To make it easiest to add the expression \( 18 - 9 \frac{4}{9} + \frac{7}{9} - 8 \), we can group the integer parts and the fractional parts separately.
- Group the whole numbers: \( 18 - 8 \)
- Group the fractional parts: \( - 9 \frac{4}{9} + \frac{7}{9} \)
Now let's calculate each group:
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Whole numbers: \[ 18 - 8 = 10 \]
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Fractional parts: First, we can rewrite \( 9 \frac{4}{9} \) as a fraction: \[ 9 \frac{4}{9} = \frac{9 \times 9 + 4}{9} = \frac{81 + 4}{9} = \frac{85}{9} \]
Now, adding the fractions: \[ -\frac{85}{9} + \frac{7}{9} = \frac{-85 + 7}{9} = \frac{-78}{9} \]
We can simplify \( \frac{-78}{9} \): \[ \frac{-78}{9} = -8 \frac{6}{9} = -8 \frac{2}{3} \]
Now, combine both results: \[ 10 - 8 \frac{2}{3} \]
To make this easier, convert \( 10 \) into a mixed number: \[ 10 = 9 + 1 \]
So: \[ 10 - 8 \frac{2}{3} = 1 + (9 - 8 \frac{2}{3}) = 1 + \left(9 - 8\right) - \frac{2}{3} = 1 + (1 - \frac{2}{3}) = 1 + \frac{1}{3} = 1 \frac{1}{3} \]
Putting it all together, the format: \[ (18 - 8) + \left(- 9 \frac{4}{9} + \frac{7}{9}\right) = 10 - \frac{78}{9} = 10 - 8 \frac{2}{3} = 1 \frac{1}{3} \]
Thus, grouping the expression as \( (18 - 8) + (- 9 \frac{4}{9} + \frac{7}{9}) \) simplifies the addition effectively.