To solve the expression \(\dfrac{8}{3} + \left(-\dfrac{9}{4}\right)\), we need to perform the addition of the two fractions. Since they have different denominators, we'll first find a common denominator.

1. The denominators are 3 and 4. The least common denominator (LCD) is 12.

2. Convert both fractions to have the common denominator of 12:

   - \(\dfrac{8}{3} = \dfrac{8 \times 4}{3 \times 4} = \dfrac{32}{12}\)
   - \(\dfrac{-9}{4} = \dfrac{-9 \times 3}{4 \times 3} = \dfrac{-27}{12}\)

3. Now, add the fractions:

   \[
   \dfrac{32}{12} + \dfrac{-27}{12} = \dfrac{32 - 27}{12} = \dfrac{5}{12}
   \]

So, \(\dfrac{8}{3} + \left(-\dfrac{9}{4}\right) = \dfrac{5}{12}\).

Would you like further details or have any other questions? Here are some related questions to consider:

1. How do you find the least common denominator (LCD)?
2. What is the process for adding fractions with different denominators?
3. How do you convert an improper fraction to a mixed number?
4. What are the steps for subtracting fractions?
5. How can you multiply and divide fractions?

**Tip:** Always simplify fractions when possible for a cleaner final answer.

Learn how to add fractions \(\frac{8}{3}\) and \(-\frac{9}{4}\) step-by-step. This problem involves finding a common denominator, converting fractions, and performing addition. Suitable for Grades 6-8 students learning about fractions and arithmetic operations.

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