Page 14 - classs 6 a_Neat

EXAMPLE 3: Simplify: 16 -[11-{8 ÷ (17 + 3 × 2 -19)}) EXAMPLE: 6. Simplify,  1  1 1  1 1 1   
 3 ÷  1 − 2   2 −− 6    
2
4
4
4
SOLUTION: The given expression SOLUTION We have:    
= 16 - [11 - {8 ÷ (17 + 3 × 2 -19)
= 16 - [11 - {8 ÷ (17 + 6 -19)
1
1
1 
1
= 16 - [11 - {8 ÷ 4] = 16 - [11 - 2]   3 ÷  1 − 1   2 −− 1      
= 16 - 9 = 7. =  4  4 2  2 4 6   
EXAMPLE 4: Simplify: 14 - [12 - {9 - (7 - 6 - 2)})  13  5 1 5 1 1   

=  ÷  −  −−   

SOLTIONS: The given expression  4  4 2 2 4 6   
= 14 - [12 -{9-(7 -6-2)}]  13  5 1 5 3 2   − 

= 14 - [12-{9-(7 - 4)} ] [removing vinculum] =  4 ÷  4 − 2 2 −    [removing bar]

= 14 - [12-{9-3}] [removing parentheses]    12   

= 14 - [12-6] [removing braces]  13  ÷ 5 − 1 5 − 1   

= 14 - 6 [removing square brackets] =   4  4 2 2 12      

= 8.
=   13  ÷  5 − 1 30 1   −     

1  2 3  1 5  4 4 2   12   
EXAMPLE 5. Simplify: 5 of  −  +÷
2  3 5  2 11 =  13  ÷ 5 −×  [removing parentheses]
1 29 
SOLUTION: The given expression   4   4 2 12    
11  2 3  1 5
= of  −  +÷  13  5 29    13  30 29   − [removing braces]
2  3 5  2 11 = 4 ÷     4 − 24    =  4 ÷     24    
11  10 9  − 1 5
= of   +÷ =  13 ÷ 1 
2  15  2 11   4 24  
11 1 1 5
= of +÷ [removing parentheses]
2 15 2 11 =   13 23 ÷  = 78 [removing square brackets]
11 1 5  4 1 
= +÷ [removing ‘of’]
30 2 11
11 1 5
= + × [removing’+’]
30 2 11
11 5
= + [removing ‘x’]
30 11
11 33 = 44
+
= [performing addition]
30 30
22 7
= = 1 ⋅
15 15