Download Math terms - definitions and examples

Number Concept
Factor - In terms of numbers, a factor is a natural number that exactly divides a given natural
number.
Example 1: 6 is a factor of 12 [since (6)(2) = 12].
Example 2: 12 is a factor of 12 [since (12)(1) = 12].
Example 3: 8 is NOT a factor of 12. [since 12 ÷ 8 = 1.5].
Zero Pair – combining of one positive and one negative integer that have the same value.
Example 1: 4 and -4
Example 2: 0.3 and -0.3
Positive Integer - A positive integer is a number greater than zero. Positive integer can be indicated
by using a plus symbol (+) in front of the number. If no symbol is shown the number is assumed to be
positive. On a number line, positive numbers are numbers to the right of zero.
Example 1: Positive integers: +10, +15, 12, 22, 123
Example 2: Positive rational numbers expressed in decimal form: +0.46, +12.5, 0.7, 15.55,
+34.0, 55.0, +15, 12
Example 3: Positive rational numbers expressed as fractions (or mixed numbers):
Negative Integer - A negative integer is a number less than zero. Negative numbers are indicated by
using a minus symbol (-) in front of the number. If no symbol is shown the number is assumed to be
positive. On a number line, negative numbers are numbers to the left of zero.
Example 1: Negative integers: -10, -15
Example 2: Negative rational numbers expressed in decimal form: -0.46, -12.5, -0.7, -15.55,
-34.0, -55.0, -15, -12
Example 3: Negative rational numbers expressed as fractions (or mixed numbers):
Repeating Decimal - A repeating decimal is a decimal number that contains a digit or group of digits
that repeat endlessly. Another name for repeating decimal is "recurring" decimal. The number of digits
that repeat is called the period of the repeating decimal. There are different ways to represent a
repeating decimal. The most common method is to put a segment over the first digit (or group of
digits) that repeat.
Examples –
Terminating Decimal- A terminating decimal is usually defined as a decimal number that contains a
finite number of digits after the decimal point. All terminating decimals are rational numbers that can
be written as reduced fractions with denominators containing no prime number factors other than
two or five.
Example 1: 0.2
Example 2: 1.5
Numerator - A numerator is the number above the line in fraction that can state one of the following:

the number of equal parts in a set to be considered.

the number of equal parts of a whole to be considered.
The numerator is the dividend of the number below the line.
Example 1: 2/3 where 2 is in the numerator position
Denominator - A denominator is the number below the line in a fraction that can state one of the
following:


the number of elements in a set.
the number of equal parts into which the whole is divided.
The denominator is the divisor of the number above the line.
Example 1: 2/3 where 3 is in the denominator position
Product - "Product" is the name given to the result of multiplying a set of factor together.
Example 1: 3 x 2 = 6
3 is the multiplicand.
2 is the multiplier.
6 is the product.
Note that 3 and 2 are also called factors.
Order of Operations - The rules of order of operations describe the sequence of operations used to
evaluate an expression.
The two main rules are as follows:
A. Perform operations inside parentheses first. When there are nested parentheses, evaluate
innermost parentheses first and "work outwards".
B. When evaluating an expression inside of parentheses (or when there are no parentheses) evaluate
in the following order:
1. Evaluate powers.
2. Perform multiplication and division from left to right.
3. Perform addition and subtraction from left to right.
These rules are used so that anyone who evaluates an expression will attain the same result.
Example 1: 2 + 3 x 4
2 + 12
14
Distributive Property - The distributive property of multiplication over addition: Multiplying a sum by a
number is the same as multiplying each addend by the number and then adding the products. The
distributive property of multiplication over subtraction: Multiplying a difference by a number is the
same as multiplying the subtrahend and the minuend by the number and then subtracting the
products.
Example: The distributive property of multiplication over addition.
3(4 + 2) = 3x4 + 3x2
3x6 = 12 + 6
18 = 18
(Both sides have a result of 18.)
The distributive property of multiplication over subtraction.
3(4 - 2) = 3x4 - 3x2
3x2 = 12 - 6
6=6
(Both sides have a result of 6.)
PATTERNS AND RELATIONS
Variable – A variable is a symbol (usually a letter) in mathematical expressions and equations.
Examples

