To subtract the mixed numbers \(2 \frac{1}{2}\) and \(2 \frac{1}{7}\), we first convert them to improper fractions.
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Convert \(2 \frac{1}{2}\): \[ 2 \frac{1}{2} = 2 \times 2 + 1 = 4 + 1 = 5 \quad \text{so it becomes} \quad \frac{5}{2} \]
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Convert \(2 \frac{1}{7}\): \[ 2 \frac{1}{7} = 2 \times 7 + 1 = 14 + 1 = 15 \quad \text{so it becomes} \quad \frac{15}{7} \]
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Now we need to subtract \(\frac{5}{2}\) from \(\frac{15}{7}\). To do this, we need a common denominator. The least common multiple (LCM) of 2 and 7 is 14.
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Rewrite each fraction with the common denominator:
- For \(\frac{5}{2}\): \[ \frac{5}{2} = \frac{5 \times 7}{2 \times 7} = \frac{35}{14} \]
- For \(\frac{15}{7}\): \[ \frac{15}{7} = \frac{15 \times 2}{7 \times 2} = \frac{30}{14} \]
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Now we can subtract the fractions: \[ \frac{30}{14} - \frac{35}{14} = \frac{30 - 35}{14} = \frac{-5}{14} \]
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Since we have a negative fraction, we can express this as a negative mixed number. The absolute value of \(-\frac{5}{14}\) is less than 1, so we keep it as is.
Thus, the final answer in mixed number form is: \[ -\frac{5}{14} \]
So the answer is: \[ [0] [5]/[14] \]
This indicates \(0\) whole, \(5\) as the numerator, and \(14\) as the denominator for the proper fraction part of the mixed number.
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