To solve the expression \( \frac{1}{4} + \frac{1}{6} \times \left( -\frac{3}{4} \right) \), follow these steps:

1. **Handle the multiplication first**:
   \[
   \frac{1}{6} \times \left( -\frac{3}{4} \right) = -\frac{3}{24} = -\frac{1}{8}
   \]

2. **Now add the fractions**:
   \[
   \frac{1}{4} + \left( -\frac{1}{8} \right)
   \]
   To add these fractions, find a common denominator. The least common denominator (LCD) of 4 and 8 is 8.

   \[
   \frac{1}{4} = \frac{2}{8}
   \]
   So the expression becomes:
   \[
   \frac{2}{8} + \left( -\frac{1}{8} \right) = \frac{2}{8} - \frac{1}{8} = \frac{1}{8}
   \]

Thus, the final answer is:
\[
\frac{1}{8}
\]

Would you like any further details or clarifications?

Here are 5 questions to explore:
1. What is the general process for adding fractions with different denominators?
2. How do you determine the least common denominator (LCD)?
3. What happens when you multiply two fractions, and how does it affect the sign?
4. How can you simplify fractions effectively?
5. What are other ways to approach solving a similar expression?

**Tip**: When adding or subtracting fractions, always look for the smallest common denominator to simplify the process.

Discover how to solve the fraction expression 1/4 + 1/6(-3/4) step by step. This problem involves multiplying and adding fractions, finding a common denominator, and working with negative numbers. Ideal for students in Grades 6-8.

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