Question

Consider the expression 150 + 150(2.5). Which statements are correct?

A)
150 + 150(2.5) = 1 + 2.5
B)
150 + 150(2.5) = 150 + 2.5
C)
150 + 150(2.5) = 150(1 + 2.5)
D)
150 + 150(2.5) = 150(3.5)
E)
150 + 150(3.5) = 525

Answer 1

The expression 150 + 150(2.5) is correctly represented as 150(3.5) which aligns with option D. This can be proven using the distributive property to factor out the common factor of 150 and simplify the expression.

Step-by-step explanation:

When considering the expression 150 + 150(2.5), the correct statement among the provided options is D. This statement can be proved by applying the distributive property of multiplication over addition, which in this case, involves factoring out the common factor of 150:

1. Identify the common factor from both terms, which is 150.
2. Factor 150 out: 150 + 150(2.5) = 150(1 + 2.5). Now, this is the expression mentioned in option C, signifying that this statement is potentially true.
3. Simplify the expression inside the parentheses: 150(3.5). This matches option D, confirming it as the correct answer.

None of the other options are correct:

• Option A (150 + 150(2.5) = 1 + 2.5) simplifies incorrectly and does not account for the initial 150.
• Option B (150 + 150(2.5) = 150 + 2.5) ignores the multiplication of 150 by 2.5.
• Option E (150 + 150(3.5) = 525) is not equivalent to the original expression and presents an incorrect equality.

Answer 2

C D E is the answer

Step-by-step explanation:

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