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Glossary and Terms: Algebra

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: 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

More Math Glossaries and Terms

Algebra glossary
Angles glossary
Figures and Shapes glossary
Fractions glossary
Graphs and lines glossary
Measurements glossary
Mathematical operations glossary
Probability and statistics glossary
Types of numbers glossary
Units of measurements glossary

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