Math Elementary arithmetic Associative law

# Associative law

The associative law (associative property) applies in addition and multiplication.

## The associative law of addition

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### Remember

In a sum with three summands, it is allowed to set or omit brackets just as you like without changing the value of the sum.
$a+(b+c)=(a+b)+c=a+b+c$

### Examples

• $5+(6+8)=(5+6)+8$
$5+14=11+8$
$19=19$

• $-9+(5+3)=(-9+5)+3$
$-9+8=-4+3$
$-1=-1$

## The associative law of multiplication

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### Merke

In a product with three factors, it is allowed to set or omit brackets just as you like without changing the value of the product.
$a\cdot (b\cdot c)=(a\cdot b)\cdot c=a\cdot b\cdot c$

### Examples

• $5\cdot(6\cdot8)=(5\cdot6)\cdot8$
$5\cdot48=30\cdot8$
$240=240$

• $-9\cdot(5\cdot3)=(-9\cdot5)\cdot3$
$-9\cdot15=-45\cdot3$
$-135=-135$