Question

which of the following expressions are equivalent to
$-9.7 \cdot -0.8 \cdot -7.8 \cdot 3.8?$

choose all answers that apply:

a $9.7 \cdot -0.8 \cdot -7.8 \cdot -3.8$

b $-9.7 \cdot 0.8 \cdot 7.8 \cdot -3.8$

c none of the above

Explanation:

Step1: Count sign of original expr.

Original: $-9.7 \cdot -0.8 \cdot -7.8 \cdot 3.8$ has 3 negative signs. Product sign: negative (odd number of negatives).

Step2: Analyze Option A sign count.

Option A: $9.7 \cdot -0.8 \cdot -7.8 \cdot -3.8$ has 3 negative signs. Product sign: negative. Now check magnitudes:
Original magnitude: $9.7 \times 0.8 \times 7.8 \times 3.8$
Option A magnitude: $9.7 \times 0.8 \times 7.8 \times 3.8$ (same as original). So Option A is equivalent.

Step3: Analyze Option B sign count.

Option B: $-9.7 \cdot 0.8 \cdot 7.8 \cdot -3.8$ has 2 negative signs. Product sign: positive (even number of negatives), which differs from original's negative sign. So Option B is not equivalent.

Answer:

A. $9.7 \cdot -0.8 \cdot -7.8 \cdot -3.8$