Question

Which of the following expressions are equivalent to -9.7 * -0.8 * -7.8 * 3.8?

A) 9.7 * 0.8 * 7.8 * 3.8
B) -9.7 * 0.8 * 7.8 * -3.8
C) -9.7 * -0.8 * 7.8 * -3.8
D) 9.7 * -0.8 * -7.8 * 3.8

Answer 1

Only the expression C) -9.7 * -0.8 * 7.8 * -3.8 is equivalent to the original expression as it contains three negative numbers and one positive number, which results in a negative product, matching the sign of the original expression.

Step-by-step explanation:

To determine which of the given expressions are equivalent to -9.7 * -0.8 * -7.8 * 3.8, we need to understand the rules for multiplying negative numbers. The product of two negative numbers is positive, and the product of a positive and a negative number is negative. Let's apply this principle to the provided expressions:

• A) 9.7 * 0.8 * 7.8 * 3.8: This is the product of four positive numbers, which is positive. So, this is not equivalent because the original expression is negative.
• B) -9.7 * 0.8 * 7.8 * -3.8: Here we have two negative and two positive numbers. Multiplying them together gives us a positive result. So, this is not equivalent because the original expression is negative.
• C) -9.7 * -0.8 * 7.8 * -3.8: This expression has three negative numbers and one positive number, resulting in a negative product. Therefore, this is equivalent to the original expression.
• D) 9.7 * -0.8 * -7.8 * 3.8: This expression also contains two negative numbers and two positive numbers. This means the result is positive, making it not equivalent to the original negative expression.

Thus, the correct answer is C) -9.7 * -0.8 * 7.8 * -3.8.