Question

choose the property of real numbers that justifies the equation.
$m\cdot \dfrac{1}{m} = 1$ select
$b\cdot 7 = 7\cdot b$ select
$6\cdot (c + 4) = 6\cdot c + 6\cdot 4$ select
$0 + a = a$ select

Explanation:

1. For $m \cdot \frac{1}{m} = 1$: A non-zero real number multiplied by its reciprocal equals 1, which is the definition of the multiplicative inverse property.
2. For $b \cdot 7 = 7 \cdot b$: The order of multiplication does not change the product, which matches the commutative property of multiplication.
3. For $6 \cdot (c + 4) = 6 \cdot c + 6 \cdot 4$: Multiplying a number by a sum is the same as multiplying the number by each term in the sum and adding the products, which is the distributive property of multiplication over addition.
4. For $0 + a = a$: Adding 0 to any real number leaves the number unchanged, which is the additive identity property.

Answer:

1. $m \cdot \frac{1}{m} = 1$: Multiplicative Inverse Property
2. $b \cdot 7 = 7 \cdot b$: Commutative Property of Multiplication
3. $6 \cdot (c + 4) = 6 \cdot c + 6 \cdot 4$: Distributive Property of Multiplication over Addition
4. $0 + a = a$: Additive Identity Property