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		A B C D E F G H I J K L M N O P Q R S T U V W Y Z Other online maths dictionaries: Intermath dictionary Maths Thesaurus, Cambridge Math dot com MathForum's maths words Eric's mathworld treasury A maths dictionary for kids Maths is fun A-Z guide Nrich topics Maths buster Gomath formula-to-go Earliest uses of maths words A dictionary of units of measurement Ronald Buelow's dictionary Saskaatchewan Education Algebra glossary Math League's dictionary Harcourt school maths glossary Words and terms sponsored by the Institute of Physics Maths symbols sponsored the Institute of Physics Statistics explained Statistics glossary The Oxford Mathematics Study Dictionary. Highly recommended. The best all round maths dictionary, helped with double-page spreads and colour. The Penguin Dictionary of mathematics. The Penguin dictionary. More advanced than the Oxford version, suitable for A-level students.
	A
	Algorithm	A set of instructions that can be repeated again and again.
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	B
	Base	Base, as in power. 3 is the base in 3⁵, 3 to the power 5, or, 3 x 3 x 3 x 3 x 3, or, 3 multiplied by itself five times. See also index and root.
	BODMAS	A reminder of the order in which operations have to carried out when working with equations and formulas. Brackets Order Division Multiplication Addition Subtraction Sometimes also called BIDMAS, where I stands for Indices.
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	C
	Common factor	A number that is a factor of two or more numbers. See also factor and highest common factor.
	Common fraction	A common fraction is written as two whole numbers, one above the other, separated by a horizontal line or dash. The denominator — the bottom number — cannot be 1 or 0. A common fraction represents a division to be done, the upper number to be divided by the bottom number. See also fraction, improper fraction, mixed number.
	Consecutive numbers	Whole numbers that follow on. 1, 2, 3,, 4... are consecutive numbers. 1837, 1838, 1839, 1840... are consecutive numbers. Consecutive numbers go in sequence from smallest to largest, one at a time.
	Co-prime	Two numbers which have a highest common factor of 1 are called co-prime numbers. See also prime numbers
	Cube root	Roots are the inverse or opposite of powers. 3³, or 3 cubed, or 3 x 3 x 3 = 27. So, the cube root of 27 = 3. The cube root of a number is always a positive. See alsosquare roots.
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	D
	Decimal fraction	Fractions of less than 1 expressed using the decimal place value system, extended to the right of the units column (separated by the decimal point) to give values for ¹/₁₀, ¹/₁₀₀, ¹/₁₀₀₀ and so on. For example, 0.735 means ⁷/₁₀ + ³/₁₀₀ + ⁵/₁₀₀₀ = ⁷³⁵/₁₀₀₀
	Denominator	The bottom number in a common fraction. For example, in the fraction ⁷/₁₀, 10 is the denominator, and 7 the numerator.
	Digit sum	The result when you add together all the digits in a number. The digit sum of 854 is 8 + 5 + 4 which equals 17. The digital root of a number is found by finding the digit sum of the digit sum, and repeating until only a single digit remains. So, the digital root of 854 is 1 + 7 which equals 8.
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	E
	Equation	Letters and numbers connected by the = sign. c=2 x pi is the equation for the circumference of a circle with a radius of 2 See also formula, expression, function, terms, like terms, substitute and symbol.
	Euclid's algorithm	A method for finding the highest common factor of two numbers. It is best explained by giving an example: Find the HCF of 64 and 24. First find the largest multiple of 24 which is less than 64: 64 = 2 x 24 + 16 The largest multiple is 48, remainder 16 to make 64. Now find the largest multiple of the remainder 16 which less than 24: 24 = 1 x 16 + 8 The largest multiple is 16, remainder 8 to make 24. Find the largest multiple of the remainder 8 which is less than or equal to 16: 16 = 2 x 8 + 0 The largest multiple is 2 x 8, remainder zero. When the remainder is 0, the last factor used is the highest common factor. In this example the HCF of 64 and 24 is 8. And who's Euclid? Click here to find out
	Expression	A mixture of numbers, letters and symbols, but not including the = sign. The symbols include +, -, x, �... but not = See also equation, formula, function, terms, like terms, substitute and symbol.
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	F
	Factor	A factor is a whole number that divides exactly into another larger whole number. So, 1, 2, 4 and 8 are the factors of 8. Two or more numbers can have a common factor. 16 and 8 have common factors 1, 2, 4 and 8. And where two or more numbers have more than one common factor, the numbers can have a highest common factor. The highest common factor of 8 and 16 is 8.
	Formula	A rule written using algebra instead of words. A general rule for working something out. c=pi x d is the formula for the circumference of a circle. See also equation, expression, function, terms, like terms, substitute and symbol. A formula for a sequence connects term to its position in the sequence.
	Fraction	A fraction is a measure of how something is to be divided up or shared out. Fractions are expressed as common fractions, decimal fractions, percentages or ratios. See also improper fraction and mixed number
	Function	A function is a rule which changes one number into another number. See also equation, expression, formula, terms, like terms, substitute and symbol.
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	G

