Ratio and Proportion Calculator
Solve direct and inverse proportions for the unknown (the rule of three), reduce a ratio to its simplest form, or share a total directly or inversely in given proportions, with the working shown.
- Proportiona / b = c / x
- Solutionx = 200 × 10 ÷ 4 = 500
- Unit rate (b ÷ a)50
How it is calculated
A ratio compares two quantities (a : b or a / b); a proportion says two ratios are equal. In direct proportion the quotient stays fixed: double the quantity and its counterpart doubles. In inverse proportion the product stays fixed: double the workers and the time halves. The rule of three finds a fourth value from three known ones by cross-multiplying. To simplify a ratio, divide both terms by their greatest common divisor; decimal terms are scaled to whole numbers first (1.5 : 2.25 = 150 : 225 = 2 : 3).
a / b = c / x → x = b × c ÷ a · a × b = c × x → x = a × b ÷ ca: known quantity · b: what goes with a · c: new quantity · x: what goes with c (the unknown). The first is direct, the second inverse proportion.- Decide which two quantities go together (people and flour, workers and days).
- If one rises in step with the other, pick direct; if it falls, pick inverse proportion.
- Put the known pair in a and b and the new quantity in c; x is worked out.
- When sharing, each part is in proportion to its ratio number (or to its inverse): part = total × ratio ÷ sum of ratios.
Example
If a recipe for 4 needs 200 g of flour, 10 people need x = 200 × 10 ÷ 4 = 500 g (direct). If 4 workers finish a job in 12 days, 6 workers take x = 4 × 12 ÷ 6 = 8 days (inverse). Sharing ₺1,200 as 2 : 3 : 5 gives 1,200 ÷ 10 = ₺120 per part: ₺240, ₺360 and ₺600.
Frequently asked questions
How do I tell direct from inverse proportion?
See what happens to one when the other grows. More people need more ingredients: direct. Higher speed means a shorter trip: inverse, since speed × time = distance stays fixed.
How do I use proportion with a map scale?
If 3 cm on the map is 45 km, then 7 cm is x = 45 × 7 ÷ 3 = 105 km. On a 1 : 25,000 map, 4 cm is 4 × 25,000 = 100,000 cm = 1 km.
How does inverse sharing work?
The parts follow the inverses of the ratio numbers. Sharing ₺1,200 inversely as 2, 3 and 5: 1/2 + 1/3 + 1/5 = 31/30, so each unit gets 1,200 ÷ 31/30 ≈ ₺1,161.29 and the parts are about ₺580.65, ₺387.10 and ₺232.26. The smallest number gets the largest part.
How do I simplify a ratio?
Divide both terms by their greatest common divisor. For 18 : 24 that is 6, giving 3 : 4. The value stays the same: 18 ÷ 24 = 3 ÷ 4 = 0.75.
What is the rule of three?
It finds the fourth value of a proportion from three known ones: write a / b = c / x and cross-multiply to a × x = b × c, so x = b × c ÷ a. Schools teach a direct and an inverse version.