Ratios and Proportions Explained
6 min read · Updated September 26, 2026 · by the SolveCalcPro editorial team
A ratio compares two quantities. A proportion says two ratios are equal. Together they let you scale recipes, read maps, split costs and compare prices.
What a ratio looks like
You can write the ratio of 2 cups flour to 3 cups milk as 2 : 3, 2/3 or “2 to 3”. Ratios can compare parts to parts (2 : 3) or a part to the whole (2 out of 5, or 2 : 5).
Simplifying a ratio
Divide both parts by their greatest common factor. 12 : 18 has a GCF of 6, so it simplifies to 2 : 3. Check with the GCF calculator for larger numbers.
Solving a proportion
If 2 : 3 = 10 : x, cross-multiply: 2 × x = 3 × 10, so x = 30 ÷ 2 = 15. The ratio calculator shows the same steps.
Map example: a scale of 2 cm : 30 km means 7 cm on the map is 7 × 15 = 105 km.
Unit rates
A unit rate compares a quantity to 1 of something. If 3 kg of apples cost $9, the unit rate is $3 per kg, so 7 kg cost $21. Unit rates make it easy to compare deals: a 500 g pack at $2.40 costs $4.80 per kg, and a 750 g pack at $3.30 costs $4.40 per kg, so the larger one is better value.
Splitting in a ratio
To share $200 in the ratio 3 : 2, add the parts (5), find one part (200 ÷ 5 = 40), then multiply: $120 and $80.
Direct and inverse proportion
In direct proportion, when one quantity doubles so does the other (cost and weight). In inverse proportion, when one doubles the other halves (speed and time for a fixed distance): 60 km/h takes 2 hours, so 120 km/h takes 1 hour.
Practice questions
Test yourself, then tap to check. Answers are calculated by the tools linked below.
- A recipe uses 3 eggs for 5 cups of flour. How many eggs for 20 cups?
Show answer
5 : 3 = 20 : x, so x =: 12
- What is 35% of 240?
Show answer
35% of 240: 84
- How many kilometres is a 26.2-mile marathon?
Show answer
26.2 mi in km: 42.1648128
Frequently asked questions
What is the difference between a ratio and a fraction?
A fraction is a part of one whole. A ratio can compare any two quantities, including part to part.
How do I know if two ratios are equal?
Cross-multiply. If A × D = B × C then A : B = C : D.
How are ratios related to percentages?
A part-to-whole ratio multiplied by 100 is a percentage: 3 : 4 is 75%.
Can ratios have more than two parts?
Yes. A concrete mix might be 1 : 2 : 3 cement, sand and gravel.
Try it yourself
Ratio CalculatorSolve proportions like A : B = C : x and simplify ratios.
Percentage CalculatorFind a percent of a number, percent change, and increases or decreases.
Unit ConverterConvert length, mass, temperature, volume, area and speed between metric and imperial units.Keep learning
How to Calculate Percentages7 min readHow to Convert Units6 min readHow to Simplify Fractions5 min readWritten and reviewed by the SolveCalcPro editorial team. Spot a mistake? Tell us. See our editorial policy.