To find the fraction of the field that is not plowed at the end of the second day, we first need to determine how much of the field has been plowed in total after the first and second days.
- Fraction plowed on the first day: \( \frac{2}{7} \)
- Fraction plowed on the second day: \( \frac{2}{3} \)
Next, we need to add these two fractions together to find the total fraction of the field that has been plowed:
To add the fractions \( \frac{2}{7} \) and \( \frac{2}{3} \), we need a common denominator. The least common multiple of 7 and 3 is 21.
Now convert the fractions:
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For \( \frac{2}{7} \): \[ \frac{2}{7} = \frac{2 \times 3}{7 \times 3} = \frac{6}{21} \]
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For \( \frac{2}{3} \): \[ \frac{2}{3} = \frac{2 \times 7}{3 \times 7} = \frac{14}{21} \]
Now, add the converted fractions: \[ \frac{6}{21} + \frac{14}{21} = \frac{20}{21} \]
This means that \( \frac{20}{21} \) of the field has been plowed.
To find the fraction of the field that is not plowed, we subtract the amount that has been plowed from the whole field (which is 1):
\[ 1 - \frac{20}{21} = \frac{21}{21} - \frac{20}{21} = \frac{1}{21} \]
Thus, the fraction of the field that is not plowed at the end of the second day is \( \frac{1}{21} \).
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