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Arithmetic

Numbers, fractions, percentages and the order of operations.

Lessons

Introductory Order of operations Brackets, powers, multiply/divide, add/subtract, and why the order is not optional. 3 + 4 * (2 - 1)^2 Introductory Fractions Adding, subtracting, multiplying and dividing fractions with a common denominator. 1/2 + 1/3 Introductory Percentages Per cent means per hundred; every percentage problem is a fraction over 100. what is 15% of 80 Introductory Powers and roots Exponent rules and simplifying square roots exactly. sqrt(50)

Arithmetic is where every other branch gets its numbers. Type any calculation and watch it evaluated one operation at a time, brackets first, then powers, then multiplication and division, then addition and subtraction.

More lessons

Whole Numbers

Introduction to Whole NumbersAdd Whole NumbersSubtract Whole NumbersMultiply Whole NumbersDivide Whole Numbers

Integers

Introduction to IntegersIntroduction to IntegersAdd IntegersSubtract IntegersMultiply and Divide IntegersSolve Equations Using Integers; The Division Property of Equality

Fractions

Introduction to FractionsVisualize FractionsMultiply and Divide FractionsMultiply and Divide Mixed Numbers and Complex FractionsAdd and Subtract Fractions with Common DenominatorsAdd and Subtract Fractions with Different DenominatorsAdd and Subtract Mixed NumbersSolve Equations with Fractions

Decimals

Introduction to DecimalsDecimalsDecimal OperationsDecimals and FractionsSolve Equations with DecimalsAverages and ProbabilityRatios and RateSimplify and Use Square Roots

Percents

Introduction to PercentsUnderstand PercentSolve General Applications of PercentSolve Sales Tax, Commission, and Discount ApplicationsSolve Simple Interest ApplicationsSolve Proportions and their Applications

The Properties of Real Numbers

Introduction to the Properties of Real NumbersRational and Irrational NumbersCommutative and Associative PropertiesDistributive PropertyProperties of Identity, Inverses, and ZeroSystems of Measurement

Metric Measurement

The Metric SystemMeasuring AreaMeasuring VolumeMeasuring WeightMeasuring Temperature

Numbers

ArithmeticFractionDecimalPercentageRatioIntegerRational numberIrrational numberReal numberPrime numberNumber lineRoundingScientific notationUnit of measurement

Some of these lessons are adapted from open texts: OpenStax Contemporary Mathematics, OpenStax Prealgebra 2e, Wikipedia. Each lesson page names its source and licence.

Symbols used here

Tap any symbol for the full definition, a picture, and what every letter in it means.

Questions people ask

Why does the order of operations matter?

Because 2 + 3 × 4 would otherwise be two different numbers. The convention (brackets, exponents, multiplication and division, addition and subtraction) exists so every reader gets the same value from the same expression.

How do I check an arithmetic answer?

Estimate first (round every number and compute roughly), then compare. If the estimate and the exact answer disagree by more than a little, one of them is wrong. The solver shows every operation, so you can find which line went astray.

Why are fractions harder than decimals?

They are not harder, they are more exact: 1/3 is a precise number, 0.333 is an approximation. Fractions need a common denominator to add, which is the one extra step people trip on.

Have a problem of your own?
Type it or draw it on the solver page: every step, a picture, the answer hidden until you ask. Solve →

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