GROUPING SYMBOLS

Evaluate the following numerical expressions.

Example 1 :

2(5) +  3(4 + 3)

Solution :

=  2(5) +  3(4 + 3)

=  2(5) +  3(7)

=  10 +  21

 =  31

Example 2 :

2[5 + (30 ÷ 6)²]

Solution :

=  2[5 + (30 ÷ 6)²]

=  2[5 + (5)²]

=  2[5 + 25]

=  2[30]

=  60

Example 3 :

[7(2) - 4] + [9 + 8(4)]

Solution :

=  [7(2) - 4] + [9 + 8(4)]

=  [14 - 4] + [9 + 32]

=  10 + 41

=  51

Example 4 :

[(4 ⋅ 3)² ⋅ 5]/(9 + 3)

Solution :

=  [(4 ⋅ 3)² ⋅ 5]/(9 + 3)

=  [(7)² ⋅ 5]/(9 + 3)

=  [49 ⋅ 5]/(9 + 3)

=  245/12

Example 5 :

4(11 + 7) - 9 ⋅ 8

Solution :

=  4(11 + 7) - 9 ⋅ 8

=  4(18) - 9 ⋅ 8

=  72 - 72

=  0

Example 6 :

288 ÷ [3(9 + 3)]

Solution :

=  288 ÷ [3(9 + 3)]

=  288 ÷ [3(12)]

=  288 ÷ [36]

=  8

Example 7 :

390 ÷ [5(7 + 6)]

Solution :

=  390 ÷ [5(7 + 6)]

=  390 ÷ [5(13)]

=  390 ÷ [45]

=  78/9

Example 8 :

(4 ⋅ 6² - 4² ⋅ 6) / 4 ⋅ 6

Solution :

=  (4 ⋅ 6² - 4² ⋅ 6) / 4 ⋅ 6

=  (4 ⋅ 36 - 16 ⋅ 6) / 4 ⋅ 6

=  (144 - 96) / 24

=  48 / 24

=  2

Example 9 :

(2 ⋅ 8² - 2² ⋅ 8)/(2 ⋅ 8)

Solution :

=  (2 ⋅ 8² - 2² ⋅ 8)/(2 ⋅ 8)

=  (2 ⋅ 64 -  4 ⋅ 8)/16

=  (128 - 32)/16

=  96/16

=  6

Example 10 :

12(9 + 5) - 6 ⋅ 3

Solution :

=  12(9 + 5) - 6 ⋅ 3

=  12(14) - 18

=  168 - 18

=  150

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