Reduce $\frac{128352}{238368}$ to its lowest terms.

### Concept & Strategy Reducing massive fractions like $\frac{128352}{238368}$ using standard division or finding the HCF is too time-consuming for an aptitude exam. Instead, we reverse-engineer the problem using the given multiple-choice options. We assume one of the options is correct, which means its denominator multiplied by some factor $k$ equals $238368$, and its numerator multiplied by the same $k$ equals $128352$. ### Step-by-Step Solution * **Given:** The fraction $\frac{128352}{238368}$. * **Calculation / Deduction:** 1. First, quickly estimate the value of the fraction to eliminate wild options. $\frac{128}{238}$ is roughly $\frac{12}{24}$ or $\frac{1}{2}$ ($0.5$). 2. Check the options based on this estimate: $\frac{3}{4} = 0.75$ (Too big) $\frac{5}{13} \approx 0.38$ (Too small) $\frac{7}{13} \approx 0.53$ (Very close) $\frac{9}{13} \approx 0.69$ (Too big) 3. Option (c) is the only logical candidate. Let's verify it strictly. 4. If $\frac{7}{13}$ is the exact ratio, then $238368 \div 13$ should give us our exact multiplier $k$. $$238368 \div 13 = 18336$$ 5. Now multiply this multiplier $k$ by the numerator $7$: $$18336 \times 7 = 128352$$ 6. This perfectly matches the original numerator, confirming our ratio. ### Exam Strategy & Shortcut **Cross-Multiplication Unit Digit Check:** If $\frac{128352}{238368} = \frac{7}{13}$, then $128352 \times 13 = 238368 \times 7$. Check just the unit digits: Left side: $2 \times 3 = 6$. Right side: $8 \times 7 = 56$ (ends in $6$). The unit digits match perfectly. Doing this mentally takes 5 seconds and solidly confirms your estimation. ### Common Pitfall Students often attempt long division to find the HCF of $128352$ and $238368$. For six-digit numbers, this is a trap designed to drain your exam time. Never calculate the HCF directly if simple fractional options are provided. ### Final Answer **Therefore, the correct answer is $\frac{7}{13}$.**