To solve \((\frac{5}{9} + \frac{5}{6})(\frac{7}{8} + \frac{3}{7})\), follow these steps:

### Step 1: Add the fractions inside each parenthesis.

#### First Parenthesis: \(\frac{5}{9} + \frac{5}{6}\)

To add these fractions, we need a common denominator. The least common denominator (LCD) of 9 and 6 is 18.

\[
\frac{5}{9} = \frac{10}{18}, \quad \frac{5}{6} = \frac{15}{18}
\]

Now, add the fractions:

\[
\frac{10}{18} + \frac{15}{18} = \frac{25}{18}
\]

#### Second Parenthesis: \(\frac{7}{8} + \frac{3}{7}\)

The LCD of 8 and 7 is 56.

\[
\frac{7}{8} = \frac{49}{56}, \quad \frac{3}{7} = \frac{24}{56}
\]

Now, add the fractions:

\[
\frac{49}{56} + \frac{24}{56} = \frac{73}{56}
\]

### Step 2: Multiply the results of both parentheses.

\[
\left(\frac{25}{18}\right) \times \left(\frac{73}{56}\right) = \frac{25 \times 73}{18 \times 56} = \frac{1825}{1008}
\]

### Step 3: Simplify the fraction (if possible).

The greatest common divisor (GCD) of 1825 and 1008 is 1, so the fraction cannot be simplified further.

Thus, the final result is:

\[
\frac{1825}{1008}
\]

Would you like more details, or do you have any questions?

Here are 5 related questions to consider:
1. How can you simplify a fraction more easily?
2. How do you find the least common denominator (LCD) of two fractions?
3. What are some common ways to check the accuracy of a fraction multiplication?
4. How do you handle mixed numbers in operations like this?
5. Can this fraction be represented as a decimal or percentage?

**Tip:** Always check if the fractions can be simplified before performing multiplication—it can save time in calculations!

Learn how to solve the expression (5/9 + 5/6)(7/8 + 3/7) step by step. This problem involves adding fractions with different denominators, finding the least common denominator (LCD), and multiplying fractions. Detailed explanation with simplified final result, suitable for students in Grades 7-9.

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