To group the expression \( 18 - 9 \frac{4}{9} + \frac{7}{9} - 8 \) in a way that makes it easier to add, it's best to group the whole numbers together and the fractions together.
- Identify the whole numbers: \( 18 \) and \( -8 \)
- Identify the fractions: \( - 9 \frac{4}{9} + \frac{7}{9} \)
So the expression can be grouped as:
\[ (18 - 8) + \left(-9 \frac{4}{9} + \frac{7}{9}\right) \]
Now, calculate each group separately:
- \( 18 - 8 = 10 \)
- To add the fractions, first convert \( -9 \frac{4}{9} \) into an improper fraction: \[ -9 \frac{4}{9} = -\frac{85}{9} \] Thus, we have: \[ -\frac{85}{9} + \frac{7}{9} = -\frac{85 - 7}{9} = -\frac{78}{9} = -\frac{26}{3} \]
Now combine the results from both groups:
\[ 10 - \frac{26}{3} \]
For easier calculations, you can convert \( 10 \) into a fraction:
\[ 10 = \frac{30}{3} \] Now combine:
\[ \frac{30}{3} - \frac{26}{3} = \frac{30 - 26}{3} = \frac{4}{3} \]
Thus, the total expression simplifies to \( \frac{4}{3} \).
So, the grouped expression is:
\[ (18 - 8) + (-9 \frac{4}{9} + \frac{7}{9}) \]
This grouping helps in calculating the sum more easily.