Let's solve the expression step by step:

\[
5 \times \frac{6}{7} + 8 \times \frac{7}{9}
\]

### Step 1: Simplify each multiplication separately.

1. \( 5 \times \frac{6}{7} = \frac{30}{7} \)
2. \( 8 \times \frac{7}{9} = \frac{56}{9} \)

### Step 2: Add the two results together.

\[
\frac{30}{7} + \frac{56}{9}
\]

To add fractions, find the common denominator. The least common denominator (LCD) of 7 and 9 is 63.

\[
\frac{30}{7} = \frac{30 \times 9}{7 \times 9} = \frac{270}{63}
\]
\[
\frac{56}{9} = \frac{56 \times 7}{9 \times 7} = \frac{392}{63}
\]

Now, add the two fractions:

\[
\frac{270}{63} + \frac{392}{63} = \frac{270 + 392}{63} = \frac{662}{63}
\]

### Final Answer:
\[
\frac{662}{63} \text{ or approximately } 10.51
\]

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How can you simplify complex fractions?
2. What is the process of finding the least common denominator for fractions?
3. What is the significance of multiplying fractions in word problems?
4. How do you convert an improper fraction into a mixed number?
5. How do you approximate fractions to decimals?

**Tip:** When adding fractions, always look for the least common denominator to simplify calculations efficiently.

Learn how to solve the expression 5×6/7 + 8×7/9 step by step. This tutorial covers key concepts in arithmetic, including multiplying whole numbers by fractions and adding fractions with different denominators. Ideal for students in Grades 5-7.

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