https://file.aiquickdraw.com/mathbot/file/1726623067668f66y2mpt.jpg

The expression given in the image is:

\[
\frac{5}{9}x - \frac{2}{3}y + xy
\]
with the values \( x = \frac{3}{5} \) and \( y = -\frac{1}{2} \).

Let's substitute the values of \( x \) and \( y \) into the expression and simplify. I'll calculate it step-by-step.

\[
\frac{5}{9} \times \frac{3}{5} - \frac{2}{3} \times \left( -\frac{1}{2} \right) + \left( \frac{3}{5} \times -\frac{1}{2} \right)
\]

Now, simplifying each term:

1. \( \frac{5}{9} \times \frac{3}{5} = \frac{15}{45} = \frac{1}{3} \)
2. \( \frac{2}{3} \times \left( -\frac{1}{2} \right) = -\frac{2}{6} = -\frac{1}{3} \)
3. \( \frac{3}{5} \times -\frac{1}{2} = -\frac{3}{10} \)

Now, adding these results together:

\[
\frac{1}{3} - \frac{1}{3} - \frac{3}{10}
\]

The \( \frac{1}{3} - \frac{1}{3} \) cancels out, so we are left with:

\[
- \frac{3}{10}
\]

Thus, the value of the expression is \( - \frac{3}{10} \).

Would you like further clarification, or do you have any other questions?

Here are some related questions for practice:
1. What is the value of \( \frac{5}{9} x \) when \( x = \frac{3}{5} \)?
2. How do you simplify the product of two fractions?
3. What happens to a term in an equation if two equal but opposite values are added together?
4. Can you explain how to add or subtract fractions with different denominators?
5. What are the properties of multiplying positive and negative numbers?

**Tip:** When multiplying fractions, multiply the numerators together and the denominators together for the product.

Simplify the expression (5/9)x - (2/3)y + xy given x = 3/5 and y = -1/2.

Learn how to simplify the expression (5/9)x - (2/3)y + xy by substituting x = 3/5 and y = -1/2. Follow a step-by-step breakdown involving algebraic concepts like substitution and fraction operations. Suitable for students in Grades 7-9.

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