To solve the expression \( \frac{1}{7} + \frac{1}{2} \), we need to find a common denominator and then add the fractions. Here are the steps:
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Find the least common denominator (LCD): The denominators are 7 and 2. The least common denominator of 7 and 2 is 14.
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Convert each fraction to have the LCD:
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For \( \frac{1}{7} \): To convert it to a denominator of 14, we multiply both the numerator and denominator by 2: \[ \frac{1 \cdot 2}{7 \cdot 2} = \frac{2}{14} \]
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For \( \frac{1}{2} \): To convert it to a denominator of 14, we multiply both the numerator and denominator by 7: \[ \frac{1 \cdot 7}{2 \cdot 7} = \frac{7}{14} \]
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Add the new fractions: Now we can add \( \frac{2}{14} \) and \( \frac{7}{14} \): \[ \frac{2}{14} + \frac{7}{14} = \frac{2 + 7}{14} = \frac{9}{14} \]
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Final answer: Hence, \( \frac{1}{7} + \frac{1}{2} = \frac{9}{14} \).
So the result is: \[ \frac{9}{14} \]
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