To evaluate the expression \( x(x + y) \) given that \( x = -2 \frac{1}{2} \) and \( y = \frac{3}{4} \), we first need to convert the mixed fraction into an improper fraction.

1. Convert \( -2 \frac{1}{2} \) to an improper fraction:
   \[
   -2 \frac{1}{2} = -\frac{5}{2}
   \]

2. Now, substitute the values of \( x = -\frac{5}{2} \) and \( y = \frac{3}{4} \) into the expression:
   \[
   x(x + y) = -\frac{5}{2} \left( -\frac{5}{2} + \frac{3}{4} \right)
   \]

3. First, find \( -\frac{5}{2} + \frac{3}{4} \). To add these fractions, we need a common denominator. The least common denominator of 2 and 4 is 4:
   \[
   -\frac{5}{2} = -\frac{10}{4}, \quad \frac{3}{4} = \frac{3}{4}
   \]
   Now, add the fractions:
   \[
   -\frac{10}{4} + \frac{3}{4} = -\frac{7}{4}
   \]

4. Now, substitute this result back into the expression:
   \[
   -\frac{5}{2} \times -\frac{7}{4}
   \]

5. Multiply the fractions:
   \[
   -\frac{5}{2} \times -\frac{7}{4} = \frac{35}{8}
   \]

Thus, the value of \( x(x + y) \) is \( \frac{35}{8} \).

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you multiply improper fractions?
2. How do you simplify a complex fraction?
3. What are common mistakes when adding fractions?
4. How do you convert a mixed number to an improper fraction?
5. What is the significance of the least common denominator?

**Tip:** Always remember to convert mixed numbers to improper fractions before performing operations like addition or multiplication.

Evaluate x(x + y) if x = -2 1/2 and y = 3/4

Learn how to evaluate the expression x(x + y) with x = -2 1/2 and y = 3/4. This step-by-step guide walks you through converting mixed numbers to improper fractions, adding fractions, and multiplying fractions. Suitable for students in Grades 6-8.

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