Maths Guides
The methods behind the calculators, explained with worked examples and the mistakes that most often give a wrong answer.
Each guide covers one area of everyday maths: what the terms mean, how each calculation is done by hand, which method fits which question, and where common shortcuts go wrong. Every guide links to the calculators that apply it.
All guides
- Percentages The five everyday percentage calculations, percentage points versus percent, successive changes, and why reversing a percentage is not the same as applying it backwards.
- Markup and margin Why a 30% markup is not a 30% margin, how to convert between the two, pricing for a target margin, and how stacked discounts combine.
- Fractions, decimals and percentages Converting between the three forms, simplifying fractions, recognising terminating and recurring decimals, and avoiding rounding errors.
- Ratios and proportions What a ratio says, how to simplify one, how to share an amount in a ratio, and how to solve proportions for recipes, maps and mixtures.
- Mean, median and mode The three common averages and the range, how each is calculated, which to use when, and how outliers and ties change the answer.
- Factors, primes, GCD and LCM Finding factors and primes, prime factorisation, and how the greatest common divisor and least common multiple simplify fractions and solve scheduling problems.
How NumberUtils calculates
- Methodology The formula, accepted input and rounding behind every calculator.