Use properties of operations and rules for multiplying signed numbers to multiply −2/5 by 3/10 . Write the answer in simplest form.(fractions)

Answer 1

To multiply the fractions \(-\frac{2}{5}\) and \(\frac{3}{10}\), we 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 can find the greatest common divisor (GCD) of 6 and 50. The GCD is 2.

   Now, we divide both the numerator and the denominator by their GCD: \[ \frac{-6 \div 2}{50 \div 2} = \frac{-3}{25} \]

Thus, the product of \(-\frac{2}{5}\) and \(\frac{3}{10}\) in simplest form is: \[ \boxed{-\frac{3}{25}} \]