Question

farmer plowed 7/12 of an acre in the morning and 10 3/6 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. () acres

Explanation:

Step1: Simplify the afternoon fraction

First, simplify \(10\frac{3}{6}\). The fraction \(\frac{3}{6}\) simplifies to \(\frac{1}{2}\), so \(10\frac{3}{6}=10\frac{1}{2}\). Convert \(10\frac{1}{2}\) to an improper fraction: \(10\frac{1}{2}=\frac{10\times2 + 1}{2}=\frac{21}{2}\). Also, the morning plowed area is \(\frac{7}{12}\).

Step2: Find a common denominator

The common denominator of 12 and 2 is 12. Convert \(\frac{21}{2}\) to twelfths: \(\frac{21}{2}=\frac{21\times6}{2\times6}=\frac{126}{12}\).

Step3: Add the two fractions

Now add \(\frac{7}{12}\) and \(\frac{126}{12}\): \(\frac{7 + 126}{12}=\frac{133}{12}\). Convert this improper fraction to a mixed number: \(\frac{133}{12}=11\frac{1}{12}\). Wait, no, wait, I think I misread the numbers. Wait, the afternoon is \(10\frac{3}{6}\) acres? Wait, no, maybe the morning is \(\frac{7}{12}\) and afternoon is \(10\frac{3}{6}\)? Wait, that seems like a typo? Wait, no, maybe the morning is \(7\frac{1}{12}\)? Wait, no, the original problem: "plowed 7/12 of an acre in the morning and 10 3/6 acres in the afternoon". Oh, so morning is \(\frac{7}{12}\) (a fraction less than 1) and afternoon is \(10\frac{3}{6}\) (a mixed number). So we need to add \(\frac{7}{12}\) and \(10\frac{3}{6}\). First, simplify \(10\frac{3}{6}\) to \(10\frac{1}{2}\) (since \(\frac{3}{6}=\frac{1}{2}\)). Then convert \(10\frac{1}{2}\) to an improper fraction: \(10\frac{1}{2}=\frac{21}{2}\). Now, find a common denominator for \(\frac{7}{12}\) and \(\frac{21}{2}\). The common denominator is 12. So \(\frac{21}{2}=\frac{21\times6}{2\times6}=\frac{126}{12}\). Then add \(\frac{7}{12}+\frac{126}{12}=\frac{133}{12}\). Convert \(\frac{133}{12}\) to a mixed number: \(133\div12 = 11\) with a remainder of 1, so \(11\frac{1}{12}\). Wait, but that seems odd because the afternoon is 10 acres and morning is less than 1, so total should be 10 + something. Wait, maybe I misread the morning: is it \(7\frac{1}{12}\) instead of \(\frac{7}{12}\)? Because \(\frac{7}{12}\) is less than 1, and afternoon is 10, so total would be 10 + \(\frac{7}{12}\) + \(\frac{3}{6}\)? Wait, no, the problem says "7/12 of an acre in the morning and 10 3/6 acres in the afternoon". So morning: \(\frac{7}{12}\) acres (about 0.58 acres), afternoon: \(10\frac{3}{6}=10\frac{1}{2}\) acres (10.5 acres). So total is \(10\frac{1}{2}+\frac{7}{12}\). Convert \(10\frac{1}{2}\) to twelfths: \(10\frac{6}{12}\) (since \(\frac{1}{2}=\frac{6}{12}\)). Then add \(\frac{7}{12}\): \(10\frac{6}{12}+\frac{7}{12}=10\frac{13}{12}=11\frac{1}{12}\). Yes, that's correct.

Answer:

\(11\frac{1}{12}\)