	Gradient	Gradient is a measure of how much you go up as you go forward when you climb a hill. It is similar to steepness or slope The gradient of a hill is the vertical distance you climb Up divided by the horizontal distance you move forward or Across. Click to see A boardshot. If the hill's gradient does not change, you can measure the gradient anywhere on the hill. The distance Up divided by Across is a constant ratio, fraction, decimal fraction or percentage. A negative gradient... means you are going downhill! Gradients can be measured in percentages, decimal fractions or fractions. Remember if Gradient = Up/Across, then the distance you climb Up = Gradient/Across. Transposing the formula, The distance you move forward horizontally can be found from Up/Gradient. The gradient of a line drawn on a graph is a measure of its slop relative to the x-axis. On a graph with a y-axis and x-axis, the graph has a positive gradient if the line is pointing up as you move from left to right along the x-axis, and negative if it points down as move forward along the x-axis.
	H
	Hexagon numbers	Numbers which can be represented by dots formed into a regular hexagon, containing other regular hexagons. The first few hexagon numbers are 1, 6, 15, 28, 45... See also square numbers, and polygon numbers.
	Highest common factor (hcf)	The largest common factor of two or more numbers. See also factor and common factor. The highest common factor of 32, 16 and 8 is... 8. The common factors of 32, 16 and 8 are 1, 2, 4 and 8. See also Euclid's algorithm.
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	I
	Imaginary numbers	Imaginary numbers are the square roots of negative numbers. They are called imaginary because the square root of a negative number cannot be real. The square root of ^-1 is called i.
	Improper fraction	A common fraction in which the numerator — the top number — is bigger than the denominator — the bottom number. Sometimes called a top-heavy fraction. For example, ⁷/₅ or ¹⁵/₉. An improper fraction can be simplied into a mixed number. See also, fraction, common fraction and proper fraction.
	Index	Index, as in power. 5 is the index in 3⁵, 3 to the power 5, or, 3 x 3 x 3 x 3 x 3, or, 3 multiplied by itself five times. 3 is the base number. See also base, root and rules for indices.
	Integer	The numbers used in counting, including 0, with a negative or positive sign in front. Integers include the negative numbers. Integers are from the set of natural numbers 1, 2, 3, 4, 5... The natural numbers do not have have either a negative or positive sign. Integers are also called whole numbers, signed numbers or directed numbers.
	Irrational numbers	Numbers which can only be written as a never-ending, non-repeating decimal fraction. Irrational numbers cannot be written in the form of a fraction where the numerator and denominator are both integers, whole numbers. The square root of any prime number is irrational. And pi, the ratio between the circumference and diameter of a circle, is irrational. Rational numbers can be written as a fraction or as a decimal fraction with a recurring pattern.
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	J
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	K
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	L
	Like terms	Terms in a formula, equation or expression with exactly the same letters.
	Lowest Common Multiple, LCM	In the lists of multiples of two or more numbers, the Lowest Common Multiple (LCM) is the lowest number which is a multiple of all the numbers. For instance, the multiples of 3 are 3, 6, 9, 12, 15, 18.... and the multiples of 5 are 5, 10, 15, 20, 25 and so on. The multiple 15 is the first number which apears in both lists of multiples. 15 is the lowest common multiple of 3 and 5. See also multiples
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	M
	Mean	An average. Add all the numbers and divide the total by the number of numbers you added. So, the mean of 2, 6, 9, 11 is 2+6+9+11 divided by 4. The answer: 7. See also median, mode and range.
