Question

choose the property of real numbers that justifies the equation.
$m\cdot0 = 0$
$\dfrac{1}{n}\cdot n = 1$
$6\cdot(8\cdot b) = (6\cdot8)\cdot b$
$c + 3 = 3 + c$
options: 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:

For \( m \cdot 0 = 0 \)

The equation \( m \cdot 0 = 0 \) follows the Multiplication Property of Zero, which states that any real number multiplied by zero equals zero.

The equation \( \frac{1}{n} \cdot n = 1 \) follows the Multiplicative Inverse Property, which states that a non - zero real number multiplied by its reciprocal (multiplicative inverse) equals 1. Here, \( \frac{1}{n} \) is the multiplicative inverse of \( n \) (where \( n
eq0 \)).

The equation \( 6\cdot(8\cdot b)=(6\cdot 8)\cdot b \) follows the Associative Property of Multiplication. This property states that for real numbers \( a\), \( b\), and \( c\), \( (a\cdot b)\cdot c=a\cdot(b\cdot c) \), which means the way we group the numbers being multiplied does not change the product.

Answer:

Multiplication Property of Zero

For \( \frac{1}{n} \cdot n = 1 \)