Algebra

Divisibility rules are quick tests that tell you whether one number divides evenly into another without having to do the full division.

Long division is a step-by-step written method for dividing large numbers, repeating the cycle of divide, multiply, subtract, and bring down.

Long multiplication breaks a multi-digit multiplication into smaller steps using partial products, then adds them together.

BODMAS gives the correct sequence for evaluating expressions with multiple operations: Brackets, Orders, Division, Multiplication, Addition, Subtraction.

Column addition lines up numbers by place value and adds from right to left, carrying any overflow into the next column.

Column subtraction lines up numbers by place value and subtracts from right to left, borrowing from the next column when needed.

An inequality compares two expressions using <, >, ≤ or ≥. Solving an inequality is like solving an equation, except that multiplying or dividing by a negative number reverses the inequality sign.

A linear equation is an algebraic equation where each term is either a constant or a single variable raised to the first power.

Substitution means replacing a letter (variable) in an expression with a given number and then calculating the result. It is used to evaluate formulae and check solutions to equations.

A system of equations is a set of two or more equations with the same variables, solved simultaneously.

A two-step equation needs exactly two operations to isolate the variable. Undo addition or subtraction first, then undo multiplication or division.

How to translate word problems into algebraic equations and solve them step by step.

To add or subtract fractions, first rewrite them with a common denominator (LCD), then add or subtract the numerators.

To divide by a fraction, multiply by its reciprocal — flip the second fraction and multiply.

Two fractions are equivalent when they represent the same value. Multiply or divide both the numerator and denominator by the same non-zero number.

Multiply fractions by multiplying numerator by numerator and denominator by denominator. No common denominator needed.

How to subtract fractions with the same and different denominators, including mixed numbers.

Foundation of mathematics covering numbers, expressions, equations, and problem-solving skills that build all higher mathematics.

Use the symbols <, >, and = to compare natural numbers, and arrange them in ascending or descending order using place value and the number line.

Every digit in a number has a place value — its position tells you how much it is worth. Learn to read, write, and expand large numbers up to millions.

Rounding replaces a number with a nearby "round" number that is easier to work with. Learn to round to the nearest 10, 100, 1 000, and 10 000.

Percent change measures how much a value has increased or decreased relative to its original value, expressed as a percentage.

A percentage is a fraction out of 100. To find a percentage of a number, multiply the number by the percentage divided by 100.

Simple interest is calculated on the original principal only. The formula I = PRT links the interest, principal, rate, and time. Compound interest is briefly introduced as interest on interest.

VAT (Value Added Tax) is a percentage added to a price. Discounts are percentages subtracted from a price. Knowing how to calculate both is an essential everyday maths skill.

Completing the square rewrites a quadratic expression ax² + bx + c in the form a(x + p)² + q. This technique is used to solve quadratics, find the vertex of a parabola, and derive the quadratic formula.

The discriminant of a quadratic equation determines how many and what type of roots the equation has.

The quadratic formula solves any quadratic equation ax² + bx + c = 0 by finding the roots in terms of a, b, and c.

Two quantities are in direct proportion when they increase and decrease at the same rate. If one doubles, the other doubles too. The relationship is written y = kx, where k is the constant of proportionality.

Two quantities are in inverse proportion when one increases as the other decreases by the same factor. The product of the two quantities is always constant, and the formula is y = k/x.

To divide a quantity in a given ratio, find the value of one part by dividing the total by the sum of the ratio parts, then multiply each ratio number by one part.

A ratio compares two quantities. A proportion states that two ratios are equal. Proportions are solved using cross-multiplication.