To evaluate the expression \( x(x + y) \) given \( x = 2 \frac{1}{3} \) and \( y = \frac{3}{4} \), let's follow these steps:

### Step 1: Convert the mixed fraction \( 2 \frac{1}{3} \) into an improper fraction.
\[
x = 2 \frac{1}{3} = \frac{7}{3}
\]

### Step 2: Substitute the values of \( x \) and \( y \) into the expression.
\[
x(x + y) = \frac{7}{3} \left( \frac{7}{3} + \frac{3}{4} \right)
\]

### Step 3: Add \( \frac{7}{3} \) and \( \frac{3}{4} \).
We need a common denominator. The least common denominator (LCD) of 3 and 4 is 12, so:

\[
\frac{7}{3} = \frac{28}{12}, \quad \frac{3}{4} = \frac{9}{12}
\]
Now, add them:
\[
\frac{28}{12} + \frac{9}{12} = \frac{37}{12}
\]

### Step 4: Multiply \( \frac{7}{3} \) by \( \frac{37}{12} \).
\[
x(x + y) = \frac{7}{3} \times \frac{37}{12} = \frac{7 \times 37}{3 \times 12} = \frac{259}{36}
\]

### Step 5: Simplify (if possible).
The fraction \( \frac{259}{36} \) cannot be simplified further, so the result is:

\[
x(x + y) = \frac{259}{36}
\]

This is the final answer.

Would you like more details on any of the steps or have any further questions?

Here are some related questions to consider:
1. How do you add fractions with different denominators?
2. What is the process for multiplying two fractions?
3. How do you convert mixed numbers to improper fractions?
4. How can you simplify fractions after multiplication?
5. How do you find the least common denominator?

**Tip:** When adding fractions, always find the least common denominator to ensure accurate calculations.

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

Learn how to evaluate the expression x(x + y) when x = 2 1/3 and y = 3/4. This step-by-step guide covers key mathematical concepts like converting mixed numbers to improper fractions, adding fractions with different denominators, and multiplying fractions. Suitable for students in Grades 6-8.

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