Solve for the unknown in a mixed-fraction equation Find the value of ? if (5/6 ÷ 6/7) × ? − (8/9 ÷ 1 3/5) + (3/4 × 3 1/3) = 2 7/9.

Introduction / Context:
This equation mixes division by fractions, multiplication by mixed numbers, and solving for an unknown factor. The strategy is to simplify each known term, isolate the variable term, and then solve for the unknown by dividing both sides by its coefficient.

Given Data / Assumptions:

• (5/6 ÷ 6/7) × ? − (8/9 ÷ 1 3/5) + (3/4 × 3 1/3) = 2 7/9.
• 1 3/5 = 8/5, 3 1/3 = 10/3, 2 7/9 = 25/9.

Concept / Approach:
Compute each operation stepwise. Division by a fraction equals multiplication by its reciprocal. Convert all mixed numbers to improper fractions early to avoid mistakes. Collect constants on one side, then solve for the unknown.

Step-by-Step Solution:
Coefficient of ?: 5/6 ÷ 6/7 = 5/6 × 7/6 = 35/36.Second term: 8/9 ÷ 8/5 = 8/9 × 5/8 = 5/9 (to be subtracted).Third term: 3/4 × 10/3 = 10/4 = 5/2.Right side: 2 7/9 = 25/9.Form equation: (35/36)·x − 5/9 + 5/2 = 25/9.Combine constants: −5/9 + 5/2 = −10/18 + 45/18 = 35/18.So (35/36)·x + 35/18 = 25/9 = 50/18.Subtract: (35/36)·x = 50/18 − 35/18 = 15/18 = 5/6.Solve: x = (5/6) ÷ (35/36) = (5/6) × (36/35) = 6/7.

Verification / Alternative check:
Substitute x = 6/7 back into the original to confirm both sides equal 25/9.

Why Other Options Are Wrong:
7/6, 1, 5/6 lead to a left-hand side different from 25/9; “None of these” is invalid since 6/7 works exactly.

Common Pitfalls:
Failing to convert mixed numbers; forgetting to apply reciprocals during division by fractions; arithmetic mistakes when combining constants.

Final Answer:
6/7