2/5-7 8/9

To solve the expression \( \frac{2}{5} - 7 \frac{8}{9} \), we first need to convert the mixed number \( 7 \frac{8}{9} \) into an improper fraction.

1. Convert \( 7 \frac{8}{9} \) to an improper fraction: \[ 7 \frac{8}{9} = \frac{(7 \times 9) + 8}{9} = \frac{63 + 8}{9} = \frac{71}{9} \]

2. Now, the expression becomes: \[ \frac{2}{5} - \frac{71}{9} \]

3. To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 5 and 9 is 45.

4. Convert each fraction to have a denominator of 45: \[ \frac{2}{5} = \frac{2 \times 9}{5 \times 9} = \frac{18}{45} \] \[ \frac{71}{9} = \frac{71 \times 5}{9 \times 5} = \frac{355}{45} \]

5. Now, perform the subtraction: \[ \frac{18}{45} - \frac{355}{45} = \frac{18 - 355}{45} = \frac{-337}{45} \]

Thus, the final answer is: \[ \frac{-337}{45} \]

If you want it in decimal form, you can divide \( -337 \) by \( 45 \), which is approximately: \[ -7.48 \]