Convert any percentage to a simplified fraction with decimal equivalent
Converting percentages to fractions is an essential maths skill covered throughout the UK National Curriculum, from Key Stage 3 through to GCSE and beyond. Percentages, fractions, and decimals are three ways of expressing the same value, and being able to move fluently between them is a requirement of the AQA, Edexcel, and OCR GCSE maths specifications. Our percentage to fraction calculator converts any percentage to a fully simplified fraction, showing the decimal equivalent and complete working. Whether you are converting a whole number percentage like 25% or a decimal percentage like 33.33%, the calculator handles the simplification automatically using the greatest common divisor. This tool is designed for UK students revising for GCSE maths exams, teachers preparing lesson materials, and anyone who needs to quickly convert a percentage to its fraction form. The step-by-step formula display helps you understand the method so you can replicate it in exams without a calculator.
To convert a percentage to a fraction: 1. Enter the percentage value in the input field. You can enter whole numbers (like 25) or decimal percentages (like 33.33). Do not include the % symbol as it is added automatically. 2. Review the results panel, which displays the simplified fraction, the decimal equivalent, and the individual numerator and denominator values. 3. Check the "Working" output to see the full conversion process, from the original percentage over 100 to the final simplified fraction. 4. For percentages greater than 100% (like 150%), the result will be an improper fraction (3/2). For 0%, the result is 0/1. 5. Use the related calculators to convert back from fractions to decimals or to explore other number conversions.
The conversion formula is straightforward: divide the percentage by 100 to create a fraction, then simplify. Step 1: Write the percentage over 100. For example, 25% = 25/100. Step 2: Find the greatest common divisor (GCD) of the numerator and denominator. GCD(25, 100) = 25. Step 3: Divide both numerator and denominator by the GCD. 25/25 = 1, 100/25 = 4. So 25% = 1/4. For decimal percentages, an extra step is needed. Take 33.33% as an example: 33.33% = 33.33/100. Multiply numerator and denominator by 100 (to remove the decimal places): 3333/10000. Then simplify by the GCD. In this case GCD(3333, 10000) = 1, so the fraction remains 3333/10000. The decimal equivalent is simply the percentage divided by 100: 25% = 0.25, 50% = 0.5, 75% = 0.75. Common conversions worth memorising for GCSE exams include: 50% = 1/2, 25% = 1/4, 75% = 3/4, 20% = 1/5, 10% = 1/10, 33.3...% = 1/3, and 12.5% = 1/8. These appear frequently in non-calculator papers. Understanding percentage-to-fraction conversion is also important for ratio and proportion questions, probability, and data handling, where values may be given in different forms that need to be compared.