Questions: 5 · (1/5)=1 (Choose one) 0+8=8 (Choose one) 7 ·(d+3)=7 · d+7 · 3 (Choose one) c · 6=6 · c (Choose one)

Solution Steps

To solve this problem, we need to identify the properties of real numbers that justify each given equation. Here are the high-level ideas for each:

1. Equation: \(5 \cdot \frac{1}{5} = 1\)
   Property: This is the Multiplicative Inverse Property, which states that any number multiplied by its reciprocal equals 1.

2. Equation: \(0 + 8 = 8\)
   Property: This is the Identity Property of Addition, which states that any number plus zero equals the number itself.

3. Equation: \(7 \cdot (d + 3) = 7 \cdot d + 7 \cdot 3\)
   Property: This is the Distributive Property, which states that multiplying a number by a sum is the same as doing each multiplication separately.

4. Equation: \(c \cdot 6 = 6 \cdot c\)
   Property: This is the Commutative Property of Multiplication, which states that the order of factors can be changed without affecting the product.

The equation \(5 \cdot \frac{1}{5} = 1\) demonstrates the property that any number multiplied by its reciprocal equals 1. This is known as the Multiplicative Inverse Property.

The equation \(0 + 8 = 8\) illustrates that adding zero to any number does not change the value of that number. This is referred to as the Identity Property of Addition.

The equation \(7 \cdot (d + 3) = 7 \cdot d + 7 \cdot 3\) shows that multiplying a number by a sum can be distributed across the terms in the sum. This is known as the Distributive Property.

Final Answer