Math Snap

STEP 1

1. We are multiplying a negative rational number by a positive decimal number.
2. The result should be expressed as a rational number.
3. We need to identify the correct answer from the given options.

STEP 2

1. Convert the decimal to a fraction.
2. Multiply the fractions.
3. Simplify the result.
4. Match the result with the given options.

STEP 3

Convert the decimal $3.875$ to a fraction.
Since $3.875$ has three decimal places, it can be expressed as:
$$3.875 = \frac{3875}{1000}$$ Simplify the fraction by finding the greatest common divisor (GCD) of $3875$ and $1000$.

STEP 4

Calculate the GCD of $3875$ and $1000$.
The GCD is $125$.
Simplify the fraction:
$$\frac{3875}{1000} = \frac{3875 \div 125}{1000 \div 125} = \frac{31}{8}$$

STEP 5

Multiply the fractions:
$$-\frac{6}{5} \times \frac{31}{8}$$ Multiply the numerators and the denominators:
$$= \frac{-6 \times 31}{5 \times 8} = \frac{-186}{40}$$

STEP 6

Simplify the fraction $\frac{-186}{40}$.
Find the GCD of $186$ and $40$, which is $2$.
Simplify:
$$\frac{-186}{40} = \frac{-186 \div 2}{40 \div 2} = \frac{-93}{20}$$

Match the simplified result $\frac{-93}{20}$ with the given options.
The correct answer is:
C. $-\frac{93}{20}$
The correct answer is:
$$\boxed{-\frac{93}{20}}$$