A Glossary of Mathematical Terms and Concepts for ESL Students

Return to CUNYMath | Resources for Students

N - P

NEGATIVE NUMBER
Any real number that is smaller than zero is a negative number.

Examples: -23, -8, -.006 are negative numbers.
number line with all numbers < 0 shaded
NON-NEGATIVE NUMBERS
Any real number that is greater than or equal to zero is a non-negative number.
Examples: 34, 5, 2.1, 0 are non-negative numbers.
number line with all numbers >= 0 shaded
NON-POSITIVE NUMBER
Any real number that is smaller than or equal to zero is a non-positive number.
Examples: -23, -8, -.006, 0 are non-positive numbers.
number line with all numbers <= 0 shaded
NUMBER
Natural Number 0, 1, 2, 3, ...
Integer ..., -3, -2, -1, 0, 1, 2, 3, ...
Even Number ..., -6, -4, -2, 0, 2, 4, 6, ...
Odd Number ... -5, -3, -1, 1, 3, 5, ...
Decimal 1.35, 0.98, -2.45, ...
Repeating Decimal .3 with a horizontal line above the 3 = .333 ...,
5.62 with a horizontal line above the 62 = 5.626262 ...,
0.037 with a horizontal line above the 7 = 0.03777 ...
Rational Number
2, 1,
3		 -.45, 27
5
A rational number is a number than can be expressed as a fraction.
Irrational Number square root of 2, square root of 5
An irrational number is a number that cannot be expressed as a fraction.
Real Number square root of 3, 2, 1.8, -9, ….
A real number is either a rational number or an irrational number. In general, we may represent a real number on the number line.
OPPOSITE
The opposite of a number is the number with the opposite sign.

Examples:
The opposite of 3 is -3.
The opposite of -5 is 5.
The opposite of n is -n.
The opposite of -2 is -(-2) = 2.
ORDER OF OPERATIONS
A mathematical expression is computed left to right with following order:
parentheses { [ (     ) ] }
exponent ( )n
multiplication multiplication sign
division ÷
addition +
subtraction -

Example:
32 - 2[ 4 + (3 + 7) ÷ 5 ]2 = 32 -2[ 4 + 10 ÷ 5 ]2
  = 32 - 2[ 4 + 2 ]2
  = 32 -2[ 6 ]2
  = 32 - 2[ 36 ]
  = 32 - 72
  = -40
PARABOLA
vertex: V (0, 0)            diagram of a parabola
focus: F (p, 0)
directrix: x = -p
equation of parabola: y2 = 4px
PERCENT
Percent means part of 100.

Examples:
23% = 23
100
4% = 4
100		 = 1
25

Percent to decimal:
45% = .45
3.7% = .037

Decimal to percent:
0.79 = 79%
3.1 = 310%
PERIMETER
Perimeter is the total length of the sides of a polygon. (See also formula and polygon.)
PLACE VALUES OF NUMBERS
Given a number 24.6 the place value of 2: tens; 4: ones; 6: tenths.

Names of place values:
..., B,
I
L
L
I
O
N
S		 H
U
N
D
R
E
D
 
M
I
L
L
I
O
N
S		 T
E
N
 
M
I
L
L
I
O
N
S		 M,
I
L
L
I
O
N
S		 H
U
N
D
R
E
D
 
T
H
O
U
S
A
N
D
S		 T
E
N
 
T
H
O
U
S
A
N
D
S		 T,
H
O
U
S
A
N
D
S		 H
U
N
D
R
E
D
S		 T
E
N
S		 O
N
E
S		 . T
E
N
T
H
S		 H
U
N
D
R
E
D
T
H
S		 T
H
O
U
S
A
N
D
T
H
S		 T
E
N
 
T
H
O
U
S
A
N
D
T
H
S		 ...
Example:
5,321,406.987 is five million, three hundred twenty-one thousand, four hundred six and nine hundred eighty-seven thousandths.
POLYNOMIAL
A polynomial is an algebraic expression that consists of a sum of terms.

( i ) 2x3y + 3xy - 5xy3 + 2xy + x + 4 is a polynomial that consists of 6 terms.

Terms: 2x3y, 3xy, -5xy3, 2xy, x, 4

Coefficients of the Terms: 2, 3, -5, 2, 1, 4 (4 is a constant.)

Like terms are terms with identical variable expressions: 3xy and 2xy

Unlike terms are terms with different variable expressions: 2x3y, 3xy, -5xy3, x, 4

To simplify a polynomial is to collect like terms. After simplification, ( i ) becomes:
( ii ) 2x3y + 5xy - 5xy3 + x + 4

Some special polynomials:
Monomial: 4x
Binomial: 2x + 3y
Trinomial: xy + 2x - 3
POLYGON
A polygon is a closed convex geometric figure with three of more sides.

a polygon of 4 sides with side, vertex, interior angle and exterior angle identified

A regular polygon is one with equal sides and equal interior angles.

a regular polygon of 6 sides     an irregular polygon of 6 sides

Some special polygons:
triangle: a polygon of     three sides
quadrilateral: a polygon of     four sides
pentagon: a polygon of     five sides
hexagon: a polygon of     six sides
heptagon: a polygon of     seven sides
octagon: a polygon of     eight sides
nonagon: a polygon of     nine sides
decagon: a polygon of     ten sides
n-gon: a polygon of     n sides
POSITIVE NUMBER
Any real number that is greater than zero is a positive number.

Examples: 5, 34, .07 are positive numbers.
number line with all number > 0 shaded
POWERS
Powers are exponential expressions. (See also exponential function and logarithmic function.)

Examples:
Powers: ax, 23, 4-2, -y to the 1/3 power
Bases of above: a, 2, 4, -y
Exponents of above: x, 3, -2, 1
3

an is read as a to the n-th power.

Some special powers:
a2 the square of a or a squared
b3 the cube of b or b cubed
-x to the 1/2 power ( = square root of x ) the square root of x
-y to the 1/3 power ( = cube root of y ) the cube root of y
a0 = 1 for all a not equal 0

Rules of powers:
a-x =  1 
ax		        a-3 =  1 
a3
 
axay = ax + y        a2a5 = a7
 
a^x / a^y = ax - y        a^5 / a^2 = a3
 
(ax)y = axy        (a3)4 = a12
PRIME NUMBER
A prime number is a natural number that has only one and itself as factors.

Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23, … are prime numbers.
PROPORTION
A proportion is an equality of two quotients (or ratios), usually involving an unknown to be solved.

Example:
6 : x = 5 : 4   or   6
x		 = 5
4
Hence:
5x = 24
 x = 4.8
PYTHAGOREAN THEOREM
For a right triangle, the sum of the square of the legs equals the square of the hypotenuse. (See also triangles.)
a2 + b2 = c2            a right triangle with shorter leg labeled 'a', longer leg labeled 'b' and hypotenuse labeled 'c'
[ A - E | F - M | N - P | Q - Z ]

Return to Glossary Contents

CUNYMath
The City University of New York