Final answer:
The value of the expression -4 (5/9 / -1/3) is found by first multiplying 5/9 by the reciprocal of -1/3, which leads to -5/3, and then multiplying that result by -4 to get the final answer of 20/3.
Step-by-step explanation:
The value of the expression -4 (5/9 / -1/3) can be determined by dividing the fractions and then multiplying by -4. Division of fractions involves multiplying by the reciprocal of the second fraction.
First, -1/3 will convert to its reciprocal, which is -3. Therefore, the division step will look like this: 5/9 multiplied by -3. Following this step, you would then multiply the result by -4.
Here's the step-by-step breakdown:
- Multiply by the reciprocal: 5/9 * -3 = -5/3 (because -1/3 becomes -3)
- Multiply by -4: -5/3 * -4 = 20/3
The final answer is 20/3, or approximately 6.67 when converted to a decimal.