Use properties of operation and rules for multiplying signed numbers to multiply -2/5 by 3/10. Write the answer in simplest form.

Answer 1

To multiply the fractions \(-\frac{2}{5}\) and \(\frac{3}{10}\), we can follow these steps:

1. Multiply the numerators: \[ -2 \times 3 = -6 \]

2. Multiply the denominators: \[ 5 \times 10 = 50 \]

3. Combine the results: \[ -\frac{6}{50} \]

4. Simplify the fraction: To simplify \(-\frac{6}{50}\), we find the greatest common divisor (GCD) of 6 and 50, which is 2.

   • Dividing both the numerator and the denominator by 2 gives: \[ -\frac{6 \div 2}{50 \div 2} = -\frac{3}{25} \]

Thus, the answer in simplest form is: \[ \boxed{-\frac{3}{25}} \]