$6425 \div 125 \times 8 = x$

### Concept & Logic Follow the standard BODMAS/PEMDAS sequence, evaluating from left to right for multiplication and division. However, knowing fraction equivalents for large numbers (like $125$) can drastically reduce calculation time. ### Step-by-Step Solution * **Given:** $$ 6425 \div 125 \times 8 = x $$ * **Calculation:** Process the division first. $$ \frac{6425}{125} = 51.4 $$ * Multiply the quotient by $8$: $$ 51.4 \times 8 = 411.2 $$ ### Exam Strategy & Shortcut This problem is engineered for a specific shortcut. Notice that $125 = \frac{1000}{8}$. Substitute this into the expression: $$ x = 6425 \div \left(\frac{1000}{8}\right) \times 8 $$ Dividing by a fraction is the same as multiplying by its reciprocal: $$ x = 6425 \times \left(\frac{8}{1000}\right) \times 8 $$ $$ x = \frac{6425 \times 64}{1000} $$ Alternatively, a faster mental shortcut: $6425 \div 125$ is the same as multiplying $6425 \times 8$ and dividing by $1000$. $6425 \times 8 = 51400$. $51400 \div 1000 = 51.4$. Finally, multiply by $8$: $51.4 \times 8 = 411.2$. ### Common Pitfall Multiplying $125 \times 8$ first to get $1000$, and then doing $6425 \div 1000 = 6.425$. Division and multiplication have the same precedence and must be executed left-to-right unless parentheses dictate otherwise. ### Final Answer **Therefore, the correct answer is 411.2.**