Question

select the correct property for each given example. (3 points)

	associative property	commutative property	distributive property
$7 + 6 = 6 + 7$	$\circ$	$\circ$	$\circ$
$4(7 + 6) = 4\cdot2 + 7\cdot6$	$\circ$	$\circ$	$\circ$

Explanation:

For \((4 + 7) + 6 = 4 + (7 + 6)\)

Step1: Recall Associative Property

The associative property of addition states that \((a + b) + c = a + (b + c)\) for any real numbers \(a\), \(b\), and \(c\).

Step2: Match with the example

In the equation \((4 + 7) + 6 = 4 + (7 + 6)\), we have \(a = 4\), \(b = 7\), and \(c = 6\). It follows the form of the associative property of addition. So this example uses the Associative Property.

For \(7 + 6 = 6 + 7\)

Step1: Recall Commutative Property

The commutative property of addition states that \(a + b = b + a\) for any real numbers \(a\) and \(b\).

Step2: Match with the example

In the equation \(7 + 6 = 6 + 7\), we have \(a = 7\) and \(b = 6\). It follows the form of the commutative property of addition. So this example uses the Commutative Property.

For \(4(7 + 6) = 4\cdot2 + 7\cdot6\) (Note: There seems to be a typo, the correct distributive form should be \(4(7 + 6)=4\times7 + 4\times6\))

Step1: Recall Distributive Property

The distributive property states that \(a(b + c)=ab + ac\) for any real numbers \(a\), \(b\), and \(c\).

Step2: Analyze the example (assuming the intended correct form)

If we correct the right - hand side to \(4\times7+4\times6\), then for \(a = 4\), \(b = 7\), and \(c = 6\), the equation \(4(7 + 6)=4\times7 + 4\times6\) follows the distributive property \(a(b + c)=ab + ac\). So this example (with correction) uses the Distributive Property.

Answer:

s:

• For \((4 + 7) + 6 = 4 + (7 + 6)\): Associative Property (select the circle under Associative Property)
• For \(7 + 6 = 6 + 7\): Commutative Property (select the circle under Commutative Property)
• For \(4(7 + 6) = 4\cdot2 + 7\cdot6\) (with the intended distributive form correction): Distributive Property (select the circle under Distributive Property)