Absolute value - The absolute value is the numerical value of a number without its plus or minus sign. It is denoted by putting two straight lines parallel to each other on each side of the number: |number|
Example: the absolute value of -5 = |-5| = 5 and the absolute value of 5 = |+5| = 5
Additive inverse - This is the opposite of a number such that when it is added to the number the sum equals zero.
Example: -5 + 5 = 0, the additive inverse of -5 is 5.
Binomial - Any polynomial that has exactly two terms.
Example: (a + b) and (4x + 12) are both binomials.
Coefficient - These are numbers in an algebraic expression that are not variables.
Example: 4x + 2y + 7, there are three coefficients in this expression; 4, 2, and 7
Equation - An equation is a mathematical statement used in algebra that has an equal sign between two algebraic expressions.
Example: 4x + 2y + 7 = 7y + 24
Exponent - An exponent indicates how many times a number, or algebraic expression, should be multiplied by itself. It is noted by a small number, or superscript, to the right of the base number. If the base number is b and the exponent a, it would look like ba. In this case b would be multiplied by itself a times.
Example: 63 = 6 x 6 x 6
Fibonacci sequence - The Fibonacci sequence is a sequence of numbers where the next number is the sum of the two numbers before it.
Example: 1,1,2,3,5,8,13,21,34,…
Finite Set - In algebra, a finite set is a set that has a fixed number of elements.
Example: [5,10,15,20,25,30] is a finite set with exactly 6 elements.
Identity element - An identity element is a number that leaves other elements unchanged when combined with them. Depending on the number set and the mathematical operation, the identity element may be different.
Example:
5 + 0 = 5. The identity element for addition is 0.
12 x 1 = 12. The identity element for multiplication is 1.
Inequality - An algebraic statement where two expressions are not equal. The sign for not equal is ≠.
Example: 7 ≠ 12
Infinite set - A number set that is not a finite set and has an infinite number of elements.
Example: The set of all integers is an infinite set (…,-3,-2,-1,0,1,2,3,…)
Negative number - Any number that is less than zero.
Example: -7
Number sentence - A number sentence is an equation or inequality written with numbers and mathematical symbols. It can be true, false, or open.
Example: 7x + 4 = 7
Origin - The origin is the point where the X and Y axis intersect on a graph. This is the point (0,0) in a two-dimensional graph.
Perfect number - A whole number greater than zero where the total of its factors (excluding the number itself) adds up to the number.
Example: The number six has the factors 1, 2, and 3 (not counting 6 itself). If you add these up 1 + 2 + 3 = 6. Other perfect numbers include 28 (1 + 2 + 4 + 7 + 14) and 496.
Positive number - Any number greater than zero.
Example: 7
Power - See exponent. The exponent is often referred to as the power of a number.
Example: 23 = 2 x 2 x 2 = 8, 8 is the third power of 2.
Real numbers - Real numbers include all rational and irrational numbers. This includes zero, positive numbers, and negative numbers. It also includes fractions, integers, and decimals.
Example: -7, 0, 3, and 7.12223 are all real numbers
Significant digit - The significant digits in a number include all of the digits starting with the first non-zero number to the left of the number and ending with the last non-zero number to the right. It can also include zeros to the right if they are considered exact.
Square - An operation where a number is multiplied by itself. It is written with a small 2 to the right of the number like X2.
Example: 72 = 7 x 7 = 49
Square root - A number that produces a given number when multiplied by itself. The symbol for square root is √.
Example: √ 49 = 7, 7 is the square root of 49 because 7 x 7 = 49.
Subset - A set where every element in the set is part of another set. Set A is a subset of B if all the elements of A are also in B.
Example: B = (1,3,5,7,9,11) A = (3,7,9), A is a subset of B.
Unknown - A number that we do not know. In an equation it is the variable that we are solving for.
Example: 2x + 7 = 22, x is the unknown
Variable - A variable is a value that may change and have different values.
Example: 2x + 4y = z, in this equation x, y, and z are variables
