A proportion says that two ratios are equal: if 3 notebooks cost 7.50, then 8 notebooks cost 7.50 × 8 ÷ 3 = 20. Type the three numbers you know and the calculator finds the fourth, shows the cross-multiplication step by step, and checks the answer by comparing the two ratios. Switch to an inverse proportion for problems where more of one thing means less of the other.
Everyday proportions, worked out
| Problem | Kind | Set-up | Answer |
|---|---|---|---|
| A recipe for 4 needs 200 g of flour. For 6? | Direct | 4 : 200 = 6 : x | 300 g |
| 3 notebooks cost 7.50. And 8? | Direct | 3 : 7.50 = 8 : x | 20 |
| A map at 1 : 25,000: what is 4 cm? | Direct | 1 : 25,000 = 4 : x | 100,000 cm = 1 km |
| A car uses 6 L per 100 km. For 350 km? | Direct | 100 : 6 = 350 : x | 21 L |
| 3 workers take 8 days. 4 workers? | Inverse | 3 × 8 = 4 × x | 6 days |
| At 60 km/h the trip takes 2 h. At 80 km/h? | Inverse | 60 × 2 = 80 × x | 1.5 h |
In a direct proportion, the amount per unit stays fixed (2.50 per notebook, 0.06 L per km). In an inverse proportion, the product stays fixed (24 worker-days, 120 km).
The method in three lines
- Write the two ratios side by side: A / B = C / X.
- Cross-multiply: A × X = B × C.
- Divide by A: X = B × C ÷ A.
For an inverse proportion the rule changes to A × B = C × X, so X = A × B ÷ C. Mixing the two up is a common slip in homework: always ask first whether doubling one side doubles or halves the other.
When a proportion does not apply
Many real situations are only roughly proportional. Nine people cannot do in one month what takes one person nine, if the work cannot be split; a room twice as large needs twice the paint but not twice the brushes; and the price of a large pack is rarely the small price multiplied. A quick check is the per-unit figure in the results: if it would not stay the same in real life, the answer is an estimate, not a rule.
The calculator runs in your browser and works offline once the site is saved, handy in a kitchen, a workshop or a classroom without Wi-Fi.
Frequently asked questions
How do I solve a proportion?
Write it as two equal fractions, cross-multiply and divide. 3/7.50 = 8/x gives 3 × x = 7.50 × 8 = 60, so x = 60 ÷ 3 = 20.
What is the rule of three?
The school name for the same method: three numbers are known, the fourth is found by multiplying two of them and dividing by the third. It is called regla de tres in Spanish and regra de três in Portuguese.
What is an inverse proportion?
When one amount goes up as the other goes down, and their product stays the same. If 3 workers need 8 days, 4 workers need 3 × 8 ÷ 4 = 6 days, as long as the work can be shared evenly.
How do I know whether it is direct or inverse?
Ask what happens when you double the first amount. If the second doubles too (twice the notebooks, twice the price), it is direct. If it halves (twice the speed, half the time), it is inverse.
Can a proportion have decimals or negative numbers?
Yes. The calculator accepts any numbers; only the known amount you divide by (A in a direct proportion, C in an inverse one) cannot be zero.
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