Expression: 2x + 3 [the variable is x]

Equation: x + 3 = 5 [the variable is x]

Equation: x + x = 2x [the variable is x]

Equation: y – 4 – x [the variable are x and y]
Coefficient – Coefficient usually refers to “numerical coefficient”, even though the term has a broader
definition.
Examples: 3x, where x is the variable and 3 is the coefficient
3x, where x is the variable and ¾ is the coefficient
4
Constant - A constant is a term that does not change.
Example : In the expression 2x + 3 there are two terms, "2x" and "3".
Since the term "2x" contains the variable "x", "2x" is NOT a constant term.
Since the term "3" contains no variables, "3" IS a constant term.
Linear Relation – a relation that has a straight line graph
Equation - An equation is a statement of equality between two expressions.
Verifying the Solution - ensures the solution satisfies any equation or inequality by using substitution.
Example:
Verify whether or not x = 3 is a solution to the conditional equation 2x - 3 = 6 - x.
Substitute x = 3 into 2x - 3 = 6 - x to see if a true or false statement results.
Since the result of the substitution is a statement which is TRUE, it has been verified that x = 3 IS a
solution to the conditional equation 2x - 3 = 6 - x.
SHAPE AND SPACE
Radius - A radius is a line segment from the centre of a circle to any location on the circle.
The word radius can also refer to the length of a line segment from the centre of a circle to any
location on the circle.
Diameter - A diameter is a line segment through the centre of a circle connecting two points on the
circle. The word diameter can also refer to the length of a line segment through the centre of a circle
connecting two points on the circle.
Circumference - Circumference is a term used to represent the distance around a circle.
C: Circumference of a circle
r: The length of the radius of a circle
d: The length of the diameter of a circle
Pi - pi is an irrational number. Since it is a non-repeating, non-terminating decimal, it cannot be
written as a fraction. The symbol for pi is "π". π = 3.141 592 653 589 793 238 462 643 383 279 ...
For calculations, pi (π) is usually approximated by using a limited number of digits after the decimal
point. To two decimal places, pi is approximately 3.14.
Perpendicular - Lines are perpendicular if they intersect at right angles (90°) to each other.
Perpendicular Bisector -
A perpendicular bisector is a line or line segment that both bisects a given line
segment and is perpendicular to it.
Transformations - A transformation of an object causes the object to change one or more of the
following:



position
size
shape
The transformed object is commonly called the image.
Translations – (slide) A translation is a transformation in geometry in which an object is moved in a
straight line without turning or changing the size or shape. Every point of an object is moved the same
distance and in the same direction. A translation arrow indicates the direction and amount of
movement.
Reflections –(flip) A reflection is a transformation in geometry in which an object is reflected in a line
to form a mirror image. Every point of an object and the corresponding point on the image are
equidistant from the line of reflection.
Rotation - (turn) A rotation is a transformation in geometry in which an object is rotated about a fixed
point called a point of rotation.
STATISTICS AND PROBABILITY
Mean - The mean (or "arithmetic mean") is a measure of central tendency of a set of data
represented by numbers.
The mean is calculated by adding up all of the values and dividing by the number of values.
The symbol for the arithmetic mean is a letter with a segment above it.
Median - The median is a measure of central tendency of a set of data represented by numbers.
The median the "middle" of a set of numbers in ascending or decending order.
The symbol for the median is usually the letter "M".
Mode - The mode is a measure of central tendency of a set of data represented by numbers.
The mode is the most frequently occurring number.
There is no standard symbol associated with the mode.
Tree Diagram - A tree diagram is a diagram using branches from locations (like a tree) to show
possibilities and relationships including:





all possible outcomes of an experiment
all possible arrangements of a set of elements
match-ups in a tournament
prime factorization of a natural number
etc.
Independent Events - Two events are independent if the occurrence of one event has no effect on the
probability the other event occurs. When the occurrence of one event DOES have an effect on the
probability the other event occurs, the events are said to be dependent.