Convert to improper fractions, solve, and simplify your answer.
$41 / 3-25 / 6=$
We are tasked with evaluating the expression \(4\frac{1}{3} - 2\frac{5}{6}\). To solve this, we first convert the mixed numbers into improper fractions. An improper fraction is one where the numerator is greater than or equal to the denominator, and it can be calculated using the formula \(A\frac{b}{c} = \frac{A \cdot c + b}{c}\).
To convert \(4\frac{1}{3}\), we multiply the whole number by the denominator and add the numerator: \(\frac{4 \times 3 + 1}{3} = \frac{12+1}{3} = \frac{13}{3}\).
To convert \(2\frac{5}{6}\), we use the same process: \(\frac{2 \times 6 + 5}{6} = \frac{12+5}{6} = \frac{17}{6}\). Now the expression becomes \(\frac{13}{3} - \frac{17}{6}\).
To subtract the two fractions, we need a common denominator. The least common multiple of 3 and 6 is 6. We scale \(\frac{13}{3}\) by multiplying both the numerator and the denominator by 2 to get \(\frac{13 \times 2}{3 \times 2} = \frac{26}{6}\).
Now, we perform the subtraction: \(\frac{26}{6} - \frac{17}{6} = \frac{26 - 17}{6} = \frac{9}{6}\).
Finally, we simplify the fraction \(\frac{9}{6}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 3: \(\frac{9 \div 3}{6 \div 3} = \frac{3}{2}\). In mixed number form, \(\frac{3}{2}\) is equal to \(1\frac{1}{2}\). Thus, the final result is \(\boxed{1\frac{1}{2}}\) or \(\boxed{\frac{3}{2}}\).
In everyday life, fractional arithmetic is essential when dealing with measurements. For example, if you are baking and a recipe calls for \(4\frac{1}{3}\) cups of flour, but you only have a measuring cup that requires you to subtract \(2\frac{5}{6}\) cups because you decided to reduce the batch size, understanding how to perform these calculations ensures your ingredients are perfectly balanced. This fundamental skill helps maintain accuracy in tasks ranging from cooking and home improvement projects to financial budgeting.