Associative property — lesson. Mathematics CBSE, Class 6.

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Regrouping the whole numbers 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 whole numbers, the change in grouping of the whole numbers will not change the result.

Consider \(a\), \(b\), and \(c\) are two whole numbers then:

\begin{array}{l} a + (b + c) = (a + b) + c \\ a \times (b \times c) = (a \times b) \times c \end{array}

Example:

2 + (9 + 4) = (2 + 9) + 4

\(=\) 15

ii)

8 \times (8 \times 4) = (8 \times 8) \times 4

\(=\) 256

This property does not apply to operations such as subtraction and division.

While subtracting (or) dividing three or more whole numbers, the change in grouping of whole numbers will change the result.

Consider \(a\), \(b\), and \(c\) are two whole numbers then:

\begin{array}{l} a - (b - c) \neq (a - b) - c \\ a \div (b \div c) \neq (a \div b) \div c \end{array}

Example:

(10 - 5) - 1 \neq 10 - (5 - 1)

\begin{array}{l} 5 - 1 \neq 10 - 4 \\ 4 \neq 6 \end{array}

ii)

(20 \div 10) \div 2 \neq 20 \div (10 \div 2)

\begin{array}{l} 2 \div 2 \neq 20 \div 5 \\ 1 \neq 4 \end{array}

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3. Associative property