Simplify ratios to their lowest terms with fraction and percentage equivalents
Ratios are a fundamental concept in UK maths education, forming a significant part of the GCSE maths specification under the "Ratio, Proportion, and Rates of Change" strand. Simplifying ratios to their lowest terms is a skill that students practise from Key Stage 3 onwards and is tested extensively in both foundation and higher tier GCSE papers. Our ratio simplifier calculator reduces any ratio to its simplest form by finding the greatest common divisor of all parts. It supports both 2-part ratios (like 12:8) and 3-part ratios (like 15:10:5), handles decimal ratios, and can scale ratios to a target value. The calculator also shows fraction and percentage equivalents for each part, along with a pie chart visualisation. Whether you are simplifying recipe proportions, solving exam questions on ratio and proportion, or comparing quantities in science or geography, this tool provides instant results with clear explanations. Teachers can use it to generate worked examples, and students can check their manual calculations during revision.
To simplify a ratio: 1. Enter the first value in "Part A" and the second value in "Part B". For example, to simplify 12:8, enter 12 and 8. 2. For a 3-part ratio (like 15:10:5), also enter the third value in "Part C". Leave Part C as 0 for 2-part ratios. 3. If you want to scale the ratio so that the largest part equals a specific number, enter that number in the "Scale largest part to" field. For example, scaling 3:4 with a target of 12 produces 9:12. 4. Review the results, which show the simplified ratio, the fraction each part represents of the total, and the percentage breakdown. 5. The pie chart provides a visual representation of the ratio, showing how the total is divided between the parts. 6. For decimal ratios like 2.5:5, the calculator automatically converts to whole numbers before simplifying (multiplying by 10 gives 25:50, which simplifies to 1:2).
Ratio simplification uses the greatest common divisor (GCD), calculated with the Euclidean algorithm. For a 2-part ratio a:b: 1. Find GCD(a, b) using repeated division. 2. Divide both parts by the GCD. Example: 12:8, GCD(12, 8) = 4, so 12/4 : 8/4 = 3:2. For a 3-part ratio a:b:c: 1. Find GCD(a, b) first. 2. Then find GCD(result, c). 3. Divide all three parts by the final GCD. Example: 15:10:5, GCD(15, 10) = 5, GCD(5, 5) = 5, so 15/5 : 10/5 : 5/5 = 3:2:1. For decimal ratios, the calculator first multiplies all parts by 10 raised to the power of the maximum number of decimal places across all parts. For 2.5:5, multiply both by 10 to get 25:50, then simplify to 1:2. The fraction of the total for each part is calculated as: part / (sum of all parts). For 3:2, Part A = 3/5 and Part B = 2/5. The percentage is the fraction multiplied by 100: Part A = 60%, Part B = 40%. Scaling works by finding the factor needed so the largest simplified part equals the target: factor = target / largest part. Then multiply all parts by this factor. For 3:4 scaled to 12: factor = 12/4 = 3, giving 9:12. Ratio skills are essential for GCSE topics including sharing amounts in a given ratio, recipe scaling, map scales, similar shapes, and probability. Understanding how to simplify and scale ratios is also valuable in subjects like chemistry (molar ratios), food technology (recipe adjustment), and geography (map reading).