Definitions to commonly used words in the topic of Stage 4 Numbers & Algebra - Fractions.
common factor
A common factor (or common divisor) of a set of numbers or an algebraic expression is a factor of each element of that set.
For example, 6 is a common factor of 24, 54 and 66
decimal
A decimal is a numeral in the decimal number system.
For example, the decimal expansion of 6 3/4 is 6.75. The integer part is 6 and the fractional part is 0.75
denominator
In the fraction a/b, b is the denominator. It is the number of equal parts into which the whole is divided in order to obtain fractional parts. For example, if a line segment is divided into 5 equal parts, each of those parts is one-fifth of the whole and corresponds to the unit fraction 1/5.
difference
A difference is the result of subtracting one number or algebraic quantity from another.
divisible
In general, a number or algebraic expression x is divisible by another y if there exists a number or algebraic expression q of a specified type for which x=yq.
A natural number mm is divisible by a natural number nn if there is a natural number q such that m=nq.
For example, 12 is divisible by 4 because 12=3×4
equation
An equation is a statement that asserts that two numbers or algebraic expressions are equal in value. An equation must include an equals sign. For example, 3 + 14 = 11 + 6
equivalent fractions
Two fractions a/b and c/d are equivalent if they are equal, that is, ad=bc.
Equivalent fractions are alternative ways of writing the same fraction.
For example, 1/2=2/4=3/6=...
expression
Two or more numbers or variables connected by operations. For example, 17−9, 8×(2+3), 2a+3b are all expressions.
Expressions do not include an equals sign.
factor
In general, a number or algebraic expression x is a factor (or divisor) of another y if there exists a number or algebraic expression q of a specified type for which y=xq.
A natural number mm is a factor of a natural number n if there is a natural number q such that n=mq.
For example, 4 is a factor of 12 because 12=3×4
fraction
The fraction a/b (written alternatively as a/b), where a is a non-negative integer and b is a positive integer, was historically obtained by dividing a unit length into b equal parts and taking a of these parts.
For example, 3/5 refers to 3 of 5 equal parts of the whole, taken together.
In the fraction abab the number a is the numerator and the number b is the denominator.
It is a proper fraction if a<b and an improper fraction otherwise.
highest common factor
The highest common factor (HCF), greatest common factor (GCF) or greatest common divisor (GCD) of a given set of natural numbers is the common divisor of the set that is greater than each of the other common divisors.
For example, 1, 2, 3 and 6 are the common factors of 24, 54 and 66 and 6 is the greatest common divisor.
inequality
An inequality is a statement that one number or algebraic expression is less than (or greater than) another. There are four types of inequalities:
multiple
A multiple of a number is the product of that number and an integer.
A multiple of a real number xx is any number that is a product of xx and an integer. For example, 4.5 and –13.5 are multiples of 1.5 because 4.5=3×1.5 and −13.5=−9×1.5
number line
A number line gives a pictorial representation of real numbers.
numeral
A figure or symbol used to represent a number. For example, –3, 0, 45, IX
numerator
In the fraction abab, a is the numerator. If an object is divided into b equal parts, then the fraction a/b represents aa of these parts taken together.
For example, if a line segment is divided into 5 equal parts, each of these parts is one-fifth of the whole and 3 of these parts taken together corresponds to the fraction 3/5.
operation
The process of combining numbers or expressions. In the primary years operations include addition, subtraction, multiplication and division. In later years operations include substitution and differentiation.
rate
A rate is a particular kind of ratio in which the two quantities are measured in different units. For example, the ratio of distance to time, known as speed, is a rate because distance and time are measured in different units (such as kilometres and hours). The value of the rate depends on the units in which the quantities are expressed.
ratio
A ratio is a quotient or proportion of two numbers, magnitudes or algebraic expressions. It is often used as a measure of the relative size of two objects. For example, the ratio of the length of a side of a square to the length of a diagonal is 3:2; that is, 3/2.
rational number
A real number is rational if it can be expressed as a quotient of integers. It is irrational otherwise.
related denominators
Denominators are related when one is a multiple of the other. For example, the fractions 1/3 and 5/9 have related denominators because 9 is a multiple of 3.
Fractions with related denominators are more easily added and subtracted than fractions with unrelated denominators because only one needs to be renamed.
For example, to add 1/3 and 5/9 we can rename 1/3 as 3/9 and then compute 3/9+5/9=8/9.
unit fraction
A unit fraction is a simple fraction whose numerator is 1, that is, a fraction of the form 1/n where n is a natural number.
whole number
A whole number is a non-negative integer, that is, one of the numbers 0, 1, 2, 3, …
Sometimes it is taken to mean only a positive integer, or any integer.