	Median	An average. The median is the middle number in a list of numbers, smalest first to biggest. So, the median of 2, 4, 7, 9, 12 is 7. If the list is made up of an even number of numbers, the median is mid-way between the two middle numbers. So, the median of 2, 4, 7, 9, 12, 15 is (7+9)/2, that is, 8. See also mean, mode and range.
	Mixed number	A number with two parts, a whole number followed by a proper fraction. For instance, 5⁷/₈ or -1³/₄. A mixed number can be negative.
	Mode	An average. The mode is the most frequent number appearing in a list of numbers. So, the mode of 1, 3, 4, 4, 7, 9, 10 is 4, which appears twice. If all the numbers in the list appear an equal number of times, then all the numbers are called the mode. See also mean, median and range.
	Multiples	A number multiplied by any other number. The multiple of a number is that number multiplied by any other number. For instance, the multiples of 6 are 6, 12, 18, 24... and so on. See also Lowest Common Multiple.
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	N
	Numerator	The top number in a common fraction. For example, in the fraction ⁷/₁₀, 7 is the numerator, and 10 is the denominator.
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P
Per cent, percentage	A type of fraction where the denominator — the bottom number — is 100. Per cent is a measure of the number of parts in every 100 parts. For example, 25 per cent means 25 in every 100 or ²⁵/₁₀₀. Common fractions, decimal fractions can also be expressed as percentages.
Perfect square	A perfect square is a number whose square root is a whole number.
Periodic decimal	See recurring decimal
Polygon numbers	Numbers which can be represented by dots arranged in the shape of a regular polygon. All the possible smaller similar polygons must be included inside. The number is named after the shape, and a sequence can be formed of all the numbers that can be represented by dots arranged into that shape. See also square numbers, and hexagon numbers.
Position	The location of a term in a sequence.
Power	Powers of numbers are made by repeated multiplication. Power, a number multiplied by itself a number of times. For instance, 3⁵ means 3 x 3 x 3 x 3 x 3. That is, 3 multiplied by itself 5 times. In this example the number 3 is the base, and 5 is the index. 3⁵ is said as "3 to the power 5", or, "3 raised to the power 5", or, the "fifth power of 3", or, "3 to the fifth". 3² is called "three squared." Squaring a negative number gives a positive number — (-2)² = +4 3³ is called "three cubed". The opposite of raising a number to a power, is taking the root of a number.
Prime factors	A prime number has only two factors — 1 and itself. Every number can be broken down into factors which are prime numbers. These are called Prime Factors. Every number can be expressed as the product of its Prime Factors. The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. The Prime factors of 24 are 2 and 3 — the only factors of 24 which are prime numbers. However, all the other factors of 24 have factors themeselves which are prime numbers. So, 24 = 2 x 2 x 2 x 3. This can be expressed as 24 = 2³ x 3.
Prime numbers	A prime number has only two factors — 1 and itself. 1 is not a prime number. The prime numbers up to 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. Any number can be written as the product of its prime factors, for instance... 720 = 2 x 2 x 2 x 2 x 3 x 3 x 5 so, 720 can be written in prime factor form as 2⁴ x 3² x 5 Mathematicians through the ages have been fascinated by prime numbers. See The Prime Pages. There are lots of odd facts about primes: For instance, 101 is prime and the first five primes add up to 101. The first three primes add up to 10, and the first 3² primes add up to 10². The number 12345678910987654321 is prime. The number made by writing out the first nine primes with zeros between them — 2030507011013017019023 — is also prime. 2¹⁰⁰² - 1 is a prime. There are also primes called Mersenne primes — only 38 have been discovered since 1452 and some people get very excited about searching for the 39th. The latest is 2^6972593 -1 which has 2,098,960 digits! You can join a world-wide computer project GIMPS to search for more in the great internet prime search... and get your name in the history books.
