To simplify the expression \( 18 - 9 \frac{4}{9} + \frac{7}{9} - 8 \) for easier addition, we can group the whole numbers and the fractions separately.
- Identify whole numbers: \( 18 \) and \( -8 \).
- Identify the fractions: \( -9 \frac{4}{9} \) and \( + \frac{7}{9} \).
Now, convert \( -9 \frac{4}{9} \) into an improper fraction to make it easier to handle with the other fraction: \[ -9 \frac{4}{9} = -\left(9 \cdot 9 + 4\right)/9 = -\frac{81 + 4}{9} = -\frac{85}{9} \]
Now rewrite the expression: \[ 18 - 8 - \frac{85}{9} + \frac{7}{9} \]
You can now group the whole numbers and the fractions:
- Whole numbers: \( 18 - 8 \)
- Fractions: \( -\frac{85}{9} + \frac{7}{9} \)
Now calculate both groups:
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Whole numbers: \[ 18 - 8 = 10 \]
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Fractions: \[ -\frac{85}{9} + \frac{7}{9} = -\frac{85 - 7}{9} = -\frac{78}{9} = -\frac{26}{3} \quad \text{(Simplifying)} \]
Now combine the results: \[ 10 - \frac{26}{3} \]
To subtract, convert \( 10 \) to a fraction with a denominator of 3: \[ 10 = \frac{30}{3} \]
Now we can subtract: \[ \frac{30}{3} - \frac{26}{3} = \frac{30 - 26}{3} = \frac{4}{3} \]
Thus, the final result of the expression \( 18 - 9 \frac{4}{9} + \frac{7}{9} - 8 \) is: \[ \frac{4}{3} \]
In conclusion, to make it easiest to add, group the expression as follows: \[ (18 - 8) + (-9 \frac{4}{9} + \frac{7}{9}) \]
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