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.
In the ratio a: b, we call a as the first term or antecedent and
b, the second term or consequent.
Ex. The ratio 6:8 represents 6/8 with antecedent = 6,
consequent =8
Rule: The multiplication or division of each term of a
ratio by the same non-zero number does not affect the ratio.
Ex. 3: 4 = 6: 8 =
12: 16 etc.
2. 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).
3. (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
4. (i) COMPARISON OF RATIOS:
We
say that (a: b) > (c: d) <=> (a/b)>(c /d).
(ii)
COMPOUNDED RATIO:
The
compounded ratio of the ratios (a: b), (c: d), (e : f) is (ace:
bdf)
5. (i) Duplicate
ratio of (a : b) is (a2 : b2).
(ii)
Sub-duplicate ratio of (a : b) is (√a : √b).
(iii)Triplicate ratio of (a : b) is (a3
: b3).
(iv) Sub-triplicate
ratio of (a : b) is (a ⅓ : b ⅓ ).
(v) If
(a/b)=(c/d), then ((a+b)/(a-b))=((c+d)/(c-d)) (Componendo and dividendo)
