A Ratio is a comparision of two quantities in the Form of a Fraction.
The ratio of two quantities 'a' and 'b' is represented as a:b or a/b. Here 'a' is called antecedent. 'b' is called consequent.
=> if a/b = c/d = e/f ..... then each ratio is equal to (a + c + e + .....)/(b + d + f + ....)
Points to remember:
- The order of terms in a ratio is important So a:b is not equal to b:a (unless both the terms are equal).
- Ratio must be expresses in the same units. In other words Ratio cannot be expressed in terms of fractions or decimals.
- Multiply or divide each term of the ratio by the same non - zero number doesn't effect the ratio
Types of Ratios:
Compound Ratio:
Ratios are compounded together by multiplying their antecedents for a new antecedent and their consequents for a new consequent.
Ex: Compound Ratio of 2/3, 3/5, 5/6
Sol: 2/3 x 3/5 x 5/6 = 2/6 = 1/3.
Duplicate Ratio:
Duplicate Ratio of a : b would be a2 : b2
Ex: Duplicate Ratio of 2:3 would be 4:9
Sub Duplicate Ratio:
Subduplicate Ratio of a : b would be √a : √b
Ex: Subduplicate Ratio of 2 : 3 would be √2 : √3
Triplicate Ratio:
Triplicate Ratio of a:b will be a3 = b3
Ex:
Triplicate Ratio of 2:3 will be 8 : 27
Sub Triplicate Ratio:
Sub Triplicate Ratio of a : b will be 3√a = 3√b
Ex: Sub triplicate Ratio of 2:3 will be 3√2 = 3√3
Inverse (or) Reciprocal Ratio:
The inverse of the given ratio is called its inverse Ratio
Ex: Inverse of a : b is
1/a : 1/b = b : a
Proportion: The equality of ratios is called proportion. If two ratios a/b = c/d then, a,b,c,d are proportional.
This is represented as a:b:c:d. Here a and d are called extreame terms and b and c are called mean terms.
d is called 4th proportional to a,b,c.
→ In any proportion
Product of means = product of extreams Concepts about the proportion:
If a/b = c/d then
1) ad = bc
2) b/a = d/c (invertendo)
3) a/c = b/d
4) c/a = d/b
5) (a + b)/b = (c + d)/d (Componendo)
6) (a + b)/b = (c + d)/d (Dividendo)
7) (a + b)/(a - b) = (c + d)/(c - d) (componendo + dividendo)
Continued proportions:
Consider the proportion 4, 6, 9. Here 4:6 :: 6 : 9, then we say that they are in continued proportion.