Proper fraction	A common fraction in which the numerator — the top number — is bigger than the denominator — the bottom number. For example, ²/₃ or ⁷/₁₀. See also fraction, improper fraction, mixed number
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R
Range	In a list of numbers, the largest number subtract the smallest number. So, in the list 2, 8, 10, 12, 13 the range is 13-2. The answer: 11. See also mean, median and mode.
Ratio	Ratio compares the size of two or more quantities. For instance, you can mix two shovels of cement to five shovels of sand. The ratio of the cement to the sand is said to be "two to seven". This can be written as 2:5, with a colon ":" standing in for the word "to". Two lorries full of cement and seven lorry loads of sand are also in the ratio of 2:5 It works so long as the units are the same... cm, tonnes, bottles, lorry loads, cupfuls, lengths, areas, volums, mass or weight. But be careful, if the sides of two fields are in ratio of 2:1, their areas will be in ratio of (2x2):(1x1), or 4:1. Ratios can also be expressed as a fraction. But again be careful... if two quantities are in the ratio of 2:5 the total number of parts is 7. The first quantity in the ratio is ²/₇ of the whole and the second quantity in the ratio is ⁵/₇ of the whole. Gradient is also a ratio... the ratio of how much you climb vertically up as you move horizontally forward. A gradient of 2:5, ²/₅, 0.4 or 40% means for every 5m you move forward you climb by 2m... or for every 100m you move forward you rise by 40m. That's a very hard climb! In French they say "raison" and in German ratio is "verhaltinis".
Rational numbers	Rational numbers can be written as a fraction ^a/_b where both a and b are integers and b is not zero. Rational numbers can also ne written as either terminating or recurring decimal fractions. ¹/₃ or 0.3 recurring is rational. See also irrational numbers
Reciprocal	The reciprocal of a number is 1 divided by that number. The reciprocal of 4 is ¹/₄ Or, the reciprocal of x is 1/x. The reciprocal of x/y is y/x
Recurring decimal	A decimal fraction which repeats itself forever. ¹/₃ gives the recurring decimal fraction 0.333333... ¹/₇ gives the recurring decimal fraction 0.142857142857142857... The recurring pattern is usually indicated by placing a dot over the first digit of the recurring pattern, and another dot over the final digit of the recurring pattern. Also known as periodic decimal. The period of a recurring decimal is the number of digits which forms the repeating pattern. So, the period of ¹/₇ or 0.142857... is 6. See also terminating decimal
Root	Roots are the inverse or opposite of powers. 3⁵, or 3 to the power 5, or 3 x 3 x 3 x 3 x 3 = 243. So, the fifth root of 243 = 3. Special roots are square roots and cube roots.
Rule	How to work out any number in a sequence. See also formula and function.
Rules for indices	Rules for manipulating numbers written in index form, aⁿ where a is the base number and n is the index. See also powers. aⁿ x a^m = a^n+m aⁿ / a^m = a^n-m (aⁿ)^m = a^nxm a^-n = 1/aⁿ where a is not zero a⁰ = 1 where a is not zero
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S
Sequence	A list of specific numbers in a certain order governed by a rule. A formula for a sequence connects its term to its position the sequence. The rules governing a sequence can include: Add on the same number Subtract the same number Multiply by the same number Divide by the same number Add the two previous numbers Add on regularly increasing numbers. See also term and position. For more help on sequences click here
