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Ratio and Proportion Basics
Ratio:
The ratio of two quantities a and b in the same units,
a/b is the fraction 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.
Eg. 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.
Eg. 4 : 5 = 8 : 10 = 12 : 15. Also, 4 : 6 = 2 : 3.
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).
Fourth Proportional:If a : b = c : d, then d is called
the fourth proportional to a, b, c.
Third Proportional: a : b = c : d, then c is called the
third proportion to a and b.
Mean Proportional: Mean proportional between a and b is v(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 Ratios:
Duplicate ratio of (a : b) is (a2 : b2)
Sub-duplicate ratio of (a : b) is (va : vb)
Triplicate ratio of (a : b) is (a3 : b3)
Sub-triplicate ratio of (a : b) is (?a: ?b)
If a/b = c/d, then (a+b) / (a-b) = (c+d) / (c-d)
[componendo and dividendo]
Variations: 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.
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