$$ \frac{5 \times 1.6 - 2 \times 1.4}{1.3} = x $$

### Concept & Formula This problem requires the application of the BODMAS rule (Brackets, Orders, Division/Multiplication, Addition/Subtraction) combined with basic decimal arithmetic. Always perform multiplication before subtraction in the numerator. ### Step-by-Step Solution **Given:** $$ \frac{5 \times 1.6 - 2 \times 1.4}{1.3} $$ **Calculation:** * Step 1: Evaluate the multiplication terms in the numerator. $$ 5 \times 1.6 = 8.0 $$ $$ 2 \times 1.4 = 2.8 $$ * Step 2: Substitute these values back into the numerator and perform the subtraction. $$ 8.0 - 2.8 = 5.2 $$ * Step 3: Now divide the resulting numerator by the denominator. $$ \frac{5.2}{1.3} $$ * Step 4: To make the division easier, multiply both the numerator and the denominator by $10$ to remove the decimals. $$ \frac{52}{13} $$ * Step 5: Perform the final division. $$ \frac{52}{13} = 4 $$ ### Exam Strategy & Shortcut **Mental Math:** Treat the decimals like whole numbers during the multiplication phase, then place the decimal point back. For example, $5 \times 16 = 80$, so $5 \times 1.6 = 8.0$. Next, $2 \times 14 = 28$, so $2 \times 1.4 = 2.8$. $8.0 - 2.8 = 5.2$. When you see $5.2 / 1.3$, immediately recognize that $13 \times 4 = 52$. Thus, $5.2 / 1.3 = 4$. This bypasses the need for written division steps. ### Common Pitfall Subtracting before multiplying. A student ignoring BODMAS might calculate $1.6 - 2 = -0.4$, which completely derails the entire calculation. Always multiply first. ### Final Answer **Therefore, the correct answer is 4.**