The expression given is:

\[
\frac{3}{5} + \frac{1}{2} \times \frac{3}{5} - \frac{5}{4}
\]

**Solution:**

Follow the order of operations (PEMDAS/BODMAS). Start with the multiplication:

1. Multiply \( \frac{1}{2} \times \frac{3}{5} \):
\[
\frac{1}{2} \times \frac{3}{5} = \frac{3}{10}
\]

2. Now, substitute back into the expression:
\[
\frac{3}{5} + \frac{3}{10} - \frac{5}{4}
\]

3. Find a common denominator for all fractions. The least common denominator (LCD) of 5, 10, and 4 is 20.

- Convert each fraction to have a denominator of 20:
\[
\frac{3}{5} = \frac{12}{20}, \quad \frac{3}{10} = \frac{6}{20}, \quad \frac{5}{4} = \frac{25}{20}
\]

4. Substitute these fractions back into the expression:
\[
\frac{12}{20} + \frac{6}{20} - \frac{25}{20}
\]

5. Combine the fractions:
\[
\frac{12 + 6 - 25}{20} = \frac{-7}{20}
\]

So, the final answer is:

\[
\boxed{-\frac{7}{20}}
\]

Would you like any further details or have questions? Here are some related problems you can try:

1. Simplify \( \frac{7}{9} + \frac{2}{3} \times \frac{5}{6} - \frac{1}{2} \).
2. What is \( \frac{4}{7} + \frac{3}{5} \times \frac{2}{3} - \frac{1}{4} \)?
3. Find the value of \( \frac{8}{9} \div \frac{2}{3} + \frac{1}{5} - \frac{3}{10} \).
4. Evaluate \( \frac{3}{8} + \frac{7}{12} \times \frac{1}{2} - \frac{5}{6} \).
5. Calculate \( \frac{9}{10} - \frac{1}{3} \times \frac{2}{7} + \frac{5}{12} \).
6. Solve \( \frac{2}{3} + \frac{1}{4} \div \frac{5}{8} - \frac{7}{9} \).
7. What is \( \frac{5}{12} \times \frac{3}{4} - \frac{1}{6} + \frac{7}{8} \)?
8. Determine the sum of \( \frac{6}{11} \) and \( \frac{2}{5} \div \frac{3}{7} \).

**Tip:** When working with addition and subtraction of fractions, always find the least common denominator before combining the fractions!

Learn how to simplify the expression 3/5 + 1/2 * 3/5 - 5/4 using fractions and order of operations. This problem involves arithmetic operations with fractions, including addition, multiplication, and subtraction. Suitable for students in Grades 6-8.

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