Let's simplify the given expression step by step:

\[
\frac{-6}{5} - \frac{2}{3}v + \frac{4}{15} + \frac{1}{3}v
\]

### Step 1: Combine like terms
We'll group the terms with \( v \) together and the constant terms together:

\[
\left( \frac{-2}{3}v + \frac{1}{3}v \right) + \left( \frac{-6}{5} + \frac{4}{15} \right)
\]

#### Simplifying the \( v \)-terms:
\[
\frac{-2}{3}v + \frac{1}{3}v = \frac{-1}{3}v
\]

#### Simplifying the constants:
To simplify the constant terms \(\frac{-6}{5} + \frac{4}{15}\), we need a common denominator. The least common denominator between 5 and 15 is 15. Rewrite the terms:

\[
\frac{-6}{5} = \frac{-18}{15}, \quad \frac{4}{15} = \frac{4}{15}
\]

Now, add them:

\[
\frac{-18}{15} + \frac{4}{15} = \frac{-18 + 4}{15} = \frac{-14}{15}
\]

### Step 2: Final expression
Now, combining the simplified terms:

\[
\frac{-1}{3}v + \frac{-14}{15}
\]

This is the simplified form of the given expression.

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. How do you find a common denominator for adding fractions?
2. What are the steps to combine like terms with variables?
3. How would you solve for \(v\) if this were an equation?
4. Can you add fractions with different denominators directly?
5. How does changing the sign of a variable term affect the expression?

**Tip:** Always simplify each term individually before combining them.

Learn how to simplify the algebraic expression -6/5 - 2/3v + 4/15 + 1/3v step by step. This solution covers combining like terms and adding fractions with different denominators, suitable for students in Grades 6-8.

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