Let's solve the expression step by step:

\[
-3 \left(\frac{7}{6}\right) + \frac{1}{2}
\]

### Step 1: Multiply \(-3\) by \(\frac{7}{6}\)
\[
-3 \times \frac{7}{6} = \frac{-21}{6}
\]

### Step 2: Simplify \(\frac{-21}{6}\)
\[
\frac{-21}{6} = -\frac{7}{2}
\]

### Step 3: Add \(-\frac{7}{2}\) and \(\frac{1}{2}\)
Since both fractions have the same denominator, you can directly add the numerators:
\[
-\frac{7}{2} + \frac{1}{2} = \frac{-7 + 1}{2} = \frac{-6}{2} = -3
\]

So, the result of the expression is:
\[
-3
\]

Would you like more details on any part of the calculation?

### Related questions:
1. How do you handle fractions when multiplying by a negative number?
2. How do you add fractions with different denominators?
3. How do you simplify fractions after addition or multiplication?
4. How does multiplying by a negative number affect the overall sign?
5. How would the result change if the signs in the expression were different?

### Tip:
Always simplify fractions whenever possible to make calculations easier!

Learn how to solve the expression -3(7/6) + 1/2 in this step-by-step guide. This arithmetic problem covers multiplying by fractions, adding fractions with the same denominator, and handling negative numbers. Perfect for students in Grades 6-8.

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