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Page No 107:

Question 1:

Simplify:
21 - 12 ÷ 3 × 2

Answer:

Given expression:
= 21 - 12 ÷ 3 ⨯ 2
= 21 - 4 ​⨯ 2               [Performing division]
= 21 - 8                     [Performing multiplication]
= 13                          [Performing subtraction]

Page No 107:

Question 2:

Simplify:
16 + 8 ÷ 4 - 2 × 3

Answer:

Given expression:
= 16 + 8 ÷ 4 - 2 ⨯ 3
= 16 + 2 - 2 ​⨯ 3               [Performing division]
= 16 + 2 - 6                     [Performing multiplication]
= 18 - 6                           [Performing addition]
= 12                               ​ [Performing subtraction]

Page No 107:

Question 3:

Simplify:
13 - (12 - 6 ÷ 3)

Answer:

Given expression:
= 13 - (12 - 6 ÷ 3 ) 
= 13 - (12 - 2)       [Performing division]
= 13 - 10 = 3
        [Performing subtraction]

Page No 107:

Question 4:

Simplify:
19 - [4 + {16 - (12 - 2)}]

Answer:

Given expression:
= 19 - [4 + {16 - (12 - 2)}]
19 - [4 + {16 - 10}]                        [Removing parentheses] 
= 19 - [4 + 6]                                    [Removing braces] 
= 19 - 10                                           [Removing square brackets] 
= 9

Page No 107:

Question 5:

Simplify:
36 - [18 - {14 - (15 - 4 ÷2 ×2)}]

Answer:

Given expression:
= 36 - [18 - {14 - (15 - 4 ÷ 2 × 2)}]
36 - [18 - {14 - (15 - 2 × 2)}]                   [Performing division]  
36 - [18 - {14 - (15 - 4)}]                         [Performing multiplication]   
=
36 - [18 - {14 - 11}]                                [Removing parentheses]  
=
36 - [18 - 3]                                            [Removing braces] 
​= 36 - 15                                                   [Removing square brackets] 
= 21

Page No 107:

Question 6:

Simplify:
27 - [18 - {16 - (5 - 4 - 1¯)}]

Answer:

Given expression:
= 27 - [18 - {16 - (5 - 4-1)}]
=
27 - [18 - {16 - (5 - 3)}]                       [Removing bar]  
=
27 - [18 - {16 - 2}]                              [Removing parentheses]  
27 - [18 - 14]                                       [Removing braces]                             
= 2
7 - 4                                                 [Removing square brackets]                             
​= 23                                                            

Page No 107:

Question 7:

Simplify:
445÷35 of 5+45×310-15

Answer:

Given expression:
  = 445 ÷35 of 5 + 45×310 - 15= 445 ÷35 × 51 + 45×310 - 15                         (Removing 'of ')= 245 ÷31 + 45×310 - 15                                 =245×13 + 45×310 - 15                                        (Removing '÷')= 85 + 45×310 - 15                                                 (Removing '×')=85 +625 - 15                                                           (Removing '×')= 40 + 6 - 525 = 41 25 = 11625

Page No 107:

Question 8:

Simplify:
23+49 of 35 ÷ 123×114-13

Answer:

Given expression:
 = 23 + 49 of 35 ÷123× 114 - 13 = 6 +49 of 35 ÷123× 114 - 13                      Removing parentheses= 109×35÷123× 114 - 13                                Removing 'of'= 23÷53× 114 - 13                                    =23×35 ×54 - 13                                                 (Removing '÷' )= 25×54 - 13                                     = 12 - 13                                                                  (Removing '×' )= 3-26 = 16

Page No 107:

Question 9:

Simplify:
713÷23 of 215+138÷234-112

Answer:

The given expression
 = 713÷23 of 215 + 138 ÷234 - 112 = 223 ÷23 of 115 + 118 ÷ 114 - 32  = 223 ÷23 ×115 + 118 ÷ 114 - 32                             Removing 'of' =223 ÷2215 + 118 ÷ 114 - 32        = 223×1522 +118 ÷ 114 - 32                    Removing '÷' =  5 + 118 × 411 - 32                                        Removing '÷'= 5 + 12 - 32                               ( On simplifying)= 10 +1 -32 = 82  = 4

Page No 107:

Question 10:

Simplify:
517-3310÷245-710

Answer:

Given expression:
= 517 - 3310÷245 - 710= 367 - 3310÷145 - 710= 367 - 3310÷28-710                            = 367 - 3310÷2110                                         Removing parentheses= 367 - 3310×1021                                          Removing '÷'= 367 - 117                                                          Removing braces= 36 - 117 = 257 = 347                                  (Simplifying)

Page No 107:

Question 11:

Simplify:
934÷216+413-112+134

Answer:

