Ratio and Proportion

Ratio and Proportion

1. What is Ratio:

The ratio of two quantities a and b in the same units, if the fraction
ab
and we write it as a : b.

In the ratio a : b, we call a as the first term which is also know as antecedent and b, the second term which is also called consequent.

2. What is Proprotion:

Equality of two ratios is called 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. Fourth, third and mean proportional

i). Fourth Proportional:

If a : b = c : d, then d is called the fourth proportional to a, b, c.

ii). Third Proportional:

a : b = c : d, then c is called the third proportion to a and b.

iii). Mean Proportional:

Mean proportional between a and b is
√ab

4. Comparison of Ratios and Compounded Ratio

i). Comparison of Ratios:

When we say that a:b > c:d, then it means
a/b>c/d

ii). Compounded Ratio:

The compounded ratio of the ratios: (a : b), (c : d), (e : f) is (ace : bdf)

Please note it is ratio of first ratio term of every ratio and second ratio term of every ratio

5. Important results of Ratio:

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)
      a3 is (a power of 3)
      b3 is (b power of 3)


iv). Sub Triplicate ratio of (a : b) is
     (a1/3:b1/3)
     a1/3 is (a power of 1/ 3)
     b1/3 is (b power of 1/3)

v).
if a/b=c/d
then a+b/a−b = c+d/c−d .,

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