Number and algebra form the foundation of Junior Cycle maths. This post covers all the key definitions you need to know — from number types and properties to the building blocks of algebra.

Number Types & Properties

Natural Numbers (ℕ)

The counting numbers: 1, 2, 3, 4, …

**Watch out! 0 is not a natural number.

Integers (ℤ)

All whole numbers, positive and negative: … −3, −2, −1, 0, 1, 2, 3, …

Watch out! Decimals and fractions are not integers.

Rational Numbers (ℚ)

Any number that can be written as a fraction a/b where a and b are integers and b ≠ 0:

½, ⅔, 5, 0.75, 0.333…

Watch out! This includes terminating and repeating decimals. The number 5 is rational because it can be written as 5/1.

Irrational Numbers (ℝ \ ℚ)

Numbers that cannot be written as a fraction. Their decimal expansion goes on forever without repeating:

√2, π, e, 0.30100100010…

Watch out! You must say both: non-terminating AND non-repeating. If the decimal repeats, it’s rational, not irrational.

Number Properties

Factor

A number that divides evenly into another number.

Example: The factors of 12 are 1, 2, 3, 4, 6, 12

Watch out! Factors are smaller than or equal to the number.

Multiple

The result of multiplying a number by any integer.

Example: The multiples of 3 are 3, 6, 9, 12, …

Watch out! Multiples are bigger than or equal to the number.

Prime Number

A natural number greater than 1 with exactly two factors: 1 and itself.

2, 3, 5, 7, 11, …

Watch out! 1 is NOT a prime — it only has one factor. Also, 2 is the only even prime.

Algebra Basics

Expression

A combination of numbers, variables, and operations with no equals sign.

Example: 3x + 5

The parts: 3 is the coefficient, x is the variable, 5 is the constant, and + is the operation.

Watch out! If it has ”=”, it’s an equation, not an expression.

Equation

A mathematical statement that two expressions are equal.

Example: 3x + 5 = 20

Watch out! Must have an equals sign. An equation can be solved; an expression cannot.

Variable

A letter or symbol used to represent an unknown or changing quantity.

Example: x in the expression 3x + 5

Constant

A fixed value that doesn’t change.

Example: 5 in the expression 3x + 5

Watch out! Constants can be any number — they’re the terms with no variable attached.

Study tip

Master these definitions for a strong foundation in maths! On the exam, use the correct terminology — saying “a number that divides evenly” is good, but saying “a factor is a number that divides evenly into another number” is better.

This post is based on an AI-generated infographic from Boomanotes — turn any study notes into visual revision aids.