Question
Alice says she knows how to calculate 4×7
because 4×7=(4×2)+(4×5)
. Is she right?
(1 point)
She is
correct
because of the
Distributive
Property.
because 4×7=(4×2)+(4×5)
. Is she right?
(1 point)
She is
correct
because of the
Distributive
Property.
Answers
GPT-4o mini
Alice is correct because of the Distributive Property.
The Distributive Property states that a multiplication can be distributed over addition. Specifically, Alice breaks down \(7\) into \(2\) and \(5\) (since \(2 + 5 = 7\)). Therefore, she calculates \(4 \times 7\) as:
\[
4 \times 7 = 4 \times (2 + 5) = (4 \times 2) + (4 \times 5)
\]
Calculating each part:
- \(4 \times 2 = 8\)
- \(4 \times 5 = 20\)
Adding these results together:
\[
8 + 20 = 28
\]
Thus, \(4 \times 7 = 28\), confirming that her method is valid and she is correct.
The Distributive Property states that a multiplication can be distributed over addition. Specifically, Alice breaks down \(7\) into \(2\) and \(5\) (since \(2 + 5 = 7\)). Therefore, she calculates \(4 \times 7\) as:
\[
4 \times 7 = 4 \times (2 + 5) = (4 \times 2) + (4 \times 5)
\]
Calculating each part:
- \(4 \times 2 = 8\)
- \(4 \times 5 = 20\)
Adding these results together:
\[
8 + 20 = 28
\]
Thus, \(4 \times 7 = 28\), confirming that her method is valid and she is correct.