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Regrouping the integers does not change the value of the sum or the result. This is called the associative property.
This property applies only to operations such as addition and multiplication.
While adding (or) multiplying three or more integers, the change in grouping of the integers will not change the result.
If \(a\), \(b\) and \(c\) are any three integers, then
\(a +\) (\(b + c\)) \(=\) (\(a + b\)) \(+ c\)
\(a ×\) (\(b × c\)) \(=\) (\(a × b\)) \(× c\)
Example:
1. (\(12 + 11\)) \(+ 1 = 12 +\) (\(1 + 11\))
2. (\(2 × 6\)) \(× 3 =\) (\(2 × 6\)) \(× 3 =\) (\(2 × 3\)) \(× 6 = 36\)
This property is not applicable to operations such as subtraction and division.
While subtracting (or) dividing three or more integers, the change in grouping of integers will change the result.
If \(a\), \(b\) and \(c\) are any three integers, then
\(a -\) (\(b - c\)) \(≠\) (\(a - b\)) \(- c\)
\(a ÷\) (\(b ÷ c\)) \(≠\) (\(a ÷ b\)) \(÷ c\).
Example:
1. (\(12 - 11\)) \(- 1 ≠ 12 -\) (\(1 - 11\))
\(1 - 1 ≠ 12 -\) (\(-10\))
\(0 ≠ 22\)
\(1 - 1 ≠ 12 -\) (\(-10\))
\(0 ≠ 22\)
2. (\(12 ÷ 6\)) \(÷ 3 ≠ 12 ÷\) (\(6 ÷ 3\))
\(2 ÷ 3 ≠ 12 ÷ 6\)
\(2 ÷ 3 ≠ 2\)
\(2 ÷ 3 ≠ 12 ÷ 6\)
\(2 ÷ 3 ≠ 2\)
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