Evaluate the expression shown below and write your answer as a fraction in simplest form.

Question

one sixth, divided by, minus, start fraction, 2, divided by, 5, end fraction, dot, start fraction, 5, divided by, 2, end fraction
6
1
​
÷−
5
2
​
⋅
2
5
​

Answer 1

To evaluate the expression \( \frac{1}{6} \div -\frac{2}{5} \cdot \frac{5}{2} \), we will follow the order of operations.

1. Evaluate the multiplication \( -\frac{2}{5} \cdot \frac{5}{2} \): \[ -\frac{2}{5} \cdot \frac{5}{2} = -\frac{2 \cdot 5}{5 \cdot 2} = -\frac{10}{10} = -1 \]

2. Now we proceed with the division \( \frac{1}{6} \div -1 \): \[ \frac{1}{6} \div -1 = \frac{1}{6} \cdot -1 = -\frac{1}{6} \]

Therefore, the evaluated expression is:

\[ \boxed{-\frac{1}{6}} \]