Certainly!
To verify the equality [tex]\(\left(\frac{-1}{2}\right) + \frac{1}{3} = \frac{1}{3} + \left(-\frac{1}{2}\right)\)[/tex], we'll carefully evaluate both sides step-by-step.
### Step 1: Evaluate the Left Side
The left side of the equation is [tex]\(\left(\frac{-1}{2}\right) + \frac{1}{3}\)[/tex].
1. Find a common denominator: The common denominator for 2 and 3 is 6.
- For [tex]\(\frac{-1}{2}\)[/tex], convert to have a denominator of 6: [tex]\(\frac{-1 \times 3}{2 \times 3} = \frac{-3}{6}\)[/tex]
- For [tex]\(\frac{1}{3}\)[/tex], convert to have a denominator of 6: [tex]\(\frac{1 \times 2}{3 \times 2} = \frac{2}{6}\)[/tex]
2. Combine the fractions:
[tex]\[
\frac{-3}{6} + \frac{2}{6} = \frac{-3 + 2}{6} = \frac{-1}{6}
\][/tex]
Thus, the value of the left side is [tex]\(\frac{-1}{6}\)[/tex].
### Step 2: Evaluate the Right Side
The right side of the equation is [tex]\(\frac{1}{3} + \left(\frac{-1}{2}\right)\)[/tex].
1. Find a common denominator: The common denominator for 3 and 2 is 6.
- For [tex]\(\frac{1}{3}\)[/tex], convert to have a denominator of 6: [tex]\(\frac{1 \times 2}{3 \times 2} = \frac{2}{6}\)[/tex]
- For [tex]\(\frac{-1}{2}\)[/tex], convert to have a denominator of 6: [tex]\(\frac{-1 \times 3}{2 \times 3} = \frac{-3}{6}\)[/tex]
2. Combine the fractions:
[tex]\[
\frac{2}{6} + \frac{-3}{6} = \frac{2 - 3}{6} = \frac{-1}{6}
\][/tex]
Thus, the value of the right side is [tex]\(\frac{-1}{6}\)[/tex].
### Step 3: Compare Both Sides
The left side is [tex]\(\frac{-1}{6}\)[/tex] and the right side is [tex]\(\frac{-1}{6}\)[/tex].
Since both sides are equal, we have:
[tex]\[
\left(\frac{-1}{2}\right) + \frac{1}{3} = \frac{1}{3} + \left(\frac{-1}{2}\right)
\][/tex]
Thus, the given equation is verified to be true.
