Problem 76 - Algebra and Trigonometry

Question

State the name of the property illustrated. $$11 \cdot(7+4)=11 \cdot 7+11 \cdot 4$$

Step-by-Step Solution

Answer

The property illustrated in this exercise is the Distributive Property.

Step 1: Examine the Equation

We need to identify which property of real numbers is illustrated by: \(11 \cdot(7+4)=11 \cdot 7+11 \cdot 4\).

Step 2: Recall Properties of Real Numbers

The key properties are:

• Commutative Property: \(a + b = b + a\) or \(a \cdot b = b \cdot a\)
• Associative Property: \((a + b) + c = a + (b + c)\) or \((a \cdot b) \cdot c = a \cdot (b \cdot c)\)
• Distributive Property: \(a(b + c) = ab + ac\)
• Identity Property: \(a + 0 = a\) or \(a \cdot 1 = a\)
• Inverse Property: \(a + (-a) = 0\) or \(a \cdot \frac{1}{a} = 1\)

Step 3: Identify the Property

The property illustrated in this exercise is the Distributive Property.