In this section, the following topics are discussed with examples

  • Introduction
  • Ratio
  • Proportion
  • Diverse and Inverse Proportion
  • Properties of Proportion
  • Examples

INTRODUCTION

Ratio

Ratio is comparison of two numbers, to find out how many times one number is greater than (or less than) the other number. It is to express one number as a fraction of other. Ratio of two quantities a and b in same units, is the fraction a/b , where b  0. It is represented as a : b, where a (Numerator) is called as an antecedent and b (Denominator) is called as a consequent.

Proportion

Proportion is a special form of algebra equation, is used to compare ratios or make equivalent fractions. The equality of two ratios is called as proportion, a / b and c / d which is represented as, a : b :: c : d in which a and d are called Extreme terms, b and c are called mean terms.

Direct and Inverse proportion:

We say that a is directly proportional to b, if a = kb for some constant k 

We say that a is inversely proportional to b, if a = k for some constant k.

PROPERTIES OF PROPORTION

  • If a, b, c and d are in proportion, a  c ,a:b::c:d then, b  

                  Product of extreme terms = Product of mean terms, i.e. ad = bc.

  • For a proportion of a:b::c:d,
  • d is the fourth proportional of a, b, c
  • c is called third proportional to a, b

People are lucky and unlucky not according to what they get absolutely, but according to the ratio between what they get and what they have been led to expect.

SAMUEL BUTLER

Example

1. Express each ratio as a fraction.

a. 3 : 4 b. 8 : 5c. 9:13 d. 15:7

 

SOLN:

a)¾

b)8/5

c)9/13

d)15/7

2.  A 30 pound ball on moon, weighs 180 pounds on the earth. How much does a 300 pound ball on Earth weighs on the moon? 

          a) 250 b)36 c)60 d)50

SOLN:

d)5  

30:180

x:300

x=(300*30)/180

x=50

3. The ratio of the sides of a certain triangle is 2:7:8. If the longest side of the triangle is 40 cm, how long are the other two sides? 

          a)20,80 b)6,14 c)10,35 d)36,56

SOLN:

 

Longest side=40

Since the ratio is 2:7:8 , multiply throughout by 5 ,

10 and 35