Question

Evaluate the expression shown below and write your answer as a fraction or mixed number in simplest form.
minus, one tenth, divided by, minus, one quarter, dot, start fraction, 9, divided by, 5, end fraction
−
10
1
​
÷−
4
1
​
⋅
5
9

Answer 1

To evaluate the expression

\[
-\frac{1}{10} \div -\frac{1}{4} \cdot \frac{9}{5},
\]

we will follow the order of operations: we first handle the division and multiplication from left to right.

1. **Division**:
\[
-\frac{1}{10} \div -\frac{1}{4} = \frac{1}{10} \cdot \frac{4}{1} = \frac{4}{10} = \frac{2}{5}.
\]

2. **Multiplication**:
Next, we will multiply \(\frac{2}{5}\) by \(\frac{9}{5}\):
\[
\frac{2}{5} \cdot \frac{9}{5} = \frac{2 \cdot 9}{5 \cdot 5} = \frac{18}{25}.
\]

Thus, the evaluation of the expression is

\[
\frac{18}{25}.
\]

This fraction is in simplest form since 18 and 25 have no common factors besides 1.

Therefore, the final answer is

\[
\boxed{\frac{18}{25}}.
\]