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We need to calculate the value of the expression $1\frac{1}{9} - \frac{2}{9} + \frac{4}{9} - 1\frac{5}{9}$.

ArithmeticFractionsMixed NumbersArithmetic Operations
2025/5/6

1. Problem Description

We need to calculate the value of the expression 119−29+49−1591\frac{1}{9} - \frac{2}{9} + \frac{4}{9} - 1\frac{5}{9}.

2. Solution Steps

First, convert the mixed numbers to improper fractions.
119=1∗9+19=1091\frac{1}{9} = \frac{1*9 + 1}{9} = \frac{10}{9}
159=1∗9+59=1491\frac{5}{9} = \frac{1*9 + 5}{9} = \frac{14}{9}
Now, substitute these values back into the original expression:
109−29+49−149\frac{10}{9} - \frac{2}{9} + \frac{4}{9} - \frac{14}{9}
Combine the fractions since they all have a common denominator of 9:
10−2+4−149=8+4−149=12−149=−29\frac{10 - 2 + 4 - 14}{9} = \frac{8 + 4 - 14}{9} = \frac{12 - 14}{9} = \frac{-2}{9}

3. Final Answer

The final answer is −29-\frac{2}{9}.

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