HOTmaths dictionary

This illustrated dictionary offers free access to over several hundred mathematical symbols, terms and definitions from the early secondary syllabus.

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Term

Definition

data

numerical information (statistics) gathered by observation, survey or measurement

Term	Definition
datum	one score or piece of information; the singular form of data (a datum or lots of data).

Related links:
Representing data — Dot plots

Term

Definition

decagon

a ten-sided polygon

Related links:
2D shapes — Plane shapes
3D shapes — Drawing solids

Term

Definition

decimal

a number of the base-ten standard numbering system, usually with a decimal point and expressing tenths, hundredths, thousandths and so on (see also decimal currency)

Related links:
Number theory — Square roots
Fractions — Adding and subtracting mixed numerals
Decimals — What is the point?
Decimals — Changing decimals to fractions
Decimals — Changing fractions to decimals
Decimals — Ordering decimals
Decimals — Adding decimals
Decimals — Subtracting decimals
Decimals — Multiplying and dividing by powers of 10
Decimals — Multiplying decimals
Decimals — Decimals of a quantity
Decimals — Dividing decimals by whole numbers
Decimals — Dividing by a decimal
Decimals — Rounding decimals
Decimals — Recurring decimals
Decimals — Money
Percentages — Changing percentages to decimals
Percentages — Changing decimals to percentages
Percentages — Percentage/fraction/decimal connection
Algebra — Substitution
Length, perimeter and area — Converting area units and estimating
Time — Time on a calculator
Pythagoras' theorem — Pythagoras, perimeter and area
Equations and inequalities — A formal approach
Circles and cylinders — Volume of a cylinder

Term	Definition
decimal currency	money system based on the decimal system Example Australian currency is a decimal currency where one dollar ($1) is equivalent to one hundred cents (100c).

Related links:
Decimals — Money

Term

Definition

decimal point

symbol that separates the whole part of a number from its fractional part

Examples
In Australia, a full point is used (37.453). Countries such as Britain use a raised full point (34

543). European countries use a decimal comma in place of the point (37,453). This number is read as "thirty seven point four five three".

Related links:
Decimals — What is the point?
Percentages — Changing percentages to decimals
Percentages — Changing decimals to percentages
Length, perimeter and area — Areas of rectangles and squares

Term	Definition
decomposition	method of subtraction in which 1 is traded to give you 10 more in the previus column Example

Related links:
Whole numbers — Subtracting whole numbers
Decimals — Subtracting decimals

Term

Definition

decrease

to make smaller; to take off (see also reduce, subtraction, discount)

Decrease 15 by 6 means:
15 − 6 = 9

Related links:
Decimals — Decimals of a quantity
Representing data — Scatter diagrams
Applying percentages — Increasing and decreasing using percentages

Term

Definition

degree
(° angle)

unit of measurement for angles, based on dividing a circle into 360 equal parts

Related links:
Time — Time on a calculator
2D shapes — Angle sum of a triangle
2D shapes — Exterior angles of triangles
2D shapes — Angle sum of a quadrilateral
Angles — How to name an angle
Angles — How to measure an angle
Angles — Types of angles
Angles — Angle theorems
Angles — Angles in parallel lines
Representing data — Sector graphs
Exploring geometry — Exploring trapeziums and kites
Exploring geometry — Exploring parallelograms and rectangles
Exploring geometry — Exploring rhombuses and squares
Exploring geometry — Constructing lines and angles

Term

Definition

degree
(° temperature)

unit of measurement for temperature (°C, °F)

Related links:
Integers — What are directed numbers?
The number plane — Plotting positive integers

Term

Definition

denominator

the bottom part of a fraction (which expresses the number of equal parts into which the whole unit is divided)

Related links:
Fractions — What is a fraction?
Manipulating algebra — Algebraic fractions

Term

Definition

descending order

from largest to smallest (the reverse of ascending order)

Example
Arranging 6, 3, 7, −5, 4 in descending order, the answer is 7, 6, 4, 3, −5.

Related links:
Integers — What are directed numbers?

Term	Definition
diagonal	a straight line drawn between one vertex of a shape and another vertex that is not adjacent A diagonal cannot be one of the edges of the shape.

Related links:
2D shapes — Plane shapes
2D shapes — Classifying quadrilaterals
Pythagoras' theorem — Pythagoras, perimeter and area
Exploring geometry — Exploring trapeziums and kites
Exploring geometry — Exploring parallelograms and rectangles
Exploring geometry — Exploring rhombuses and squares
Exploring geometry — Constructing lines and angles

Term

Definition

diameter

a line interval passing through the centre of a circle with its end points on the circumference

The diameter is twice as long as the circle's radius).

