IS-over-OF Heuristic for Percentages
A simple heuristic to calculate what percent one number is of another by placing the part over the whole and dividing.
THE IDEA
IS-over-OF Formula
The IS-over-OF formula is a heuristic for converting a ratio to a percentage. It states:
IS / OF = decimal percentage
Then multiply by 100 to get the percent.
Example: Jelly Beans
In a jar of 90 jelly beans:
- Red: 45 beans → IS (45) over OF (90) = 0.5 → 50%
- Yellow: 36 beans → 36/90 = 0.4 → 40%
- Green: 9 beans → 9/90 = 0.1 → 10%
These percentages can then be converted to probabilities (0.5, 0.4, 0.1) and used in a Probability Tree.
When to use it
Calculating test scores as percentages (e.g., 45 correct out of 50 = 90%).
Determining discount percentages during shopping (e.g., $15 off $75 = 20% off).
Converting survey response counts to percentages (e.g., 120 out of 200 = 60%).
Computing probabilities from parts and whole in simple random experiments.
FROM THEORY TO EVERYDAY LIFE
In practice
Jelly Beans I
Compute the percentage of red, yellow, and green beans in a jar of 90 beans: red=45, yellow=36, green=9. Using IS-over-OF: red=45/90=50%, yellow=36/90=40%, green=9/90=10%.
A MOMENT TO REFLECT
Put it to work.
How can the IS-over-OF heuristic help you quickly estimate percentages in everyday situations?
Why is it important to correctly identify which number is 'IS' and which is 'OF'?
What other types of problems (besides jelly beans) could benefit from this heuristic?
CONTINUE THE CONVERSATION
Source texts
- The Thinkers Toolkit by Morgan D Jones