Proportions & Scaling
Proportions compare two quantities and describe how they scale relative to each other.
Practice This ConceptUnderstanding Proportions & Scaling
A proportion says "A is to B as C is to D". If Germany exports 2.69× what France exports, that proportion holds regardless of the currency unit. Proportions are critical for reading EPSO data tables — you must quickly spot which country is 2× or 3× another.
Formula
$\frac{A}{B} = \frac{C}{D}$
Key Rules
- If A/B = C/D, then A×D = B×C (cross-multiplication)
- Doubling both the part and the whole keeps the proportion the same
- A ratio of 1:2 means the second is twice the first
- Proportions are unit-independent: 2:1 in millions = 2:1 in billions
Examples in Action
1
1576 : 586
=
2.69 : 1
German vs French exports
2
If 25% of 800 = 200
=
then 25% of 1600 = 400
Scaling: double the whole, double the part
3
3 : 5 = 6 : ?
=
10
Cross multiply: 3×? = 5×6 → ? = 10
Common Errors
- Comparing absolute numbers when proportions are asked
- Ignoring that different-sized countries need proportional comparison, not absolute
- Confusing "A is 3× B" with "A is 300% of B" (same thing, different framing)
Pro Tip
When EPSO shows data for countries of very different sizes, think "per capita" or "as a percentage" — not raw numbers.