a student multiplied a number by 3/5 instead of 5/3. what is the percentage error in the calculation?

June 28, 2026

Here’s a comprehensive, friendly‑explanatory styled post following your structure about the given problem.

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.