Page 26 - ICSE Math 8

III. Associative Property: “Division of rational numbers is not associative.”
p r u  p r u p r  u
Thus, if , and are three non-zero rational numbers, then ÷ ÷ ≠ ÷ ÷ .
q s v   q s   v q   s v  

 1  − 1 2 1  − 1 2
Example 30: Check if  ÷   ÷ = ÷  ÷ .
 2  3  5 2  3 5 
 1  − 1  2  1  3   2  1  − 3  2
Solution: LHS =  ÷    ÷ =  ×    ÷ =  ×    ÷
 2  3   5  2  − 1  5  2  1   5
(
3)
=  1 ×−  ÷ 2 = − 3 ÷ 2 = −3 × 5 = ( −3) × 5 = −15


×
 21×  5 2 5 2 2 22 4
1)
1  − 1 2 1  − 1 5 1 { ( −× 5 } 1  − 5
RHS = ÷  ÷  = ÷  ×  = ÷ = ÷  
×
2  3 5  2  3 2  2 32 2  6 
1  6  1  − 6  1×−( 6) 1×−( 3) −3
= ×   = ×   = = =
2  − 5  2  5  25× 15× 5
Thus, LHS ≠ RHS
IV. Role of One: “A rational number divided by ‘1’ is the rational number itself.”
p p p
So, if is a non-zero rational number, then ÷ 1 = .
q q q
7 −6 −8
Example 31: Evaluate: (a) ÷ 1 (b) ÷ 1 (c) ÷−1( )
9 11 15
7 7 −6 −6 −8  8 8
− 
()
1
Solution: (a) ÷ 1 = (b) ÷=1 (c) ÷− =−   =
9 9 11 11 15  15  15
p
V. Rational Number Divided by Itself: If q is a non-zero rational number, Try This
p p p q
then ÷ = × = 1. Evaluate.
q q q p
6
6
Thus, “A rational number divided by itself results in 1.” (a) ÷ (b) –8 ÷ –8
5 5 9 9
2
A rational number divided by its additive inverse results in –1, i.e., (c) ÷ –2 (d) –7 ÷ –7
11
3
11
3
p  − p
q ÷   q   =−1.
EXERCISE 1.7

8 2 4 36 − 12 6 6
1. Divide: (a) by (b) 0 by (c) by (d) by
15 6 43 48 14 7 7
2. Simplify and express your answer as a rational number in the standard form.
5 3 −20 8 21 14 −16 15
(a) ÷ (b) ÷ (c) ∏ (d) ÷
12 − 14 32 15 25 10 35 −12
3. Show that a ÷ (b ÷ c) ≠ (a ÷ b) ÷ c.
3 −7 −2 1 −1 −4 −12 −3
(a) a = , b = , c = 5 (b) a = , b = , c = (c) a = , b = , c =
2 6 3 2 7 9 20 5
5
4. The product of two rational numbers is –20. If one of the numbers is , find the other number.
6

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