To solve the problem [tex]\( -7 + \frac{1}{3} \)[/tex], we start by understanding that we are performing an addition operation between a negative whole number and a positive fraction.
1. Identify the components:
- The whole number is [tex]\( -7 \)[/tex].
- The fraction is [tex]\( \frac{1}{3} \)[/tex].
2. Perform the addition:
- When you add [tex]\( \frac{1}{3} \)[/tex] to [tex]\( -7 \)[/tex], you are essentially slightly increasing a negative number towards zero.
Let's break this down:
- The whole number part remains [tex]\( -7 \)[/tex].
- Adding [tex]\( \frac{1}{3} \)[/tex] moves us a third of the way towards [tex]\( 0 \)[/tex].
3. Combine the results:
- The addition of [tex]\( -7 \)[/tex] and [tex]\( \frac{1}{3} \)[/tex] yields [tex]\( -6 \frac{2}{3} \)[/tex].
- In decimal form, [tex]\( \frac{2}{3} \approx 0.67 \)[/tex].
4. Express the result as a mixed number:
- The mixed number representation is [tex]\( -6 \frac{2}{3} \)[/tex].
Given these steps, we can conclude the result of [tex]\( -7 + \frac{1}{3} \)[/tex] is [tex]\( -6 \frac{2}{3} \)[/tex].
Therefore, the answer is:
[tex]\[ \boxed{-6 \frac{2}{3}} \][/tex]