Square	To "square" a number you multiply it by itself. So, the square of 2 is 2 x 2, or 4. The square of, say, 5.67 is 5.67 x 5.67. The opposite of square, to go the other way, is to square root. So, 2 is the square root of 4, 2 x 2. A perfect square is a number whose square root is a whole number. See also square numbers. A square is a four-sided shape with equal sides, equal corners of 90^o and perpendicular bissected diagonals. A square is a special form of a rectangle and parallelogram.
Square numbers	Square numbers can be made by squaring other whole numbers. They can be represented by the same number of dots laid out in a square. The first few square numbers are 1, 4, 9, 16, 25, 36, 49, 64, 81... See also triangular or triangle numbers.
Square root	The square root of a number is another number which can be multiplied by itself, or squared, to equal the number. Square roots can be positive or negative. Remember two negatives are a positive. So, the square root of 4 is both ⁺2 and ^-2. Roots are the inverse or opposite of powers. 3², or 3 squared, or 3 x 3 = 9. So, the square root of 9 = 3. The square root of a number is, strictly speaking, + or -. A negative multiplied by a negative is a positive. In some problems recording the root as + or - is essential. See also cube roots.
Standard form	A way of writing any number using powers of 10. Very useful for calculations with very large numbers and very small small numbers. Also used to estimate calculations. Numbers in standard form are written as a number between 1 and 10, but not including 10, multiplied by a power of 10 in index form. For instance, the distance between the earth and the sun is 93,000,000 miles (give a mile or two). That's a long way. In standard form this is written as 9.3 x 10⁷. 9.3 multiplied by 10⁷ = 93,000,000 Note: Standard form is not 10 to the power of the number of zeros. 93 x 10⁶ is not in standard form as 93 is not a number between 1 and 10. Instead, count the hops needed to move the decimal point. Very small numbers can also be written in standard form. For instance, bacteria are about 0.000006 m long. That's tiny. In standard form it is written as 6 x 10^-6. So, how many bacteria can you line up between the earth and the sun!? 93,000,000 divided by 0.000006! Or, 9.3 x 10⁷/6 x 10^-6 = 1.55555 x 10¹³. That's 15,555,555,555,555 bacteria between here and the sun!
Substitute	Put numbers into a formula. Replace letters with numbers in a formula.
Symbol	Any sign used in maths The symbols include +, -, x, �, =, >, <...
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T
Term	A number in a sequence. The term also has a position in the sequence. In algebra, terms are the letters separated by + and - signs. See also like terms.
Terminating decimal	A decimal fraction which ends after a definite numberof digits. For instance, ¹/₂ = 0.5 See also terminating decimal
Top heavy fraction	An improper fraction, where the numerator — the top number — is bigger than the denominator — the bottom number. For example, ⁷/₅ or ¹⁵/₉. An improper fraction can be simplied into a mixed number. See also, fraction, common fraction and proper fraction.
Triangle numbers	Numbers which can be represented by dots making up triangles. The first few triangle numbers are 1, 3, 6, 10, 15, 21... The n^thtriangle number can be calculated from n(n+1)/2. See also polygon numbers
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U
Unit fraction	A common fraction where the numerator — the top number — is always 1. For example, ¹/₂, ¹/₃, ¹/₄, ¹/₅, ¹/₆... Unit fractions were used by the ancient Egyptians to express common fractions. See The Eye of Horus, Egyptian fractions. Common fractions were expressed as the sum of unit fractions. For example: ²/₅ = ¹/₃ + ¹/₁₅ ²/₉ = ¹/₆ + ¹/₁₈ ²/₉₉ = ¹/₆₆ + ¹/₁₉₈ The Egyptians constructed detailed tables of unit fractions which were used for multiplication and division of fractions and mixed numbers.
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The Pifactory dictionary

