Questions: What is the quotient if 4/15 of 40 is divided by 1/2 of 8/12? Reduce, if possible.

Solution Steps

To solve this problem, we need to follow these steps:

1. Calculate \(\frac{4}{15}\) of 40.
2. Calculate \(\frac{1}{2}\) of \(\frac{8}{12}\).
3. Divide the result from step 1 by the result from step 2.
4. Simplify the quotient, if possible.

To find \(\frac{4}{15}\) of 40, we compute: \[ \frac{4}{15} \times 40 = \frac{160}{15} = 10.6667 \]

Next, we calculate \(\frac{1}{2}\) of \(\frac{8}{12}\): \[ \frac{1}{2} \times \frac{8}{12} = \frac{8}{24} = \frac{1}{3} \approx 0.3333 \]

Now, we divide the result from Step 1 by the result from Step 2: \[ \frac{10.6667}{0.3333} = 32.0 \]

Final Answer