Page 38 - Start Up Mathematics_8 (Non CCE)

Example 3: Simplify the following:
1
−
   4  − 1  1   − 1

–1
–4
3
(a) {(8) × (5) } ÷ (2) (NCERT) (b)    −   
   5   4   
1 
–1
–1 –1
–1 –1
–1
(c) {(6) – (9) } + {(2) – (3) } (d)  1  − 2 +  1  − 2 +    − 2 (NCERT)
 
 
 2   3   4 
{ 1 } 1  ()5  ()2 4 { 555 } ()2 4
3
××
–1
3
–4
Solution: (a) {(8) × (5) } ÷ (2) = 8 × 5 () 3 ÷ 2 () 4 =  8  1 = 8 × 1
 ×

2
125 2 ××× 2 125 16× 125 × 2 250
2
= × = = = = 250
8 1 81× 11× 1
1
−
1
−
4
5
   − 1 1   − 1  1 1  − 1 { } { } { } − 1
1

−
516−
11
−
4 
(b)    −     =  −  = − = =
   5   4      4   1   4 1 4 4


  5   4  




1 4 −4
= = =
 − 11  − 11 11

  4 
1
−
1
1
1
1
–1 –1
–1
–1 –1
–1
−
−
+
(c) {(6) – (9) } + {(2) – (3) } = { } { } − 1
9
6
3
2
{ } { } { } {} − 1
−
1
1
1
−
−
32
32−
−
1
1
= 18 + 6 = 18 + 6
1 1
= + = 18 + 6 = 24
 1   1 

  18   6  

 1  − 2  1  − 2  1  − 2 1 1 1
(d)   +   +   = + +
 2   3   4   1  2  1  2  1  2
     
 2   3   4 
1 1 1 2 () 2 3 () 2 4 () 2
= + + = + +
1 () 2 1 () 2 1 () 2 1 () 2 1 () 2 1 () 2
2 () 2 3 () 2 4 () 2
2
2
2
= (2) + (3) + (4) = 4 + 9 + 16 = 29
 1  2
Example 4: By what number should   be multiplied to get the product as 15?

3 
Solution: Let the required number be x.
 1  2  1  2
  × x = 15 ⇒ x ×   = 15 ( Multiplication is commutative)
 3   3 
 1  2
⇒ x = 15 ÷  
 3 
 3  2
2
⇒ x = 15 ×   = 15 × (3) = 15 × 9 = 135
 1 
So, the required number is 135.
30