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:

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.

Answer:

• (A) \((5 \times 5) \times (5 \times 2)\)
• (B) \((5 \times 5) \times 2\) (Correct answer)
• (C) \(25 \times 2\) (Correct answer)