Chapter 1 Rational Numbers

, Chapter-1: Rational Numbers
Exercise 1.1 (Page 14 of Grade 8 NCERT)

Q1. Using appropriate properties find:
−2 3 5 3 1 2  −3  1 3 1 2
(i )  + −  (ii )   −  + 
3 5 2 5 6 5  7  6 2 14 5

Difficulty Level: Easy

What is the known/given?
Rational numbers with addition subtraction and multiplication.

What is the unknown?
Result of addition, subtraction and multiplication of rational numbers.

Reasoning:
By using commutativity of multiplication and addition getting the answer.

Solution (i):
−2 3 5 3 1
=  + − 
3 5 2 5 6

3 −2 5 3 1
=  + −  [By commutativity of multiplication]
5 3 2 5 6

3 −2 3 1 5
=  −  + [Commutativity of addition]
5 3 5 6 2
[Rearranging to take a common]
3  −2 1  5
=  −  +
5  3 6 2
3  −4 − 1  5
=  +
5  6  2
3 −5 5
=  +
5 6 2
1 5
=− +
2 2
−1 + 5
=
2
4
= =2
2
Answer (i): 2

, Solution (ii):
2  −3  1 3 1 2
=   −  + 
5  7  6 2 14 5
Rearranging
2  −3  2 1 1 3
=   +  − 
5  7  5 14 6 2
2
Taking common
5
2  −3  1  1 3
=    +  −  [by distributivity]
5  7  14  6 2
2  −3  2 + 1  1 3
=  − 
5  14  6 2
2  −6 + 1  1
=
 −
5  14  4
2 −5 1
=  −
5 14 4
−1 1
= −
7 4
(−1 4) (1 7)
= −
(7  4) (4  7)
4 7
=− −
28 28
−4 − 7
=
28
11
=−
28
11
Answer (ii): = −
28

Q2. Write the additive inverse of each of the following

2 −5 −6 2 19
(i) (ii) (iii) (iv) (v)
8 9 −5 −9 −6

Difficulty Level: Easy

What is the known/given?
Rational numbers

What is the unknown?
Additive inverse.