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.

Learn how to simplify the algebraic expression 3a - 2b when a = 1/3 and b = 1. This step-by-step solution explores basic algebraic concepts such as substitution and simplification. Suitable for students in Grades 6-8.

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