To add the mixed numbers \( 1 \frac{1}{4} \) and \( 1 \frac{1}{3} \), we first convert them to improper fractions.
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Convert \( 1 \frac{1}{4} \): \[ 1 \frac{1}{4} = 4 \cdot 1 + 1 = 5/4 \]
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Convert \( 1 \frac{1}{3} \): \[ 1 \frac{1}{3} = 3 \cdot 1 + 1 = 4/3 \]
Next, we need to add these two fractions. To do that, we need a common denominator. The least common multiple (LCM) of 4 and 3 is 12.
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Convert \( \frac{5}{4} \) to have a denominator of 12: \[ \frac{5}{4} = \frac{5 \cdot 3}{4 \cdot 3} = \frac{15}{12} \]
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Convert \( \frac{4}{3} \) to have a denominator of 12: \[ \frac{4}{3} = \frac{4 \cdot 4}{3 \cdot 4} = \frac{16}{12} \]
Now we can add the fractions: \[ \frac{15}{12} + \frac{16}{12} = \frac{15 + 16}{12} = \frac{31}{12} \]
Next, we convert \( \frac{31}{12} \) back to a mixed number: \[ 31 \div 12 = 2 \quad \text{(whole number part)} \] The remainder is: \[ 31 - 12 \cdot 2 = 7 \]
So, the mixed number is: \[ 2 \frac{7}{12} \]
In simplest form, the final answer is: \[ 2 \frac{7}{12} \]
In the requested format: \[ [2] [7]/[12] \]