To evaluate the expression \( 11 \frac{2}{9} - (-4) \), we first rewrite \( 11 \frac{2}{9} \) as an improper fraction.
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Convert \( 11 \frac{2}{9} \) to an improper fraction: \[ 11 \frac{2}{9} = \frac{11 \times 9 + 2}{9} = \frac{99 + 2}{9} = \frac{101}{9} \]
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Next, we subtract \( -4 \), which is the same as adding \( 4 \): \[ -(-4) = +4 \]
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Convert \( 4 \) to a fraction with the same denominator: \[ 4 = \frac{4 \times 9}{9} = \frac{36}{9} \]
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Now we can combine the fractions: \[ \frac{101}{9} + \frac{36}{9} = \frac{101 + 36}{9} = \frac{137}{9} \]
The result \( \frac{137}{9} \) is already in the simplest form. To express this as a mixed number:
- Divide \( 137 \) by \( 9 \) to find the whole number part and the remainder:
- \( 137 \div 9 = 15 \) remainder \( 2 \)
Thus, we can write: \[ \frac{137}{9} = 15 \frac{2}{9} \]
Putting it all together, the final simplified expression is: \[ 15 \frac{2}{9} \]
So, \( 11 \frac{2}{9} - (-4) = 15 \frac{2}{9} \) can be presented as: \[ [15] [2]/[9] \]
Thus, the answer is \([15] [2]/[9]\).