A farmer plowed \( 1011 / 12 \) acres in the morning and \( 11 / 2 \) acres in the afternoon. How many acres did the farmer plow in all? Write your answer as a fraction or as a whole or mixed number.
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To find the total acreage plowed by the farmer, we need to add the two fractions: \( \frac{1011}{12} \) and \( \frac{11}{2} \). First, we need a common denominator. The least common multiple of 12 and 2 is 12. Now, convert \( \frac{11}{2} \) to twelfths: \[ \frac{11}{2} = \frac{11 \times 6}{2 \times 6} = \frac{66}{12} \] Now we can add the two fractions: \[ \frac{1011}{12} + \frac{66}{12} = \frac{1011 + 66}{12} = \frac{1077}{12} \] To convert \( \frac{1077}{12} \) to a mixed number, divide 1077 by 12: 1077 divided by 12 is 89 with a remainder of 9. Thus, \[ \frac{1077}{12} = 89 \frac{9}{12} \] We can simplify \( \frac{9}{12} \) to \( \frac{3}{4} \). So, the total acreage plowed is: \[ 89 \frac{3}{4} \] The farmer plowed a total of \( 89 \frac{3}{4} \) acres.
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