$$ \frac{3+4 \div 2 \times 3}{4+3 \times 2 \div 3} = x $$

### Concept & Rule This question strictly tests the application of the BODMAS rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction) applied independently to a numerator and a denominator. Division and Multiplication have the same priority, so you must process them strictly from left to right as they appear in the expression. ### Step-by-Step Solution * **Step 1:** Evaluate the numerator using BODMAS. Expression: $3 + 4 \div 2 \times 3$ First, perform Division: $4 \div 2 = 2$. The expression becomes: $3 + 2 \times 3$. Next, perform Multiplication: $2 \times 3 = 6$. The expression becomes: $3 + 6$. Finally, Addition: $3 + 6 = 9$. Numerator $= 9$. * **Step 2:** Evaluate the denominator using BODMAS. Expression: $4 + 3 \times 2 \div 3$ First, evaluate Multiplication and Division left-to-right. Multiplication appears first: $3 \times 2 = 6$. The expression becomes: $4 + 6 \div 3$. Next, Division: $6 \div 3 = 2$. The expression becomes: $4 + 2$. Finally, Addition: $4 + 2 = 6$. Denominator $= 6$. * **Step 3:** Form the final fraction and simplify. $$ x = \frac{9}{6} $$ Divide numerator and denominator by 3: $$ x = \frac{3}{2} $$ ### Exam Strategy & Shortcut To avoid rewriting steps, group operations mentally. In the numerator, identify $4 \div 2 \times 3$ as a single operational block resulting in 6. In the denominator, identify $3 \times 2 \div 3$ as another block resulting in 2. You immediately get $\frac{3+6}{4+2} = \frac{9}{6} = \frac{3}{2}$. Speed comes from isolating multiplication/division chains from the addition terms. ### Common Pitfall The most common trap is ignoring left-to-right execution for Division and Multiplication. In the denominator ($4 + 3 \times 2 \div 3$), a student might wrongly divide $2 \div 3$ first to get a fraction, complicating the sum. Always process $\times$ and $\div$ sequentially from left to right. ### Final Answer **Therefore, the correct answer is \frac{3}{2}.**