Page 84 - Maths Skills - 7

82 Maths

INTRODUCTION Building A
In our daily life, there are many occasions when we compare two quantities.
Suppose we are comparing the heights of two buildings. Building B
Building A is two times taller than Building B or Building B is half of Building A’s height.
Yet another example is where we compare speeds of car and man.

The speed of a car is ten times the speed of a man.
All these comparisons can be written in the form of ratio.
Like for 1st example;

Height of building A : Height of building B is 2 : 1
And in other example;
Speed of car : Speed of man is 10 : 1.

RATIO

A comparison by division is called ratio. For example; student Fact-o-meter
A scored 40 marks out of 50 whereas student B scored 36 marks Only similar things can be
out of 50. compared, i.e. marks to marks,
So, the ratio of A : B will be 40 : 36 or, 10 : 9. weight to weight, length to

It means that for every 10 marks that A got, B got 9 marks. length, area to area, etc.

PROPORTION
An equality of two ratios is called a proportion, represented as ‘: :’. A proportion can be written in different ways.
For example;
3
(i) As equivalent fraction: = 12 (ii) As two equivalent ratios: 3 : 5 = 12 : 20
5 20
(iii) As in proportion: 3 : 5 : : 12 : 20
Here, each number is called a term, i.e., there are four terms in a proportion, viz., 3 is the first means
term, 5 is the second, 12 is the third and 20 is the fourth term. 3 : 5 : : 12 : 20

The first and the fourth terms in the proportion are called the extreme terms or extremes extremes
whereas the second and the third terms are called the middle terms or means.

To find if the given two ratios are in proportion or not, we first find the product of their extremes and means.
If the product of means equals the product of extremes, then the ratios are in proportion.
i.e., If a : b : : c : d, then ad = bc
a c
or, If, = then ad = bc
b d
Using the above relation we can find the missing term of the proportion.
For example; If a : 20 : : 3 : 5, find ‘a’ Fact-o-meter
a 3
Here, = Condition of Proportionality
20 5 Here, a : b : : c : d
or, a × 5 = 20 × 3 a c
b = d

or, a = 20 × 3 or a × d = b × c
5
⇒ a = 12 i.e., product of extremes = product of means