Question

Which of these illustrates the associative property of multiplication?

• A. $(4\times 5)\times 6=4\times (5\times 6)$
• B. $(4+5)\times 6=(4\times 6)+(5\times 6)$
• C. $4\times \left(56\right)=\left(45\right)\times 6$
• D. $4+5=5+4$

Answer 1

The correct option is A $(4\times 5)\times 6=4\times (5\times 6)$

Addition and multiplication, both are associative for whole numbers.

ie, $(a+b)+c=a+(b+c)$

$(a\times b)\times c=a\times (b\times c)$

So, $(4\times 5)\times 6=4\times (5\times 6)$ illustrates associative property of multiplication.

But $(4+5)\times 6=(4\times 6)+(5\times 6)$
It is in the form $(a+b)\times c=(a\times c)+(b\times c)\Rightarrow$
Distributive property

$4\times \left(56\right)\ne \left(45\right)\times 6$

$4+5=5+4$
It is in the form
$a+b=b+a\Rightarrow$
Commutative property.