Given expression:
= 934 ÷ 216 + 413 - 112 + 134 = 394 ÷ 136 + 133 - 32 + 74 = 394 ÷ 136 + 133 - 6+74                            = 394 ÷ 136 + 133 - 134                                         Removing parentheses= 394 ÷ 136 + 52 -3912                                          = 394 ÷ 136 + 1312                                                          Removing braces= 394 ÷ 26 +1312     = 394 ÷3912                                                                            (Removing square brackets)= 394 × 1239 = 3                                                                    (Removing '÷')

Page No 107:

Question 12:

Simplify:
4110-212-56-25+310-415

Answer:

Given expression:
 = 4110- 212 - 56 - 25 + 310-415  = 4110 - 52 - 56 - 25 +  310-415  = 4110 - 52 - 56 - 12 +9 - 8 30                         = 4110 - 52 - 56 - 1330                                        Removing parentheses = 4110 - 52 - 25 -1330                                         = 4110 - 52 - 1230                                                       Removing braces= 4110 - 75 -1230     = 4110 -6330                                                                       (Removing square brackets)= 123 - 6330 = 6030 = 2                                                                   

Page No 107:

Question 13:

Simplify:
156+223-334 345÷912

Answer:

Given expression:
= 156+ 223 - 334 345÷ 912 = 116 + 83 - 154 195 ÷ 192  = 116 + 83 - 154 195 × 219                          = 116 + 83 - 154 × 25                                        Removing parentheses= 116 + 83 - 32                                                         Removing braces                           = 116 + 16 - 96                                                        = 116 + 76                                                                        (Removing square brackets)= 186 = 3                                                                   

Page No 107:

Question 14:

Simplify:
445÷215-12114-14-15¯

Answer:

Given expression:
= 445 ÷ 215 - 12114 - 14 - 15= 245 ÷ 115 - 1254 - 14 - 15 = 245 ÷ 115 - 1254 - 120                             Removing bar                  = 245 ÷ 115 - 1225 - 120                                            = 245 ÷ 115 - 12 × 2420                                     Removing parentheses=245 ÷ 115 - 1220                                                 Removing '×'                           = 245 ÷ 44 - 1220                                                                                                   = 245÷3220                                                                    Removing braces   = 245 × 2032                                                                  (Removing '÷')= 34 × 4 = 3                                                                   

Page No 107:

Question 15:

Simplify:
712-214÷114-1232-13-16¯

Answer:

Given expression:
= 712-214÷ 114- 1232 - 13 - 16= 152-94÷ 54- 1232 - 13 - 16= 152-94÷ 54- 1232 - 16                                    Removing bar                  = 152-94÷ 54- 129 -16                                         = 152-94÷ 54- 12×43                                              Removing parentheses=  152-94÷ 54- 23                                                       Removing '×'                           = 152-94÷  15 - 812                                                      Removing braces                                            =152-94÷712                                                                       = 152-94×127                                                                     (Removing '÷')= 152 - 277                                                                               Removing square brackets  = 105 - 5414 =5114 = 3914



Page No 108:

Question 1:

8 + 4 ÷ 2 × 5 = ?
(a) 30
(b) 50
(c) 18
(d) none of these

Answer:

(c ) 18

Explanation:
= 8 + 4 ÷ 2 × 5
= 8 + 2 × 5
= 8 + 10 = 18 

Page No 108:

Question 2:

54 ÷ 3 of 6 + 9 = ?
(a) 117
(b) 12
(c) 65
(d) none of these

Answer:

 ( b ) 12

Explanation:
= 54 ÷ 3 of 6 + 9
= 54 ÷ (3  x 6) + 9
= 54 ÷ 18 + 9
= 3 + 9 = 12

Page No 108:

Question 3:

13 − (12 − 6 ÷ 3) = ?
(a) 11
(b) 3
(c) 73
(d) none of these

Answer:

(b ) 3

Explanation:
= 13 - (12 - 6 ÷ 3)
= 13 - (12 - 2)
= 13 - 10 = 3

Page No 108:

Question 4:

1001 ÷ 11 of 13 = ?
(a) 7
(b) 1183
(c) 847
(d) none of these

Answer:

(a ) 7

Explanation:
= 1001 ÷  11 of 13 
= 1001 ÷ ( 11 x 13)
= 1001 ÷ 143 = 7

Page No 108:

Question 5:

133 + 28 ÷ 7 − 8 × 2 = ?
(a) 7
(b) 121
(c) 30
(d) none of these

Answer:

(b) 121

Explanation:
Given expression:
= 133 + 28 ÷ 7 - 8 ⨯ 2
= 133 + 4 - 8 ​⨯2              [Performing division]
= 133 + 4 - 16                 [Performing multiplication]
= 137 - 16                       [Performing addition]
= 121                              [Performing subtraction]

Page No 108:

Question 6:

3640 − 14 ÷ 7 × 2 = ?
(a) 3636
(b) 1036
(c) 1819
(d) none of these

Answer:

(a) 3636

Explanation:
Given expression:
= 3640 - 14 ÷ 7 ⨯ 2
​= 3640 - 2  ​⨯2               [Performing division]
= 3640 - 4                    [Performing multiplication]
= 3636                          [Performing subtraction]

