To solve the given problem, we need to translate the provided mathematical statement into an equation and solve it step-by-step.
The statement says: "The difference of [tex]\( f \)[/tex] and [tex]\( \frac{1}{3} \)[/tex] is [tex]\( \frac{2}{3} \)[/tex]."
1. Translate the Statement into an Equation:
The phrase "the difference of [tex]\( f \)[/tex] and [tex]\( \frac{1}{3} \)[/tex]" means we subtract [tex]\( \frac{1}{3} \)[/tex] from [tex]\( f \)[/tex]. Thus, the equation can be written as:
[tex]\[
f - \frac{1}{3} = \frac{2}{3}
\][/tex]
2. Solve for [tex]\( f \)[/tex]:
To find [tex]\( f \)[/tex], we need to isolate [tex]\( f \)[/tex] on one side of the equation. We can do this by adding [tex]\( \frac{1}{3} \)[/tex] to both sides of the equation:
[tex]\[
f - \frac{1}{3} + \frac{1}{3} = \frac{2}{3} + \frac{1}{3}
\][/tex]
Simplifying the left side, we have:
[tex]\[
f = \frac{2}{3} + \frac{1}{3}
\][/tex]
3. Perform the Arithmetic:
Now, we need to add the fractions on the right side. Since the denominators are the same, we can add the numerators directly:
[tex]\[
\frac{2}{3} + \frac{1}{3} = \frac{2 + 1}{3} = \frac{3}{3}
\][/tex]
4. Simplify the Fraction:
Finally, simplify [tex]\( \frac{3}{3} \)[/tex]:
[tex]\[
\frac{3}{3} = 1
\][/tex]
Therefore, the value of [tex]\( f \)[/tex] is:
[tex]\[
f = 1
\][/tex]
