Question

which two expressions are equivalent to (5 \times (5 \times 2))?

choose 2 answers:

a ((5 \times 5) \times (5 \times 2))

b ((5 \times 5) \times 2)

c (25 \times 2)

Explanation:

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<reasoning>

Evaluate the original expression

We calculate the value of the given expression:
\[
5 \times (5 \times 2)
\]
Using Basic Multiplication:
\[
5 \times 2 = 10
\]
Then:
\[
5 \times 10 = 50
\]

Apply the associative property

Using the Associative Property of multiplication, we can regroup the factors:
\[
5 \times (5 \times 2) = (5 \times 5) \times 2
\]
This matches option (B).

Simplify the regrouped expression

We simplify the grouped terms:
\[
(5 \times 5) \times 2 = 25 \times 2
\]
This matches option (C).

Verify the remaining option

We evaluate option (A):
\[
(5 \times 5) \times (5 \times 2) = 25 \times 10 = 250
\]
Since \(250
eq 50\), option (A) is incorrect.
</reasoning>

<answer>
<mcq-option>(A) \((5 \times 5) \times (5 \times 2)\)</mcq-option>
<mcq-correct>(B) \((5 \times 5) \times 2\)</mcq-correct>
<mcq-correct>(C) \(25 \times 2\)</mcq-correct>
</answer>

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Answer:

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<reasoning>

Evaluate the original expression

We calculate the value of the given expression:
\[
5 \times (5 \times 2)
\]
Using Basic Multiplication:
\[
5 \times 2 = 10
\]
Then:
\[
5 \times 10 = 50
\]

Apply the associative property

Using the Associative Property of multiplication, we can regroup the factors:
\[
5 \times (5 \times 2) = (5 \times 5) \times 2
\]
This matches option (B).

Simplify the regrouped expression

We simplify the grouped terms:
\[
(5 \times 5) \times 2 = 25 \times 2
\]
This matches option (C).

Verify the remaining option

We evaluate option (A):
\[
(5 \times 5) \times (5 \times 2) = 25 \times 10 = 250
\]
Since \(250
eq 50\), option (A) is incorrect.
</reasoning>

<answer>
<mcq-option>(A) \((5 \times 5) \times (5 \times 2)\)</mcq-option>
<mcq-correct>(B) \((5 \times 5) \times 2\)</mcq-correct>
<mcq-correct>(C) \(25 \times 2\)</mcq-correct>
</answer>

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