Given $168 \times 32 = 5376$, then $5.376 \div 16.8$ is equal to

### Concept & Logic Multiplication and division are inverse operations. If $A \times B = C$, then $C \div A = B$. Decimal points shift this base result by powers of $10$. ### Step-by-Step Solution * Start with the given base relationship: $$ 168 \times 32 = 5376 $$ This can be rewritten as: $$ \frac{5376}{168} = 32 $$ * The target expression to evaluate is: $$ \frac{5.376}{16.8} $$ * Convert the decimal numbers to their integer equivalents with powers of $10$: $$ = \frac{5376 \times 10^{-3}}{168 \times 10^{-1}} $$ * Group the integers and simplify the powers: $$ = \left( \frac{5376}{168} \right) \times 10^{(-3 - (-1))} $$ $$ = 32 \times 10^{-2} $$ $$ = 0.32 $$ ### Exam Strategy & Shortcut The dividend $5.376$ has $3$ decimal places, and the divisor $16.8$ has $1$ decimal place. The quotient will have $3 - 1 = 2$ decimal places. Apply this to the base integer answer of $32$ to get $0.32$. ### Common Pitfall Miscounting the net decimal places. If a student adds the decimal places instead of subtracting them during division, they might choose $0.0032$ or a similarly incorrect option. ### Final Answer **Therefore, the correct answer is $0.32$.**