Page No 108:

Question 7:

100 × 10 − 100 + 2000 ÷ 100 = ?
(a) 29
(b) 920
(c) none of these

Answer:

(b) 920

Explanation:
Given expression:
= 100 ⨯ 10 - 100 + 2000 ÷ 100
​= 100 ⨯ 10 - 100 + 20                  [Performing division]
= 1000 - 100 + 20                        [Performing multiplication]
= 1020 -100                                 [Performing addition]
= 920                                   ​        [Performing subtraction]

Page No 108:

Question 8:

27 - [18 - {16 - (5 - 4 - 1¯)] = ?
(a) 25
(b) 23
(c) none of these

Answer:

(b) 23
Explanation:

Given expression:
= 27 - [18 - {16 - (5 - 4-1)}]
=  27 - [18 - {16 - (5 - 3)}]                          (Removing bar)
= 27 - [18 - {16 - 2}]                                   (Removing parentheses)
= 27 - [18 - 14]                                            (Removing braces)
= 27 - 4                                                        (Removing square brackets)
= 23

Page No 108:

Question 9:

32 - [48 ÷ {36 - (27 - 16 - 9¯)}] = ?
(a) 29
(b) 52017
(c) none of these

Answer:

(a) 29
Explanation:
Given expression:
= 32 - [48 ÷ {36 - ( 27 - 16-9)}]
=  32 - [48 ÷ {36 - ( 27 - 7)}]                    (Removing bar)
= 32 - [48 ÷ {36 -20}]                               (Removing parentheses)
= 32 - [48 ÷ 16]                                          (Removing braces)
= 32 - 3                                                      (Removing square brackets)
= 29

Page No 108:

Question 10:

8 − [28 ÷ {34 − (36 − 18 ÷ 9 × 8)}] = ?
(a) 6
(b) 649
(c) none of these

Answer:

(a ) 6

Explanation: 
Given expression:
= 8 - [28 ÷ {34 - (36 - 18 ÷ 9 × 8)}]                        [Performing division]
= 8 - [28 ÷ {34 - (36 - 2 ×  8)}]                               [Performing multiplication]
= 8 - [28 ÷ {34 - (36 - 16)}]
= 8 - [28 ÷ {34 - 20}]                                              [Removing parentheses]
= 8 - [28 ÷ 14]                                                         [Removing braces]
= 8 - 2 = 6                                                               [Removing square brackets]



Page No 109:

Question 1:

Simplify:
16 - [11 + {8 - 6 - 4 - 2¯}]

Answer:

We have:
    16 - [11 + {8 - (6 -4-2 )}]
= ​16 - [11 + {8 - (6 - 2)}]         (Removing bar)
= ​16 - [11 + {8 - 4}]                 
= ​16 - [11 + 4]                           (Removing barces)
= 16 - 15                                          (Removing square brackets)
= 1

Page No 109:

Question 2:

Simplify:
16 + 8 ÷ 4 - 2 × 3

Answer:

We have:
  16 + 8 ÷ 4 - 2 × 3
16 + 2 - 2 × 3             (Division)
16 + 2 - 6                   (Multiplication)
= 18 - 6                           (Addition)
= 12

Page No 109:

Question 3:

Simplify:
36 - [18 - {14 - (15 - 4 ÷ 2 × 2)}]

Answer:

Given expression:
   36 - [18 - {14 - (15 - 4 ÷ 2 × 2)}]                                     [Performing division]
= 36 - [18 - {14 - (15 - 2 × 2)}]                                           [Performing multiplication]
= 36 - [18 - {14 - (15 - 4)}]      
= 36 - [18 - {14 - 11}]                                                        [Removing parentheses]
= 36 - [18 - 3]                                                                    [Removing braces]
= 36 - 15                                                                           [Removing square brackets]
= 21

Page No 109:

Question 4:

15 + 5 ÷ 5 × 2 = ?
(a) 8
(b) 2
(c) 17
(d) none of these

Answer:

(c) 17
We have:
15 + 5 ÷ 5 x 2 
= 15 +1 x 2              (Performing division)
= 15 + 2                  (Performing multiplication)
= 17

Page No 109:

Question 5:

16 - 2 ÷ 7 + 6 × 2 = ?
(a) 16
(b) 14
(c) 2757
(d) none of these

Answer:

(c) 2757
We have:
16 - 2 ÷ 7 +  6 × 2  
= 16 - 27 + 6 × 2                                                                [Performing division]
= 16 - 27 + 12                                                                    [Performing multiplication]
= 28 - 27                                                                            [Performing addition]
=  281 -27  = 196 -27  = 1947 = 2757                                   [Performing subtraction]

Page No 109:

Question 6:

54 ÷ 3 of 6 + 9 = ?
(a) 117
(b) 12
(c) 65
(d) none of these

Answer:

(b)12

We have: 
    54 ÷ 3 of 6 + 9
= 54 ÷ 18 + 9
= 3 + 9
= 12



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