To make the expression \( 18 - 9 \frac{4}{9} + \frac{7}{9} - 8 \) easier to add, we can group similar types of numbers together.
First, let's convert \( 9 \frac{4}{9} \) into an improper fraction: \[ 9 \frac{4}{9} = 9 + \frac{4}{9} = \frac{81}{9} + \frac{4}{9} = \frac{85}{9} \]
Now, rewrite the entire expression using this improper fraction: \[ 18 - \frac{85}{9} + \frac{7}{9} - 8 \]
Next, combine the whole numbers \( 18 \) and \( -8 \). \[ 18 - 8 = 10 \]
Now the expression is: \[ 10 - \frac{85}{9} + \frac{7}{9} \]
We can combine the fractions: \[ -\frac{85}{9} + \frac{7}{9} = \frac{-85 + 7}{9} = \frac{-78}{9} \]
Now, substituting back: \[ 10 - \frac{78}{9} \]
To combine \( 10 \) and \( -\frac{78}{9} \), convert \( 10 \) into a fraction with a denominator of \( 9 \): \[ 10 = \frac{90}{9} \] Thus, the expression becomes: \[ \frac{90}{9} - \frac{78}{9} = \frac{90 - 78}{9} = \frac{12}{9} \]
Finally, simplify \( \frac{12}{9} \): \[ \frac{12}{9} = \frac{4}{3} \]
Therefore, the final result of the expression \( 18 - 9 \frac{4}{9} + \frac{7}{9} - 8 \) is: \[ \frac{4}{3} \]
Thus, the best way to group the original expression would be \( (18 - 8) + (- 9 \frac{4}{9} + \frac{7}{9}) \).
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