Page 26 - Start Up Mathematics_8 (Non CCE)

 1  − 1  2 1  − 1 2
Example 41: Check if  ÷    ÷ = ÷  ÷  ? (NCERT)
 2  3   5 2  3 5
 1  − 1  2  1  3   2  1  − 3  2
Solution:  ÷    ÷ =  ×    ÷ =  ×    ÷
 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 2 × 2 4
1)
1 ÷   − 1 ÷  = 1 ÷  − 1 ×  = 1 ÷ { ( −× 5 } = 1 ÷  − 5

5
2
×
2  3 5  2  3 2  2 32 2   6  
1  6  1  − 6 1 ×−( 6) 1 ×−( 3) − 3
= ×   = ×   = = =
×
2  − 5 2  5  2 × 5 15 5
So,   1 ÷ −  1      ÷ 2 ≠ 1 ÷  −  1 ÷ 2  
2   3   5 2  3 5  Remember
IV. Role of One p − p
−
“A rational number divided by ‘1’ is the rational number itself.” q ÷( 1) = q
p p p
So, if is a non-zero rational number, then ÷ 1 = .
q q q
7 −6 −8
Example 42: Evaluate: (a) ∏ 1 (b) ÷ 1 (c) ÷−1( )
9 11 15

7 7 −6 −6 −8 8
1
Solution: (a) ÷= (b) ÷=1 (c) ÷− =1( )
9 9 11 11 15 15
V. Rational Number Divided by Itself
p p p p q
If q is a non-zero rational number, then q ÷ q = q × p = 1.

Thus, “A rational number divided by itself results in 1.”

p  − p
A rational number divided by its additive inverse results in –1, i.e., q ÷   q   =−1.

6 6  −  8  −  8 2  − 2  −  7 7
Example 43: Evaluate: (a) ∏ (b)   ÷   (c) ÷   (d)   ÷
5 5  9   9  3  3   11  11
6 6  −  8  −  8 2  − 2  −  7 7
Solution: (a) ÷ = 1 (b)   ÷   = 1 (c) ÷   =− 1 (d)   ÷ = −1
5 5  9   9  3  3   11  11

EXERCISE 1.8

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

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