(6-3 5/12)-(3-1 1/12)

To solve the expression \((6 - 3 \frac{5}{12}) - (3 - 1 \frac{1}{12})\), let's break it down step by step. 1. Convert the mixed numbers to improper fractions: - For \(3 \frac{5}{12}\): \[ 3 \frac{5}{12} = \frac{3 \times 12 + 5}{12} = \frac{36 + 5}{12} = \frac{41}{12} \] - For \(1 \frac{1}{12}\): \[ 1 \frac{1}{12} = \frac{1 \times 12 + 1}{12} = \frac{12 + 1}{12} = \frac{13}{12} \] 2. Now rewrite the original expression with the improper fractions: \[ (6 - \frac{41}{12}) - (3 - \frac{13}{12}) \] 3. Convert the whole numbers to fractions with a common denominator: - For \(6\) (which is \(\frac{6 \times 12}{12} = \frac{72}{12}\)) - For \(3\) (which is \(\frac{3 \times 12}{12} = \frac{36}{12}\)) 4. Substitute back into the equation: \[ \left( \frac{72}{12} - \frac{41}{12} \right) - \left( \frac{36}{12} - \frac{13}{12} \right) \] 5. Calculate each part: - First part: \[ \frac{72}{12} - \frac{41}{12} = \frac{72 - 41}{12} = \frac{31}{12} \] - Second part: \[ \frac{36}{12} - \frac{13}{12} = \frac{36 - 13}{12} = \frac{23}{12} \] 6. Now perform the subtraction: \[ \frac{31}{12} - \frac{23}{12} = \frac{31 - 23}{12} = \frac{8}{12} \] 7. Simplify \(\frac{8}{12}\): \[ \frac{8}{12} = \frac{2}{3} \] Thus, the final result of the expression \((6 - 3 \frac{5}{12}) - (3 - 1 \frac{1}{12})\) is: \[ \frac{2}{3} \]