Question
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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.

Ask by Hammond Wilson. in the United States
Feb 24,2025

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Tutor-Verified Answer

Answer

The farmer plowed a total of 359/4 acres, which is equal to 89 3/4 acres.

Solution

To find the total number of acres plowed, add the two amounts: 1. Morning: 1011/12 acres 2. Afternoon: 11/2 acres First, convert 11/2 to a fraction with denominator 12:  11/2 = (11 × 6) / (2 × 6) = 66/12 Now add the two fractions:  1011/12 + 66/12 = (1011 + 66) / 12 = 1077/12 Next, simplify 1077/12 by dividing numerator and denominator by 3:  1077 ÷ 3 = 359 and 12 ÷ 3 = 4 Thus, the simplified sum is:  359/4 As a mixed number, 359/4 is equal to 89 3/4 (since 4 goes into 359 exactly 89 times with a remainder of 3). So, the farmer plowed a total of 359/4 acres, or 89 3/4 acres.

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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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