To identify the choice that best shows the Distributive Property, we need to understand what the Distributive Property is. The Distributive Property in mathematics states that for any numbers [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex]:
[tex]\[ a \times (b + c) = (a \times b) + (a \times c) \][/tex]
Let's go through each option to determine which one fits this property:
1. [tex]\( 1 \times 6 = 6 \)[/tex]
- This equation demonstrates the multiplicative identity property, not the Distributive Property.
2. [tex]\( 6 + (10 \times 7) = (6 \times 10) + 7 \)[/tex]
- This equation does not correctly distribute the multiplication across addition; it’s mixing multiplication and addition incorrectly.
3. None of these answers show the Distributive Property.
- We need to further verify the next options to confirm if this statement is true.
4. [tex]\( 6 \times (10 + 7) = (6 \times 10) + (6 \times 7) \)[/tex]
- This is a perfect example of the Distributive Property. Here, the number [tex]\( 6 \)[/tex] is distributed and multiplied both by [tex]\( 10 \)[/tex] and [tex]\( 7 \)[/tex], demonstrating [tex]\( a \times (b + c) = (a \times b) + (a \times c) \)[/tex].
5. [tex]\( 6 \times 10 = 10 \times 6 \)[/tex]
- This equation showcases the Commutative Property of Multiplication, not the Distributive Property.
Given the options, the best choice that shows the Distributive Property is:
[tex]\[ 6 \times (10 + 7) = (6 \times 10) + (6 \times 7) \][/tex]
Thus, the correct answer is:
[tex]\( 4 \)[/tex]