Other online maths dictionaries:

The Oxford Mathematics Study Dictionary. Highly recommended. The best all round maths dictionary, helped with double-page spreads and colour.

The Penguin Dictionary of mathematics. The Penguin dictionary. More advanced than the Oxford version, suitable for A-level students.

A

Algorithm

A set of instructions that can be repeated again and again.

B

Base

Base, as in power.

3 is the base in 35, 3 to the power 5, or, 3 x 3 x 3 x 3 x 3, or, 3 multiplied by itself five times.

See also index and root.

BODMAS

A reminder of the order in which operations have to carried out when working with equations and formulas.

Brackets

Order

Division

Multiplication

Addition

Subtraction

Sometimes also called BIDMAS, where I stands for Indices.

C

Common factor

A number that is a factor of two or more numbers.

See also factor and highest common factor.

Common fraction

A common fraction is written as two whole numbers, one above the other, separated by a horizontal line or dash.

The denominator — the bottom number — cannot be 1 or 0.

A common fraction represents a division to be done, the upper number to be divided by the bottom number.

See also fraction, improper fraction, mixed number.

Consecutive numbers

Whole numbers that follow on.

1, 2, 3,, 4... are consecutive numbers. 1837, 1838, 1839, 1840... are consecutive numbers.

Consecutive numbers go in sequence from smallest to largest, one at a time.

Co-prime

Two numbers which have a highest common factor of 1 are called co-prime numbers. See also prime numbers

Cube root

Roots are the inverse or opposite of powers.

33, or 3 cubed, or 3 x 3 x 3 = 27.

So, the cube root of 27 = 3.

The cube root of a number is always a positive.

See alsosquare roots.

D

Decimal fraction

Fractions of less than 1 expressed using the decimal place value system, extended to the right of the units column (separated by the decimal point) to give values for 1/10, 1/100, 1/1000 and so on.

For example, 0.735 means 7/10 + 3/100 + 5/1000 = 735/1000

Denominator

The bottom number in a common fraction.

For example, in the fraction 7/10, 10 is the denominator, and 7 the numerator.

Digit sum

The result when you add together all the digits in a number.

The digit sum of 854 is 8 + 5 + 4 which equals 17.

The digital root of a number is found by finding the digit sum of the digit sum, and repeating until only a single digit remains.

So, the digital root of 854 is 1 + 7 which equals 8.

E

Equation

Letters and numbers connected by the = sign.

c=2 x pi is the equation for the circumference of a circle with a radius of 2

See also formula, expression, function, terms, like terms, substitute and symbol.

Euclid's algorithm

A method for finding the highest common factor of two numbers. It is best explained by giving an example:

Find the HCF of 64 and 24.

First find the largest multiple of 24 which is less than 64:

64 = 2 x 24 + 16

The largest multiple is 48, remainder 16 to make 64.

Now find the largest multiple of the remainder 16 which less than 24:

24 = 1 x 16 + 8

The largest multiple is 16, remainder 8 to make 24.

Find the largest multiple of the remainder 8 which is less than or equal to 16:

16 = 2 x 8 + 0

The largest multiple is 2 x 8, remainder zero.

When the remainder is 0, the last factor used is the highest common factor.

In this example the HCF of 64 and 24 is 8.

And who's Euclid? Click here to find out

Expression

A mixture of numbers, letters and symbols, but not including the = sign.

The symbols include +, -, x, �... but not =

See also equation, formula, function, terms, like terms, substitute and symbol.

F

Factor

3 is the base in 3⁵, 3 to the power 5, or, 3 x 3 x 3 x 3 x 3, or, 3 multiplied by itself five times.

3³, or 3 cubed, or 3 x 3 x 3 = 27.

Fractions of less than 1 expressed using the decimal place value system, extended to the right of the units column (separated by the decimal point) to give values for ¹/₁₀, ¹/₁₀₀, ¹/₁₀₀₀ and so on.

For example, 0.735 means ⁷/₁₀ + ³/₁₀₀ + ⁵/₁₀₀₀ = ⁷³⁵/₁₀₀₀

For example, in the fraction ⁷/₁₀, 10 is the denominator, and 7 the numerator.

The square root of ^-1 is called i.

For example, ⁷/₅ or ¹⁵/₉.

5 is the index in 3⁵, 3 to the power 5, or, 3 x 3 x 3 x 3 x 3, or, 3 multiplied by itself five times. 3 is the base number.