To subtract the mixed numbers \(4 \frac{2}{3}\) and \(1 \frac{1}{9}\), follow these steps:
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Convert the mixed numbers into improper fractions:
- For \(4 \frac{2}{3}\): \[ 4 \frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3} \]
- For \(1 \frac{1}{9}\): \[ 1 \frac{1}{9} = \frac{1 \times 9 + 1}{9} = \frac{9 + 1}{9} = \frac{10}{9} \]
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Subtract the improper fractions: To subtract \(\frac{14}{3} - \frac{10}{9}\), we first need a common denominator. The least common multiple of 3 and 9 is 9.
Convert \(\frac{14}{3}\) to a fraction with a denominator of 9: \[ \frac{14}{3} = \frac{14 \times 3}{3 \times 3} = \frac{42}{9} \]
Now we can subtract: \[ \frac{42}{9} - \frac{10}{9} = \frac{42 - 10}{9} = \frac{32}{9} \]
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Convert the result back to a mixed number: To convert \(\frac{32}{9}\) back to a mixed number, divide 32 by 9: \[ 32 \div 9 = 3 \quad \text{(whole number part)} \] The remainder is: \[ 32 - (9 \times 3) = 32 - 27 = 5 \] So, \(\frac{32}{9} = 3 \frac{5}{9}\).
Therefore, the result of \(4 \frac{2}{3} - 1 \frac{1}{9}\) is \(3 \frac{5}{9}\).