Question

choose the property of real numbers that justifies the equation.
$4\cdot(c + 6)=4\cdot c + 4\cdot 6$
$a + 0 = a$
$\frac{1}{n}\cdot n = 1$
$9\cdot b = b\cdot 9$

Explanation:

For the equation \( 4\cdot(c + 6)=4\cdot c + 4\cdot 6 \)

Step1: Recall Distributive Property

The Distributive Property of multiplication over addition states that for real numbers \( a \), \( b \), and \( c \), \( a\cdot(b + c)=a\cdot b + a\cdot c \).

Step2: Match with Given Equation

In the equation \( 4\cdot(c + 6)=4\cdot c + 4\cdot 6 \), we have \( a = 4 \), \( b = c \), and \( c = 6 \) (using the notation from the distributive property formula). So it follows the Distributive Property.

For the equation \( a + 0 = a \)

The Additive Identity Property states that adding zero to a number does not change the number, i.e., for any real number \( a \), \( a+0 = a \). So this equation is justified by the Additive Identity Property.

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

The Multiplicative Inverse Property states that for a non - zero real number \( n \), the product of the number and its reciprocal ( \( \frac{1}{n} \) is the reciprocal of \( n \) when \( n
eq0 \)) is 1, i.e., \( n\cdot\frac{1}{n}=1 \) (or \( \frac{1}{n}\cdot n = 1 \)). So this equation is justified by the Multiplicative Inverse Property.

For the equation \( 9\cdot b = b\cdot 9 \)

Answer:

s:

• \( 4\cdot(c + 6)=4\cdot c + 4\cdot 6 \): Distributive Property
• \( a + 0 = a \): Additive Identity Property
• \( \frac{1}{n}\cdot n = 1 \): Multiplicative Inverse Property
• \( 9\cdot b = b\cdot 9 \): Commutative Property of Multiplication