Let's solve the expression $3a - 2b$ given that $a = \frac{1}{3}$ and $b = 1$.

Substitute the values of $a$ and $b$ into the expression:

$3 \left(\frac{1}{3}\right) - 2(1)$

Now, simplify the expression step by step:

1. Multiply $3$ by $\frac{1}{3}$:

$3 \times \frac{1}{3} = 1$

2. Multiply $2$ by $1$:

$2 \times 1 = 2$

3. Subtract the results:

$1 - 2 = -1$

So, the value of the expression $3a - 2b$ is $-1$.

Would you like more details on any part of this calculation or have any questions?

Here are 5 related questions you might find interesting:

1. What would the expression $3a - 2b$ equal if $a = 2$ and $b = \frac{1}{2}$?
2. How does the expression change if $b$ is doubled?
3. What if both $a$ and $b$ were negative? How would that affect the result?
4. Can you express the same formula $3a - 2b$ graphically for varying values of $a$ and $b$?
5. How would you solve $3a - 2b = 0$ for $a$ in terms of $b$?

Tip: When substituting fractions into expressions, always simplify each term before combining them to avoid errors.