Ratio & Proportion
Ratio:- It is a comparison between two or more numbers. By using this ratio we can decide one number is more or less than the other.
Ex:
2 : 5
A : B = 3 : 7
Here if total is 10 then the value of A will be 3 and value of B will be 7.
⟶ A is antecedent and B is consequent
⟶ The comparison should always be done of the same quantity.
⟶ If numerator and denominator are multiplied or divided by the same number then the value of the ratio will not change.
Ex: x : y
● \(\frac{{x \times a}}{{y \times a}} = \frac{{xa}}{{ya}} = \frac{x}{y}\) = x : y
● \(\frac{{\frac{x}{a}}}{{\frac{y}{b}}} = \frac{x}{y}\)
Proportion:- When two ratios are equal then the 4 quantities comparising them are said to be in proportion.
⟶ if \(\frac{a}{b} = \frac{c}{d}\)
then a : b :: c : d
Here a and d are extremes and b and c are means
⟶ a : b :: c : d ⟹ ad = bc
⟶ Componedndo: If \(\frac{a}{b} = \frac{c}{d}\) = then \(\frac{{a + b}}{b} = \frac{{c + d}}{d}\)
⟶ Dividendo: If \(\frac{a}{b} = \frac{c}{d}\) then \(\frac{{a – b}}{b} = \frac{{c – d}}{d}\)
⟶ Componendo and Dividendo: \(\frac{a}{b} = \frac{c}{d}\) = then \(\frac{{a + b}}{{a – b}} = \frac{{c + d}}{{c – d}}\)
Continued Proportion:- If a, b, c are such that a : b = b : c then these numbers are said to be in continued proportion.
then b² = ac