Let's subtract [tex]\(-\frac{2}{3} - \left(-1 \frac{1}{3}\right)\)[/tex] step-by-step.
1. Convert the Mixed Fraction to an Improper Fraction:
First, convert the mixed fraction [tex]\(-1 \frac{1}{3}\)[/tex] into an improper fraction.
[tex]\[
-1 \frac{1}{3} = -1 - \frac{1}{3}
\][/tex]
To convert this, let's combine the whole number and the fractional part:
[tex]\[-1 - \frac{1}{3} = -\frac{3}{3} - \frac{1}{3} = -\frac{4}{3}\][/tex]
So, [tex]\(-1 \frac{1}{3}\)[/tex] is equivalent to [tex]\(-\frac{4}{3}\)[/tex].
2. Subtraction of Negative Fractions:
Next, we will perform the subtraction [tex]\(-\frac{2}{3} - \left(-\frac{4}{3}\right)\)[/tex].
Remember, subtracting a negative number is the same as adding its positive counterpart. Thus, this becomes:
[tex]\[
-\frac{2}{3} - \left(-\frac{4}{3}\right) = -\frac{2}{3} + \frac{4}{3}
\][/tex]
3. Find a Common Denominator and Perform the Addition:
Since both fractions already have the same denominator, we can directly add the numerators:
[tex]\[
-\frac{2}{3} + \frac{4}{3} = \frac{-2 + 4}{3} = \frac{2}{3}
\][/tex]
So, the result of the subtraction [tex]\(-\frac{2}{3} - \left(-1 \frac{1}{3}\right)\)[/tex] is [tex]\(\frac{2}{3}\)[/tex].
Therefore, the final answer is:
[tex]\[
\boxed{\frac{2}{3}}
\][/tex]
