Guides
Plain explanations of the methods behind the calculators — the formulas, the worked examples, and the places people usually go wrong. Every guide links to the tool that does the same job for you.
Percentages
How to Calculate a Discount, Percent Off, Tax and TipThe mental shortcuts for percentages off, adding sales tax and working out a tip, plus what to do when two…X Out of Y as a PercentageTurn any score into a percentage: 15 out of 20, 26 out of 30, 20 out of 25 and the…How to Calculate PercentageHow to calculate percentage: divide the part by the whole, then multiply by 100. The percentage formula, finding a percentage…How to Calculate Percentage IncreaseThe percentage increase formula is (new − old) ÷ old × 100. Learn how to calculate percentage increase and decrease,…Percentage of a PercentageHow to find a percentage of a percentage: convert both to decimals and multiply. Examples, stacked discounts, repeated changes and…Percent Difference vs Percent ChangePercent difference vs percent change: the percent difference formula, when to use each one, worked examples, and why 40 and…
Fractions
How to Divide FractionsDividing fractions is multiplying by the reciprocal. This guide walks through fraction by fraction, whole numbers both ways, and mixed…Fraction to Decimal ChartA printable fraction to decimal chart for halves through sixteenths, plus how to convert in both directions and how to…How to Multiply FractionsHow to multiply fractions: multiply across, cancel common factors first, and handle whole numbers, mixed numbers, area models and word…How to Add FractionsHow to add fractions with the same or different denominators, add mixed numbers, and subtract fractions, with worked examples and…How to Simplify FractionsHow to simplify fractions to lowest terms using the GCF, repeated division or prime factors, with improper fractions, mixed numbers…Equivalent FractionsEquivalent fractions name the same amount, like 1/2, 2/4 and 3/6. Learn to make them, find a missing number, test…
Factors & primes
What Is a Prime Number?What is a prime number? A whole number above 1 whose only factors are 1 and itself. See the 25…Prime and Composite NumbersPrime and composite numbers explained: how to tell them apart, why 0 and 1 are neither, the composite numbers to…How to Find GCF and LCMHow to find the GCF and LCM of two or more numbers: listing factors and multiples, prime factorization, the ladder…
Number basics
What Are Integers? Definition, Examples and Sign RulesWhat are integers? The whole numbers, their negatives and zero. See examples, how integers sit on the number line, and…Rational NumbersRational numbers are any number you can write as a fraction of two integers. See examples, how to spot one…Whole Numbers and Natural NumbersWhole numbers are 0, 1, 2, 3 and up; natural numbers are the counting numbers. See where 0 fits under…Number Line – How to Read, Plot and Calculate on OneA number line puts every number at a point on a straight line. Learn to read its scale, plot fractions…Place Value – Charts for Whole Numbers and DecimalsPlace value is what a digit is worth based on its position. See place value charts for whole numbers and…
Arithmetic
Negative Number RulesThe sign rules for negative numbers, why subtracting a negative adds, and how the number line makes every case obvious.…Commutative Property and Associative PropertyThe commutative property and associative property, with examples for addition and multiplication, why subtraction breaks them, and the identity property.Distributive PropertyThe distributive property explained: a(b + c) = ab + ac, why it works, how to use it for mental…How to Do Long DivisionHow to do long division step by step: divide, multiply, subtract, bring down. Worked examples with remainders, zeros, two-digit divisors…
Decimals
Exponents & roots
Exponent RulesExponent rules explained: the product, quotient and power rules, zero and negative exponents, and fractional exponents, with worked examples and…Scientific NotationScientific notation writes any number as a × 10ⁿ. Learn to convert large and small numbers both ways, then multiply,…Square Root of 2The square root of 2 is about 1.41421356. See √2 to 100 decimal places, a simple proof that it is…
Rounding
Averages
How to Calculate Your Final GradeWork out a final grade when assignments carry different weights, convert the result to a letter grade, and find the…How to Find the Mean and AverageThe four averages, the formula for each, and how to pick the right one. Covers why the mean misleads on…How to Find Median ValuesHow to find the median: sort the numbers and take the middle one, or average the middle two. Examples for…How to Find ModeHow to find mode in any data set: tally the values, pick the one that appears most often, and handle…How to Find the RangeHow to find the range of a data set: subtract the smallest value from the largest. Examples with negatives and…