What is 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.
We read it as a is to b.
In the ratio a:b, we call
a as the first term or
antecedent
b, the second
term or consequent.
For Example
The
ratio 7: 5 represents 7/5 with antecedent = 7, consequent = 5.
Note:
The
multiplication or division of each term of a ratio by the same non-zero number does not affect
the ratio.
For Example
5: 4 = 20: 16 = 10: 8 etc.
What is PROPORTION?
The equality of two ratios is called proportion.
If a: 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
= Product of extremes.
Thus, a: b:: c : d <=> (b x c) = (a x d).
Few terms
(i) Fourth Proportional:
If a : b = c: d, then
d is called the fourth proportional to
a, b, c.
(ii) Third Proportional:
If a: b = b:
c, then c is called the third proportional to a
and b.
(iii) Mean Proportional:
Mean proportional between a and b is
square root of ab
(iv) COMPARISON OF RATIOS:
We say that (a: b) > (c: d) <=> (a/b)>(c /d).
(v)
COMPOUNDED RATIO:
The
compounded ratio of the ratios (a: b), (c: d), (e : f) is (ace:
bdf)
TYPES OF RATIOS
(i)
Duplicate ratio
(a : b) is (a2 : b2).
(ii) Sub-duplicate ratio
(a : b) is (√a : √b).
(iii)Triplicate ratio
(a : b) is (a3 : b3).
(iv) Sub-triplicate ratio
(a : b) is (a ⅓ : b ⅓ ).
(v) (Componendo and Dividendo)
If (a/b)=(c/d), then
((a+b)/(a-b))=((c+d)/(c-d))
ALTERNATIVELY:
(i) We say that x is directly proportional to y, if
x = ky for some constant k and
we write, x ∞ y.
(ii) We say that x is
inversely proportional to y, if xy = k for some constant k and
we write, x∞(1/y)
