business mathematics

Ratio and Proportions concepts

Ratio and Proportions:


Ratio is denoted by ":"
The form of ratio is a:b. Here a,b are called terms.

1.Ratio:
The ratio of two qualities a and b in the same units, is the fraction a/b and we write it as a:b. In the ratio, a:b, we call ‘a’ as the first term of antecedent and b, the second term consequent.
Ex: The ratio 5:9 represents 5/9 with antecedent=5 ,consequent=9

2.Rule:
The multiplication or division of each term of 9 ratio by the same non-zero number does not affect the ratio.


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 and d are in proportion. Here a and b are called extremes, while b and c are called mean terms.
Product of means=product of extremes
Thus, a:b::c:d => (b*c)=(a*d)


4.Fourth proportional:
If a:b::c:d, then d is called the fourth
proportional to a,b and c.

5.Third proportional:
If a:b::b:c, then c is called third
proportional to a and b.

6.Mean proportional:
Mean proportional between a and b is SQRT(a*b).


7.Comparision of Ratios:
We say that (a:b)>(c:d) => (a/b)>(c/d)

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

9.Duplicate Ratio:
If (a:b) is (a2: b2 )

Sub-duplicate ratio of (a:b) is (SQRT(a):SQRT(b))

Triplicate ratio of (a:b) is (a3: b3 )

Sub-triplicate ratio of (a:b) is (a1/3: b1/3 ).
If a/b=c/d, then (a+b)/(a-b)=(c+d)/(c-d) (componend o and dividend o)