Page 35 - ICSE Math 8

 1  2 Try These
⇒ x = 15 ÷  
 3  1. {(6) – (9) } + {(2) – (3) }
–1
–1 –1
–1 –1
–1
 3  2  1  − 2  1  − 2  1  − 2
2
⇒ x = 15 ×   = 15 × (3) = 15 × 9 = 135 2. Find   +   +   .
 1   2   3   4 
So, the required number is 135.
EXERCISE 2.1
p
1. Write the following in the form q .

− 
−
(a) (–2) –3 (b)  1  − 2 (c)  4   −2 (d)  − 3   − 3 (e)  3  −3

 


 5
 2
4 
7 
2. Evaluate.    − 1 − 1 − 1 
1 
–2
2
–2 0
0
–2
–1
(a) {(7) + (4) } × (2) (b) {(3) + (4) – (5) } (c)  1  +    +  1 
 
 
 3   4   6 
3
−
   1  − 3  1     − 3

1
–1 –1
–1
–1 –1
–1
(d)    −    ÷   (e) {(7) – (8) } – {(3) – (4) }
   3   2     
4
3. Simplify.
 1  − 3 − 1 1 –1 –1 2 –1 –1 3
(a)   × 3 () × (b) {(5) × (4) } (c) {(3) ÷ (4) }
 3  9 − 2 − 2 − 3


1 
1
2
–1
–1 –1
2
(d) {(5) ÷ (3) } × (2) –1 (e) {(4) – (3 )} ×  3  − 3 (f)      ×  1    
 ÷  
 
 
4
 4     3   2     
2
–5
–5
2
–7
2
–5
(g) {(3) + (2) – (4) } ÷  3  2 (h) {(3) × (10) × 125} ÷ {(5) × (6) }
 
 2 
–1
–1
4. By what number should (–6) be multiplied to get the product as (15) ?
 4 −3  16  − 2
− 
5. By what number should   be divided to get the quotient as   ?
 5   25 
6. Divide the sum of  −  1  −2 and  −  1  −2 by the difference of  1  − 1 and  1  − 1 .

 
 

 2   3   5   4 
More Examples
Example 4: Simplify using the laws of exponent and write the result in exponential form.
–7
8
–3
–3
(a) (5) × (5) (b) (4) × (3) –3 (c) (6) ÷ (6) –3
–5
3 –2
(d) (2 ) (e) ()4 − 6 (f) (2) ÷ (2) 3
()5 − 6
n
m
8
–3
Solution: (a) (5) × (5) = (5) 8 + (–3) = (5) 8 – 3 = (5) 5 { (x) × (x) = (x) m + n }
n
–3
n
–3
–3
n
(b) (4) × (3) = (4 × 3) = (12) –3 { (x) × (y) = (xy) }
n
(c) (6) ÷ (6) = (6) –7 – (–3) = (6) –7 + 3 = 6 –4 { (x) ÷ (x) = (x) m – n }
–3
–7
m
mn
3 –2
m n
(d) (2 ) = (2) 3 × (–2) = (2) –6 { (x ) = (x) }
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