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1.2 Learn Basic Properties and Operations

Properties

The associative property applies when we are adding or multiplying more than two numbers. It states that we can group the numbers however we would like without changing the result.

In the property, parentheses show which operation is performed first.

Associative property $$(a + b) + c = a + (b + c)$$ and $$(ab)c = a(bc)$$

Examples

$$\begin{array}{l}\;\;\;( - 7 + 4) + 6\\ = - 3 + 6\\ = 3 \end{array}$$ and $$\begin{array}{l}\;\;\;\; - 7 + (4 + 6)\\ = - 7 + 10\\= 3\end{array}$$ The result is 3 no matter how the numbers are grouped.

positive 5 times negative 1 times negative 3 = negative 5 times negative 3 = positive 15 becomes positive 5 times negative 1 times negative 3 = positive 5 times positive 3 = 15

In this example, the numbers in red were multiplied first.

It is often helpful to group the numbers with like signs. When adding or multiplying many numbers, make a group of positive numbers and a group of negative numbers. After finding the sum or product of the groups separately, combine the results.