Questions: Number Theory and the Real Number System Properties of real numbers Choose the property of real numbers that justifies the equation. -9+9=0 (Choose one) 3 ·(6 · n)=(3 · 6) · n (7+m) · 5=7 · 5+m · 5 (Choose one) 1 · 2=2

Number Theory and the Real Number System
Properties of real numbers

Choose the property of real numbers that justifies the equation.
-9+9=0 (Choose one)
3 ·(6 · n)=(3 · 6) · n
(7+m) · 5=7 · 5+m · 5 (Choose one)
1 · 2=2

Transcript text: Number Theory and the Real Number System Properties of real numbers Choose the property of real numbers that justifies the equation. -9+9=0 (Choose one) 3 ·(6 · n)=(3 · 6) · n (7+m) · 5=7 · 5+m · 5 (Choose one) 1 · 2=2

Solution

Solution Steps

Step 1: Identify the property for \(-9 + 9 = 0\)

The equation \(-9 + 9 = 0\) demonstrates the Additive Inverse Property. This property states that for any real number \(a\), there exists a number \(-a\) such that \(a + (-a) = 0\).

Step 2: Identify the property for \(3 \cdot (6 \cdot n) = (3 \cdot 6) \cdot n\)

The equation \(3 \cdot (6 \cdot n) = (3 \cdot 6) \cdot n\) demonstrates the Associative Property of Multiplication. This property states that for any real numbers \(a\), \(b\), and \(c\), \((a \cdot b) \cdot c = a \cdot (b \cdot c)\).

Step 3: Identify the property for \((7 + m) \cdot 5 = 7 \cdot 5 + m \cdot 5\)

The equation \((7 + m) \cdot 5 = 7 \cdot 5 + m \cdot 5\) demonstrates the Distributive Property. This property states that for any real numbers \(a\), \(b\), and \(c\), \(a \cdot (b + c) = a \cdot b + a \cdot c\).

Final Answer

\(-9 + 9 = 0\) is justified by the Additive Inverse Property.
\(3 \cdot (6 \cdot n) = (3 \cdot 6) \cdot n\) is justified by the Associative Property of Multiplication.
\((7 + m) \cdot 5 = 7 \cdot 5 + m \cdot 5\) is justified by the Distributive Property.

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