Page 56 - Math_Genius_V1.0_C7_Flipbook

D:\Surender Prajapati\CBSE_ICSE_Book_New\CBSE\Grade-7\Math_Genius-7\Open_File\03_Chapter\03_Chapter
\ 15-Nov-2024 Surender Prajapati Proof-6 Reader’s Sign _______________________ Date __________

1. Represent the following fractions on the number line.

2 7 8 3
(a) (b) (c) (d) 1
5 8 9 7
14
2. Write three equivalent fractions of .
18
3 7
3. Which is greater: or ?
7 9
3 5
4. The sum of two fractions is . If one of them is , find the other.
4 8

Introduction of Rational Numbers

Raunak: Yesterday, my maths teacher taught in the class about such negative fractions called
Rational numbers and we need to extend our number system to include such numbers. Let me
explain you.

1 2 4
Suppose, over the last three years my father earned a profit of , ,and of his annual turnover.
10 15 7
1 2 4
We can represent these profit fractions as + , + ,and+ .
10 15 7
3
But this year he incurred a loss of of the total capital invested.
4
 3 
We can also represent this loss as −  of the total capital invested. This is neither an integer nor

a fraction.  4 
So, we need to extend our number system to include such
numbers, this type of numbers is called rational numbers.
p Knowledge Desk
‘A number that can be expressed in the form of , where p and The term 'rational' comes from
q
q both are integers and q ≠ 0 is called a rational number. the word 'ratio'. So, a rational
number is a number that can
4 −3 4 be expressed as the ratio of
For example: and are rational numbers, as in , p = +4
7 4 7 two integers. (*you will learn
−3 about the ratio later on).
and q = + 7, both are integers and 7 ≠ 0 and in , p = –3 and
4
q = +4, both (–3) and 4 are integers and 4 ≠ 0.

Quick Check
Write a rational number whose:
(a) numerator is a negative integer and denominator is a positive integer.
(b) numerator is a positive integer and denominator is a negative integer.
(c) numerator and denominator both are negative integers.
(d) numerator and denominator both are positive integers.

Mathematics-7 54