of the ratios (a : b), (c : d), (e : f) is (ace : bdf).
Duplicate ratio of (a : b) is (a^{2} : b^{2}).
Sub-duplicate ratio of (a : b) is ( √a : √b )
Triplicate ratio of (a : b) is (a^{3} : b^{3}).
Sub-triplicate ratio of (a : b) is _{= }^{ 1 }_{ : }^{ 1 } ^{a3}^{b3}
If ^{a}/_{b} = ^{c}/_{d}
then ^{a+b}/_{a-b} = ^{c+d}/_{c-d}
VARIATION :
We say that x is directly proportional to y, if x = ky for some constant k and
we write, x = y.
We say that x is inversely proportional to y, if xy = k for some constant k and we, write :
x = ^{1}/_{y}