Ratio Calculator
Simplify a ratio, or solve the proportion a:b = c:x for the missing value — recipes, scale models, mixing.
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Simplify a ratio
Solve proportion: a : b = c : x
How Ratio and Proportion Solving Works
A ratio compares two quantities and is simplified by dividing both sides by their greatest common divisor — 12:18 simplifies to 2:3 because both numbers divide evenly by 6. A proportion states that two ratios are equal (a:b = c:d) and is solved with cross multiplication: a × d = b × c. Rearranged to solve for an unknown x in a:b = c:x, this becomes x = (b × c) ÷ a.
Worked example: a recipe for 4 people needs 300 g of flour. To scale it for 7 people, set up the proportion 4:300 = 7:x, cross-multiply to get 4 × x = 300 × 7, then solve: x = 2100 ÷ 4 = 525 g. The same cross-multiplication logic underlies map scales — a 1:50,000 map means 1 cm on paper equals 50,000 cm (500 m) in reality, so measuring 3 cm on the map and solving 1:50,000 = 3:x gives a real-world distance of 150,000 cm (1.5 km).
What to Know
- Cross multiplication only works when the proportion is set up correctly. The order of terms matters — a:b = c:x must keep corresponding quantities on the same side (both "people" on one side, both "grams" on the other) or the result will be wrong.
- Recipes scale linearly, but not everything does. Doubling ingredients for double the servings works for flour and sugar, but cooking times, seasoning intensity, and leavening agents (like yeast or baking powder) often don't scale proportionally — proportion math handles quantities, not chemistry or timing.
- Map scale ratios compress huge distances into small numbers. A 1:50,000 scale means every 1 unit on the map represents 50,000 of the same unit in reality — always convert to a consistent unit (cm to cm, or inches to inches) before applying the ratio.
- Mixing ratios (paint, fuel, chemical solutions) use the same math. A 1:50 fuel-to-oil ratio means for every 50 parts of fuel, use 1 part oil — scale both sides by the same factor to get the volumes you actually need.
Frequently Asked Questions
How do I scale a recipe for a different number of servings?
Set up a proportion: (original servings):(original amount) = (new servings):(x). For a recipe serving 4 that needs 300 g flour, scaling to 7 people gives 4:300 = 7:x. Cross-multiply: 4 × x = 300 × 7 = 2100, so x = 525 g. Apply the same ratio to every ingredient in the recipe.
How does cross multiplication actually work?
In a proportion a:b = c:d, cross multiplication states that a × d = b × c — you multiply diagonally across the equals sign. When solving for an unknown, say x in a:b = c:x, this becomes a × x = b × c, which rearranges to x = (b × c) ÷ a.
How do map scales like 1:50,000 actually work?
A 1:50,000 scale means 1 unit of measurement on the map equals 50,000 of that same unit in real life. So 1 cm on the map represents 50,000 cm (500 m) in reality. To find a real-world distance, measure the map distance in cm, then solve the proportion 1:50,000 = (measured cm):x.
How do I mix a 1:50 two-stroke fuel-to-oil ratio?
For every 50 parts of gasoline, add 1 part oil. Per liter (1000 ml) of gasoline: 1000 ÷ 50 = 20 ml of oil. Scale up proportionally — for 5 liters of gasoline, use 100 ml of oil (5 × 20 ml).
What's the difference between a ratio and a proportion?
A ratio is a single comparison between two quantities (like 3:4). A proportion is a statement that two ratios are equal (like 3:4 = 6:8) — it's an equation used to find an unknown value when you know one ratio and part of another. Every proportion contains two ratios; a ratio alone doesn't imply any equation to solve.
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