GROUPING SYMBOLS
About "Grouping symbols"
Grouping symbols :
By using the concept grouping-symbols, we can easily evaluate an algebraic expression.
Grouping-symbols are,
{ } - Braces
( ) - Parentheses
[ ] - Brackets
They indicate that the expression within the grouping symbol is to be evaluated first.
If we have more than one grouping symbol, we have to evaluate the expression within the innermost grouping symbols
Let us see some example problems based on the above concept.
Example 1 :
Evaluate the following expression.
2(5) + 3(4 + 3)
Solution :
= 2(5) + 3(4 + 3)
= 2(5) + 3(7)
= 10 + 21
= 31
Example 2 :
Evaluate the following expression.
2 [5 + (30 ÷ 6)²]
Solution :
= 2 [5 + (30 ÷ 6)²]
= 2 [5 + (5)²]
= 2 [5 + 25]
= 2 [30]
= 60
Example 3 :
Evaluate the following expression.
[7(2) - 4] + [9 + 8(4)]
Solution :
= [7(2) - 4] + [9 + 8(4)]
= [14 - 4] + [9 + 32]
= 10 + 41
= 51
Example 4 :
Evaluate the following expression.
[(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 :
Evaluate the following expression.
4(11 + 7) - 9 ⋅ 8
Solution :
= 4(11 + 7) - 9 ⋅ 8
= 4(18) - 9 ⋅ 8
= 72 - 72
= 0
Example 6 :
Evaluate the following expression.
288 ÷ [3(9 + 3)]
Solution :
= 288 ÷ [3(9 + 3)]
= 288 ÷ [3(12)]
= 288 ÷ [36]
= 8
Example 7 :
Evaluate the following expression.
390 ÷ [5(7 + 6)]
Solution :
= 390 ÷ [5(7 + 6)]
= 390 ÷ [5(13)]
= 390 ÷ [45]
= 78/9
Example 8 :
Evaluate the following expression.
(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 :
Evaluate the following expression.
(2 ⋅ 8² - 2² ⋅ 8) / 2 ⋅ 8
Solution :
= (2 ⋅ 8² - 2² ⋅ 8) / 2 ⋅ 8
= (2 ⋅ 64 - 4 ⋅ 8) / 2 ⋅ 8
= (128 - 32) / 16
= 96 / 16
= 6
Example 10 :
Evaluate the following expression.
12(9 + 5) - 6 ⋅ 3
Solution :
= 12(9 + 5) - 6 ⋅ 3
= 12(14) - 18
= 168 - 18
= 150
After having gone through the stuff given above, we hope that the students would have understood "Grouping-symbols".
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