Let's solve the given expression step by step:

The expression is:

\[
\left(\frac{5/8 \times 3/10}{3/8}\right) + \left(\frac{3/4 \times 5/6}{1 \frac{1}{4}}\right)
\]

### Step 1: Simplify the first part

\[
\frac{5/8 \times 3/10}{3/8}
\]

- First, multiply \( \frac{5}{8} \) by \( \frac{3}{10} \):

\[
\frac{5 \times 3}{8 \times 10} = \frac{15}{80}
\]

- Now divide by \( \frac{3}{8} \):

\[
\frac{15/80}{3/8} = \frac{15}{80} \times \frac{8}{3} = \frac{15 \times 8}{80 \times 3} = \frac{120}{240} = \frac{1}{2}
\]

So, the first part simplifies to \( \frac{1}{2} \).

### Step 2: Simplify the second part

\[
\frac{3/4 \times 5/6}{1 \frac{1}{4}}
\]

- First, multiply \( \frac{3}{4} \) by \( \frac{5}{6} \):

\[
\frac{3 \times 5}{4 \times 6} = \frac{15}{24} = \frac{5}{8}
\]

- Convert \( 1 \frac{1}{4} \) to an improper fraction:

\[
1 \frac{1}{4} = \frac{5}{4}
\]

- Now divide \( \frac{5}{8} \) by \( \frac{5}{4} \):

\[
\frac{5/8}{5/4} = \frac{5}{8} \times \frac{4}{5} = \frac{20}{40} = \frac{1}{2}
\]

So, the second part simplifies to \( \frac{1}{2} \).

### Step 3: Add the two simplified parts

\[
\frac{1}{2} + \frac{1}{2} = 1
\]

### Final Answer:

The value of the expression is \( 1 \).

Would you like any details or have any questions?

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Here are 5 related questions for further practice:

1. Simplify the expression: \( \left(\frac{7/9 \times 4/5}{2/3}\right) + \left(\frac{2/3 \times 5/7}{2 \frac{1}{5}}\right) \).
2. Evaluate: \( \frac{2/3 \times 5/8}{4/5} + \frac{6/7 \times 1/3}{5/9} \).
3. Simplify \( 1 \frac{2}{5} + \frac{3}{4} \times \frac{5}{6} \).
4. Solve \( \frac{7/8 \times 4/5}{3/4} \times \frac{3}{7} \).
5. Find the value of \( \left(\frac{9/10 \times 2/3}{1/5}\right) - \left(\frac{4/7 \times 5/9}{1/2}\right) \).

**Tip:** When multiplying fractions, always remember to multiply the numerators together and the denominators together, then simplify the fraction if possible.

Learn how to simplify the complex fraction expression (5/8 * 3/10) / 3/8 + (3/4 * 5/6) / 1 1/4 step by step. This problem involves fractions and arithmetic operations, suitable for Grades 5-6 students.

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