a student multiplied a number by 3/5 instead of 5/3. what is the percentage error in the calculation?
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A student multiplied a number by 3/5 instead of 5/3 — What is the
percentage error?
Quick Scoop
It’s one of those classic math slip‑ups that sneak into exams or homework! A student was meant to multiply a number by 5 3\frac{5}{3}35 but accidentally used 3 5\frac{3}{5}53 instead. The difference between those two fractions might look small, but the error in the result is actually quite large. Let’s unpack this carefully.
Step‑by‑step solution
Let the correct number be xxx.
- Correct result = x×53=5x3x\times \frac{5}{3}=\frac{5x}{3}x×35=35x
- Incorrect result = x×35=3x5x\times \frac{3}{5}=\frac{3x}{5}x×53=53x
Now, the error in calculation is:
Error=Incorrect result−Correct result\text{Error}=\text{Incorrect result}-\text{Correct result}Error=Incorrect result−Correct result
Substitute the values:
Error=3x5−5x3=x(9−2515)=−16x15\text{Error}=\frac{3x}{5}-\frac{5x}{3}=x\left(\frac{9-25}{15}\right)=-\frac{16x}{15}Error=53x−35x=x(159−25)=−1516x
Since we care about the percentage error in magnitude , we use:
Percentage error=∣Error∣Correct result×100\text{Percentage error}=\frac{|\text{Error}|}{\text{Correct result}}\times 100Percentage error=Correct result∣Error∣×100
=16x155x3×100=1615×35×100=64%=\frac{\frac{16x}{15}}{\frac{5x}{3}}\times 100=\frac{16}{15}\times \frac{3}{5}\times 100=64%=35x1516x×100=1516×53×100=64%
So, the percentage error is 64%.
That means the student’s answer is 64% less than the correct answer.
In simple terms
- The correct multiplier: 1.6667
- The wrong multiplier: 0.6
- The wrong result turns out to be much smaller — missing over half of the intended value.
Quick comparison table
| Parameter | Value/Expression |
|---|---|
| Correct multiplier | $$\frac{5}{3}$$ = 1.6667 |
| Wrong multiplier | $$\frac{3}{5}$$ = 0.6 |
| Correct result | $$\frac{5x}{3}$$ |
| Wrong result | $$\frac{3x}{5}$$ |
| Difference | $$-\frac{16x}{15}$$ |
| Percentage error | 64% |
Mathematical insight 🌟
This kind of mix‑up — inverting ratios — produces a very large relative error because fractions less than 1 and greater than 1 swap their impact drastically. A good mental check: if the question says “multiply by 5/3,” the result should increase, not decrease.
TL;DR
✅ A student multiplied by 35\frac{3}{5}53 instead of 53\frac{5}{3}35.
✅ The error in calculation = 64% (less than correct value). Information
gathered from public forums or data available on the internet and portrayed
here.
