Ratio and Proportion Formulas

As you know Ratio is a relation between two quantities or number , and proportion is a ratio of ratios.

Here are some basic formulas related to Ratio and Proportion in mathematics:

Ratio and Proportion formulas:

1> A ratio of “a” and “b” is denoted by a:b and is read as: “a is to b”.

in a ratio the first part ( “a” in our example ) is called Antecedent and second part ( “b” in our example ) is called Consequent.

2> A duplicate ratio is the ratio of second degree of the original ratio. For example the duplicate ratio of $\dfrac{a}{b}$ is $\dfrac{a^2}{b^2}$

3> A triplicate ratio is the ratio of third degree of the original ratio. For example the triplicate ratio of $\dfrac{a}{b}$ is $\dfrac{a^3}{b^3}$

4> A sub-Duplicate ratio is the ratio of half degree of the original ratio. For example the sub-duplicate ratio of $\dfrac{a}{b}$ is $\sqrt{\dfrac{a}{b}}$

5> A sub-triplicate ratio is the ratio of one third degree of the original ratio. For example the sub-triplicate ratio of $\dfrac{a}{b}$ is $\sqrt[3]{\dfrac{a}{b}}$

6> The ratio obtained by multiplying two or more ratios term wise is called compounded ratio.
for example compounded ratio of ratios $\dfrac{a}{b}$ , $\dfrac{c}{d}$ , $\dfrac{e}{f}$ is $\dfrac{a.c.e}{b.d.f}$

7> The ratio obtained by adding two or more ratios term wise is called “Addendo”.
for example Addendo ratio of ratios $\dfrac{a}{b}$ , $\dfrac{c}{d}$ , $\dfrac{e}{f}$ is $\dfrac{a+c+e}{b+d+f}$

7> A proportion of ratios “a:b” and “c:d” is denoted by: a:b :: c:d
where “a” and “d” are called Extremes and “b” and “c” are called means.

8> If in a proportion a:b :: b:c :: c:d , $\dfrac{a}{b} = \dfrac{b}{c} =\dfrac{c}{d} = k$ then the proportion is said to be a continued proportion of a , b, c &d.

9> If a:b :: b:c :: c:d or $\dfrac{a}{b} = \dfrac{b}{c} =\dfrac{c}{d} = k$ is a continued proportion then,
c = dk , b=ck=dk² and a=bk=ck²=dk³

10> A proportion a:b :: c:d or $\dfrac{a}{b} = \dfrac{c}{d}$ can also be re-written as:

a> $\dfrac{b}{a} = \dfrac{d}{c}$ and is called “Invertendo”.

b> $\dfrac{a}{c} = \dfrac{b}{d}$ and is called “Alternando” .

c> $\dfrac{a+b}{c} = \dfrac{c+d}{c}$ and is called “Componendo”.

d> $\dfrac{a-b}{c} = \dfrac{c-d}{c}$ and is called “Dividendo”.

e> $\dfrac{a+b}{a-b} = \dfrac{c+d}{c-d}$ and is called “Componendo and Dividendo”.

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