Page 30 - ICSE Math 8

2. Find:
1
5
(a) two rational numbers between −2 and . (b) five rational numbers between −3 and .
3 4 2 3
3 3 −2 −1
(c) ten rational numbers between and . (d) three rational numbers between and .
5 4 3 3

AT A GLANCE

p
¾ A rational number is a number that can be expressed as , p and q both being integers and q ≠ 0.
q
p p p × n pn
¾ If is a rational number and n is an integer with n ≠ 0, then = = .
q q q × n qn
p p p ÷ n
¾ If is a rational number and n is an integer with n ≠ 0, then = .
q q q ÷ n
p r
¾ q = s only when (p × s) = (q × r)

¾ Closure property: The rational numbers are closed under addition, subtraction, multiplication and division
(excluding division by 0).
¾ Commutative property: The rational numbers are commutative under addition and multiplication.
Subtraction and division are not commutative for rational numbers.
¾ Associative property: Addition and multiplication are associative for rational numbers. Subtraction and
division are not associative for rational number.
¾ Zero (0) is the additive identity for addition of rational numbers.
− p p
¾ is the additive inverse of .
q q
¾ 1 is called the multiplicative identity for multiplication.

q p p 

¾ p is known as the multiplicative inverse (or reciprocal) of q q ≠ 0 .


¾ Multiplication is distributive over addition.
p r p s p r
¾ If q and are two non-zero rational numbers, then q ÷ r = q × s .
s
p p p p p
¾ For any rational number , ÷=1 and ÷ = 1.
q q q q q
p r 1  p r 
¾ If q and are two non-zero rational numbers, then 2 ×  q + s  is a rational number lying exactly
s


between p and r .
q s

MENTAL MATHS

1. Choose the correct option.
(a) 3 times (–6) times (–15) divided by 5 is:
(i) –54 (ii) 48 (iii) 54 (iv) –48
2
(b) The multiplicative inverse of 2 is:
5
−12 5 12 −5
(i) (ii) (iii) (iv)
5 12 5 12

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