Question

choose the property of real numbers that justifies the equation.
$9\cdot\left(m + 3\
ight)=9\cdot m + 9\cdot 3$ select
$7 + \left(-7\
ight)=0$
$2\cdot\dfrac{1}{2}=1$
$8 + b = b + 8$
commutative property of addition
associative property of addition
additive identity property
additive inverse property
distributive property
commutative property of multiplication
associative property of multiplication
multiplicative identity property
multiplicative inverse property
multiplication property of zero

Explanation:

First Equation: \( 9 \cdot (m + 3) = 9 \cdot m + 9 \cdot 3 \)

The Distributive Property states that \( a \cdot (b + c) = a \cdot b + a \cdot c \). Here, \( a = 9 \), \( b = m \), and \( c = 3 \), so the equation follows the Distributive Property.

The Additive Inverse Property states that for any real number \( a \), \( a + (-a) = 0 \). Here, \( a = 7 \), so \( 7 + (-7) = 0 \) follows the Additive Inverse Property.

The Multiplicative Inverse Property states that for any non - zero real number \( a \), \( a \cdot \frac{1}{a}=1 \). Here, \( a = 2 \), so \( 2\cdot\frac{1}{2}=1 \) follows the Multiplicative Inverse Property.

Answer:

Distributive Property

Second Equation: \( 7 + (-7) = 0 \)