Certainly! Let's carefully analyze the expressions given:
[tex]\[ 5(g + h) = 5g + 5h \][/tex]
This statement can be explained through one of the fundamental properties of arithmetic operations. Here is a detailed step-by-step explanation:
1. Understand the Expression:
- On the left side of the equation, we have a number (5) being multiplied by the sum of two variables, [tex]\( g + h \)[/tex].
- On the right side of the equation, we have the same number (5) being multiplied by each variable separately, and then these products are added together.
2. Identify the Property:
- The key to understanding this equality is recognizing that there is a specific arithmetic property that allows us to break down a multiplication over addition into separate multiplications added together.
3. Apply the Property:
- The property that allows us to distribute the multiplication across the addition inside the parentheses is known as the Distributive Property.
4. Define the Distributive Property:
- The Distributive Property states that for any numbers [tex]\( a, b, \)[/tex] and [tex]\( c \)[/tex]:
[tex]\[ a(b + c) = ab + ac \][/tex]
- In our case, [tex]\( a = 5 \)[/tex], [tex]\( b = g \)[/tex], and [tex]\( c = h \)[/tex].
5. Match to Our Example:
- Applying the Distributive Property to our expression:
[tex]\[ 5(g + h) = 5g + 5h \][/tex]
By following these steps, we can clearly see that the reason why the initial expressions are equal is due to the Distributive Property.
Therefore, the correct property is:
C. Distributive
