$1 \frac{1}{3}-\frac{1}{2}$
To evaluate the expression \(1 \frac{1}{3} - \frac{1}{2}\), we first analyze the terms. The expression consists of a mixed number and a simple fraction. A mixed number of the form \(A \frac{B}{C}\) is defined as \(A + \frac{B}{C}\). Our objective is to simplify this expression by converting it into a common fractional form and performing the subtraction.
First, convert the mixed number \(1 \frac{1}{3}\) into an improper fraction. Since \(1 \frac{1}{3} = 1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3}\), we combine the terms:
\[1 \frac{1}{3} = \frac{4}{3}\]
Now the expression is simplified to \(\frac{4}{3} - \frac{1}{2}\).
To subtract the fractions \(\frac{4}{3}\) and \(\frac{1}{2}\), we need a common denominator. The least common multiple (LCM) of the denominators 3 and 2 is 6. We scale each fraction accordingly:
\[\frac{4}{3} = \frac{4 \times 2}{3 \times 2} = \frac{8}{6}\]
\[\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}\]
Now that the fractions have a common denominator, perform the subtraction:
\[\frac{8}{6} - \frac{3}{6} = \frac{8 - 3}{6} = \frac{5}{6}\]
The calculation yields the final value of \(\frac{5}{6}\).
Think of this calculation like baking a cake. If a recipe calls for \(1 \frac{1}{3}\) cups of flour, but you accidentally remove \(\frac{1}{2}\) of a cup while measuring, you are left with \(\frac{5}{6}\) of a cup. Understanding how to handle fractions with different denominators is essential in everyday tasks like cooking, carpentry, or managing shared resources where you need to combine or subtract precise portions of a whole.