To determine which property is represented by the equation \(6(7+2.25) = 42 + 13.5\), let's analyze the equation step-by-step and see how it fits with the mathematical properties provided in the options.
1. Understand the Equation:
Given equation: \(6(7 + 2.25) = 42 + 13.5\)
2. Break Down the Equation:
The left-hand side of the equation is \(6(7 + 2.25)\), which means multiplying 6 by the sum of 7 and 2.25.
The right-hand side of the equation is \(42 + 13.5\).
3. Apply the Property:
To understand which property is being used, let's simplify the left-hand side by distributing the multiplication:
[tex]\[
6(7 + 2.25) = 6 \cdot 7 + 6 \cdot 2.25
\][/tex]
4. Perform the Multiplications:
[tex]\[
6 \cdot 7 = 42
\][/tex]
[tex]\[
6 \cdot 2.25 = 13.5
\][/tex]
So,
[tex]\[
6(7 + 2.25) = 42 + 13.5
\][/tex]
5. Compare with the Right-Hand Side:
The simplified left-hand side \(42 + 13.5\) matches exactly with the right-hand side of the equation.
6. Identify the Property:
The property used here is the Distributive Property.
The Distributive Property states that \(a(b + c) = ab + ac\). In this context, \(6(7 + 2.25) = 6 \cdot 7 + 6 \cdot 2.25\), which simplifies to \(42 + 13.5\), showing that the equation is a perfect example of the Distributive Property.
Therefore, the property represented by the equation \(6(7 + 2.25) = 42 + 13.5\) is:
a. Distributive Property
