The question asks us to identify which option correctly demonstrates the use of the distributive property with real numbers. The distributive property states that for any three real numbers [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex],
[tex]\[ a(b + c) = ab + ac. \][/tex]
Let's evaluate each given option:
1. [tex]\( 2 \cdot 7 = 7 \cdot 2 \)[/tex]
- This equation demonstrates the commutative property of multiplication, which states that the order of multiplication does not affect the product. Therefore, this is not an example of the distributive property.
2. [tex]\( (2 \cdot 7) \cdot 9 = 2 \cdot (7 \cdot 9) \)[/tex]
- This equation illustrates the associative property of multiplication, which states that the grouping of factors does not affect the product. This is not an example of the distributive property.
3. [tex]\( (2 + 7) + 9 = 2 + (7 + 9) \)[/tex]
- This equation shows the associative property of addition, which states that the grouping of addends does not affect the sum. This is not an example of the distributive property.
4. [tex]\( 2(7 + 9) = (2)(7) + (2)(9) \)[/tex]
- This equation applies the distributive property correctly. Here, [tex]\(2\)[/tex] is distributed over the sum [tex]\(7 + 9\)[/tex], breaking it down into the individual products [tex]\(2 \cdot 7\)[/tex] and [tex]\(2 \cdot 9\)[/tex]. This is the correct use of the distributive property.
Therefore, the option that correctly shows the distributive property being applied to real numbers is:
[tex]\[ \boxed{4} \][/tex]
