Question

Evaluate the expression shown below and write your answer as a fraction or mixed number in simplest form.
one sixth, divided by, start fraction, 1, divided by, 15, end fraction, dot, one ninth
6
1
​
÷
15
1
​
⋅
9
1
​

Answer 1

To evaluate the expression

\[
\frac{1}{6} \div \frac{1}{15} \cdot \frac{1}{9}
\]

we can follow these steps:

1. **Dividing by a fraction:** Dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we have:

\[
\frac{1}{6} \div \frac{1}{15} = \frac{1}{6} \cdot \frac{15}{1} = \frac{15}{6}
\]

2. **Simplifying \(\frac{15}{6}\):**

\[
\frac{15}{6} = \frac{5}{2} \quad \text{(dividing the numerator and denominator by 3)}
\]

3. **Now we multiply by \(\frac{1}{9}\):**

\[
\frac{5}{2} \cdot \frac{1}{9} = \frac{5 \cdot 1}{2 \cdot 9} = \frac{5}{18}
\]

Thus, the final answer is

\[
\frac{5}{18}
\]

This is in simplest form.