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A ratio shows how many times one quantity is of another; a proportion is an equality of two ratios. Scaling a recipe, converting a map scale to real distance, mixing solutions, or solving "if 3 people do it in 5 days, how long for 6" all rest on ratios and proportions. The tool does two jobs: it reduces a ratio to its simplest form, and it solves a proportion for the unknown.
Pick the mode, enter the numbers, and the simplified ratio or the unknown value appears instantly.
How is it calculated?
Two modes
1. Simplify a ratio (a : b): the two numbers are divided by their greatest common factor (GCF) to reach the simplest form. The ratio 18 : 24, divided by their GCF of 6, becomes 3 : 4. The tool also shows the percentage equivalent.
2. Solve a proportion (a/b = c/x): if two ratios are equal, cross-multiplication finds the unknown: a × x = b × c → x = (b × c) ÷ a. This is the "cross products" rule.
Direct and inverse proportion
- Direct proportion: as one rises the other rises in step (more fabric → more dresses). Solved by cross-multiplication.
- Inverse proportion: as one rises the other falls in step (more workers → less time). Here the products are constant (workers × time = constant); you must set the proportion up inversely.
Missing this distinction is the most common error: "if 6 workers finish in 4 days, how long for 12 workers" is inverse proportion — the answer is 2 days, not 8.
Where it is used
- Cooking: scaling a recipe up or down by servings.
- Maps/scale: at 1:100,000, how many km is 3 cm in reality.
- Mixtures: concrete, paint, fertiliser ratios.
- Work-rate problems: worker-time, speed-time calculations.
Worked example
Simplify 18 : 24: the GCF of the two numbers is 6, so dividing both gives 3 : 4 (about 43% to 57% as percentages). For a proportion: if a map shows 2 cm representing 5 km, how many km is 7 cm? In 2/5 = 7/x, cross-multiply: 2 × x = 5 × 7 → x = 35 ÷ 2 = 17.5 km. But note "if 6 workers finish in 4 days, how long for 12 workers" is INVERSE proportion — double the workers halves the time, so the answer is 2 days; mistaking it for direct proportion and answering 8 is the classic error.
FAQ
How do I simplify a ratio?+
Divide both numbers by their greatest common factor (GCF). The ratio 18 : 24 divided by its GCF of 6 becomes 3 : 4. The tool shows the simplified ratio and its percentage equivalent.
How do I solve a proportion for the unknown?+
By cross-multiplication in a/b = c/x: x = (b × c) ÷ a. For example 2/5 = 7/x gives x = (5 × 7) ÷ 2 = 17.5. This is the "cross products" rule.
What is the difference between direct and inverse proportion?+
In direct proportion one rises as the other rises; in inverse proportion one falls as the other rises. Worker-time problems are inverse: more workers means less time.
If 6 workers finish in 4 days, how long for 12 workers?+
2 days. This is inverse proportion: doubling the workers halves the time (workers × time is constant: 6×4 = 24 = 12×2). Mistaking it for direct proportion and answering 8 is a common error.
How do ratios relate to percentages?+
A ratio compares two quantities; a percentage expresses a ratio out of 100. The ratio 3:4 converts to 3/(3+4) = 43% to 57% as percentages.
How do I convert a map scale with a proportion?+
A scale is a proportion: at 1:100,000, 1 cm on the map is 100,000 cm = 1 km in reality. Multiply the map length by the scale to get the real distance.