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Multiply two numbers, one integer and one fraction, both negative.

Check the final answer first, then review the worked steps.

Answer

14

Step-by-step solution

  1. Identify the operation: The problem asks to multiply two numbers: $-6$ and $-\frac{7}{3}$.
  2. Determine the sign of the product: When multiplying two negative numbers, the result is positive. So, $(-6) \times (-\frac{7}{3})$ will be positive.
  3. Rewrite the integer as a fraction: To multiply, it's helpful to write $-6$ as a fraction, which is $-\frac{6}{1}$.
  4. Multiply the fractions: Multiply the numerators together and the denominators together: $$-\frac{6}{1} \times -\frac{7}{3} = \frac{(-6) \times (-7)}{1 \times 3}$$
  5. Calculate the product of the numerators: $(-6) \times (-7) = 42$.
  6. Calculate the product of the denominators: $1 \times 3 = 3$.
  7. Form the resulting fraction: The product is $\frac{42}{3}$.
  8. Simplify the fraction: Divide the numerator by the denominator: $42 \div 3 = 14$.