Difference Method
💡To compare two fractions, form a new fraction from the gaps between their tops and bottoms, then compare that with the smaller original.
Try it — estimate a fraction
liveKeep the first two significant digits, then divide.
- 1
Truncate both to two significant digits
4,873 → 4,800, 61,200 → 61,000
- 2
Divide the trimmed numbers
4,800 / 61,000 ≈ 0.08
- 3
As a percentage
≈ 7.87% (exact 7.96%)
⏱️ Practice against the clock
A worked example
Comparing 61/240 and 65/250: the difference fraction is 4/10 = 40%. Since 40% is larger than the base fraction, the second one is bigger.
Compare the gap instead
To tell which of two close fractions is bigger, do not work them both out. Build a fraction from the differences of the tops and bottoms and compare that. For 61/240 against 65/250, the gaps are 4 and 10, so the new fraction is 4/10, or 40%.
That 40% beats the roughly 25% you started with, which means the slice you are adding is richer than the original. So 65/250 is the bigger one.
When it is worth the bother
This pays off when two fractions are neck and neck and all you want is which one wins, not their exact sizes. One quick comparison does the job of two full divisions.
It will not hand you the actual values, and it does not need to. Most data questions are really asking which is bigger, so answer that and move on.
Questions people ask
When is the difference method worth using? ▾
When two fractions are close and you only need to know which is larger, not their exact values. It replaces two divisions with one quick comparison.
Does it tell me the actual values? ▾
No, and that is the point. It answers "which is bigger?" directly, which is often all a data-analysis question is really asking.