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

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

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