Questions: Number Theory and the Real Number System Properties of real numbers Choose the property of real numbers that justifies the equation. 0 · 5 = 0 Choose one 7 + (-7) = 0 Choose one (s · t) · c = s · (t · c) Choose one (6 + 8) + 9 = 6 + (8 + 9) Choose one Explanation Check

Number Theory and the Real Number System Properties of real numbers Choose the property of real numbers that justifies the equation. 0 · 5 = 0 Choose one 7 + (-7) = 0 Choose one (s · t) · c = s · (t · c) Choose one (6 + 8) + 9 = 6 + (8 + 9) Choose one Explanation Check
Transcript text: Number Theory and the Real Number System Properties of real numbers Choose the property of real numbers that justifies the equation. 0 · 5 = 0 | Choose one 7 + (-7) = 0 | Choose one (s · t) · c = s · (t · c) | Choose one (6 + 8) + 9 = 6 + (8 + 9) | Choose one Explanation Check
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Solution

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Solution Steps

Step 1: Identify the property for \( 0 \cdot 5 = 0 \)

The equation \( 0 \cdot 5 = 0 \) is justified by the Multiplicative Property of Zero, which states that any number multiplied by zero equals zero.

Step 2: Identify the property for \( 7 + (-7) = 0 \)

The equation \( 7 + (-7) = 0 \) is justified by the Additive Inverse Property, which states that the sum of a number and its additive inverse (negative) is zero.

Step 3: Identify the property for \( (s \cdot t) \cdot c = s \cdot (t \cdot c) \)

The equation \( (s \cdot t) \cdot c = s \cdot (t \cdot c) \) is justified by the Associative Property of Multiplication, which states that the grouping of factors does not affect the product.

Final Answer

  1. \( 0 \cdot 5 = 0 \) is justified by the Multiplicative Property of Zero.
  2. \( 7 + (-7) = 0 \) is justified by the Additive Inverse Property.
  3. \( (s \cdot t) \cdot c = s \cdot (t \cdot c) \) is justified by the Associative Property of Multiplication.
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