Multiply two numbers, one integer and one fraction, both negative.
Check the final answer first, then review the worked steps.
Problem
Multiply two numbers, one integer and one fraction, both negative.
Answer
14
Step-by-step solution
- Identify the operation: The problem asks to multiply two numbers: $-6$ and $-\frac{7}{3}$.
- Determine the sign of the product: When multiplying two negative numbers, the result is positive. So, $(-6) \times (-\frac{7}{3})$ will be positive.
- Rewrite the integer as a fraction: To multiply, it's helpful to write $-6$ as a fraction, which is $-\frac{6}{1}$.
- Multiply the fractions: Multiply the numerators together and the denominators together: $$-\frac{6}{1} \times -\frac{7}{3} = \frac{(-6) \times (-7)}{1 \times 3}$$
- Calculate the product of the numerators: $(-6) \times (-7) = 42$.
- Calculate the product of the denominators: $1 \times 3 = 3$.
- Form the resulting fraction: The product is $\frac{42}{3}$.
- Simplify the fraction: Divide the numerator by the denominator: $42 \div 3 = 14$.