Solve $1\frac{4}{5} + 20 - 280 \div 25 = x$

### Concept & Rule This problem is a direct test of the **BODMAS rule** mixed with **Fraction and Decimal Conversions**. To solve this efficiently, it is often easier to convert simple mixed fractions and division operations into decimals, perform the linear addition/subtraction, and convert back to a fraction if required by the options. ### Step-by-Step Solution **Calculation:** Step 1: Convert the mixed fraction into a decimal. $$ 1\frac{4}{5} = 1 + 0.8 = 1.8 $$ Step 2: Process the division component. $$ 280 \div 25 $$ To divide by 25 easily, multiply the number by 4 and divide by 100. $$ 280 \times 4 = 1120 \rightarrow \frac{1120}{100} = 11.2 $$ Step 3: Substitute the decimal values back into the equation. $$ 1.8 + 20 - 11.2 = x $$ Step 4: Perform addition and subtraction from left to right. $$ 21.8 - 11.2 = x $$ $$ x = 10.6 $$ Step 5: Convert the final decimal back to a mixed fraction. $$ 10.6 = 10 + \frac{6}{10} = 10\frac{3}{5} $$ ### Exam Strategy & Shortcut **Fraction Isolation:** Keep whole numbers and fractions separate to avoid creating large improper fractions. Equation: $1 + \frac{4}{5} + 20 - \frac{280}{25}$ Simplify $\frac{280}{25}$ by dividing by 5: $\frac{56}{5}$ Convert $\frac{56}{5}$ to a mixed fraction: $11\frac{1}{5}$ Now evaluate: $(1 + 20 - 11) + (\frac{4}{5} - \frac{1}{5})$ Whole numbers: $21 - 11 = 10$ Fractions: $\frac{3}{5}$ Combine: $10\frac{3}{5}$. This skips decimals entirely! ### Common Pitfall Students often convert everything into a massive single fraction, calculating $\frac{9}{5} + \frac{100}{5} - \frac{56}{5}$. While this works here because the denominators happen to align easily to 5, it forms a bad habit that wastes time on harder questions. Treat whole numbers and fractional parts independently when adding or subtracting. ### Final Answer **Therefore, the correct answer is $10\frac{3}{5}$.**