Related links:
2D shapes — Line of symmetry
Circles and cylinders — Pi and the circumference
Circles and cylinders — Area of a circle

Term	Definition
difference	the result of subtraction Example The difference between 13 and 9 is 4, since 13 − 9 = 4.

Related links:
Fractions — Adding and subtracting fractions
Fractions — Adding and subtracting mixed numerals
Decimals — Subtracting decimals
Integers — Adding and subtracting integers
Algebra — Words into algebra
Algebra — Adding and subtracting terms
Equations and inequalities — Equations to solve problems
Manipulating algebra — Reading algebra
Analysing data — The mode, the median and range
Analysing data — Analysing stem-and-leaf plots

Term

Definition

digit

one of the numerical symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9

Example
The number 2691 is made up of the digits 2, 6, 9 and 1.

Related links:
Whole numbers — Place value and expanded notation
Number theory — Divisibility tests
Decimals — Recurring decimals
Measuring solids — Capacity
Time — Timetables and charts
Representing data — Stem-and-leaf plots
The number plane — Comparing lines and equations

Term

Definition

digital clock

a modern type of clock that displays the time as digits

Related links:
Time — Time of day

Term	Definition
dimension	a magnitude (size) showing the extent of a set of points A single point has 0 dimensions. A line has 1 dimension (length). A flat surface has 2 dimensions (length, breadth). A solid or volume has 3 dimensions (length, breadth, depth).

Related links:
Length, perimeter and area — Converting area units and estimating
Measuring solids — Volume of rectangular prisms
Measuring solids — Volume of any prism
Measuring solids — Surface area
Measuring solids — Capacity
2D shapes — Plane shapes
3D shapes — Faces, edges and vertices
Circles and cylinders — Volume of a cylinder

Term

Definition

directed number

a number with a positive or negative sign, indicating that it is measured in a certain direction from zero along a number line

Example

Measuring temperature above and below zero degrees

Related links:
Integers — What are directed numbers?
Integers — Adding and subtracting integers
Integers — Two signs together
Integers — Multiplying integers
Integers — Dividing integers
Integers — Mixing the operations
The number plane — Plotting positive integers
The number plane — Extending the number plane
The number plane — Graphs from equations
The number plane — Equations from lines
The number plane — Comparing lines and equations
The number plane — Intersecting lines

Term

Definition

discount

an amount subtracted from a price, usually to sell goods faster

Examples
Items on sale might be advertised as HALF PRICE or as 20% OFF.

Related links:
Applying percentages — Percentage of a quantity
Applying percentages — Finding the whole amount

Term	Definition
discrete data	data that can be counted; measurements where only certain values can occur Examples The number of children in a family The number of times you catch a bus

Related links:
Representing data — Line, conversion and step graphs
Representing data — Organising data into tables

Term	Definition
disjoint sets	sets without any elements in common; sets that have the empty set as their intersection Example These two sets are disjoint sets because they have no elements in common.

Related links:
Set theory — Applying Venn diagrams
Set theory — Set relationships and Venn diagrams

Term

Definition

distance

how far apart two objects are (length)

Related links:
Integers — Multiplying integers
Length, perimeter and area — Measuring length
Length, perimeter and area — Perimeter
Angles — Points, lines and intervals
Representing data — Scatter diagrams
Representing data — Travel graphs
Congruent and similar shapes — Drawing similar figures
Ratios and rates — Rates

Term	Definition
distributive law	adding numbers then multiplying the total gives the same answer as multiplying each number first then adding the products (see also expanding) Examples (4 + 5) × 7 = (4 × 7) + (5 × 7) (3 − b) × c = (3 × c) − (b × c)

Related links:
Whole numbers — Multiplying whole numbers

Term	Definition
divided bar graph	a rectangle divided into smaller rectangles along its length in proportion to the data

Related links:
Representing data — Divided bar graphs

Term

Definition

dividend

the number being divided (see also division)

Related links:
Whole numbers — Dividing whole numbers
Whole numbers — Long division methods

Term	Definition
divisibility test	a way to determine whether a whole number is divisible by another whole number, without actually doing the division Example To test whether a number is divisible by 3, check whether the sum of its digits is divisible by 3: 57 is divisible by 3 since 5 + 7 = 12, and 12 is divisible by 3.