Question

choose the difference that is less than 8.
$8\frac{1}{5} - \frac{1}{5}$
$8\frac{2}{5} - \frac{4}{5}$
$8\frac{3}{5} - \frac{2}{5}$
$8\frac{4}{5} - \frac{3}{5}$

Explanation:

Step1: Analyze the first option

The first expression is \(8\frac{1}{5}-\frac{1}{5}\). Subtract the fractions: \(\frac{1}{5}-\frac{1}{5} = 0\), so the result is \(8 + 0=8\).

Step2: Analyze the second option

The second expression is \(8\frac{2}{5}-\frac{4}{5}\). First, convert the mixed number to an improper fraction: \(8\frac{2}{5}=\frac{42}{5}\). Then subtract: \(\frac{42}{5}-\frac{4}{5}=\frac{38}{5}=7\frac{3}{5}\), which is less than 8.

Step3: Analyze the third option

The third expression is \(8\frac{3}{5}-\frac{2}{5}\). Subtract the fractions: \(\frac{3}{5}-\frac{2}{5}=\frac{1}{5}\), so the result is \(8+\frac{1}{5}=8\frac{1}{5}\), which is greater than 8.

Step4: Analyze the fourth option

The fourth expression is \(8\frac{4}{5}-\frac{3}{5}\). Subtract the fractions: \(\frac{4}{5}-\frac{3}{5}=\frac{1}{5}\), so the result is \(8+\frac{1}{5}=8\frac{1}{5}\), which is greater than 8.

Answer:

The second option: \(8\frac{2}{5}-\frac{4}{5}\) (or the middle - second boxed expression in the original problem's display)