Question

2/3 divided 2 to the 4th power + ( 3/4 + 1/6) divided by 1/3

Answer 1

To solve the expression \( \frac{2}{3} \div 2^4 + \left( \frac{3}{4} + \frac{1}{6} \right) \div \frac{1}{3} \), we can break it down into two parts.

1. **Calculate the first part:**
\[
2^4 = 16
\]
Now we calculate:
\[
\frac{2}{3} \div 16 = \frac{2}{3} \times \frac{1}{16} = \frac{2}{48} = \frac{1}{24}
\]

2. **Calculate the second part:**
First, we need to find \( \frac{3}{4} + \frac{1}{6} \). To do this, we need a common denominator. The least common multiple of 4 and 6 is 12.

\[
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
\]
\[
\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}
\]
Now, we can add:
\[
\frac{9}{12} + \frac{2}{12} = \frac{11}{12}
\]

Now we calculate:
\[
\left( \frac{11}{12} \right) \div \frac{1}{3} = \frac{11}{12} \times 3 = \frac{33}{12} = \frac{11}{4}
\]

3. **Add both parts together:**
\[
\frac{1}{24} + \frac{11}{4}
\]
Now, we need a common denominator for these fractions. The least common multiple of 24 and 4 is 24.

\[
\frac{11}{4} = \frac{11 \times 6}{4 \times 6} = \frac{66}{24}
\]

Now we can add:
\[
\frac{1}{24} + \frac{66}{24} = \frac{67}{24}
\]

Thus, the final answer is:
\[
\frac{67}{24}
\]