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# Math : Glossary

# Glossary: sub-module 1 of 3 of math hub

## Terms

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Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

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Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

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Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

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Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

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Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

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Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

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Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

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Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

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Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

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Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

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This glossary contains common math terms that you will encounter in all areas of math. Use this glossary to review common math terms, or to look up a word you have encountered that you do not know the meaning of. If you cannot find the word you are looking for here, try looking it up in the Prealgebra - opens in a new window eBook.

Are you confident in your knowledge of math terms? Put your knowledge to the test! If there are words you don't yet know, you can find the definitions in the tabs.

Click on a term to view the definition.

A base is a number or variable that is raised to an exponent.

In the exponential expression:

b to the x power, **b** is the base and **x** is the exponent.

Source: "Base (Algebra) - opens in a new window" by David E. McAdams, All Math Words Encylopedia - opens in a new window is licensed under CC BY-SA 4.0 - opens in a new window / A derivative from the original work - opens in a new window

A binomial is a polynomial with two terms.

The expression:

2x + 3y

is a binomial because there are two terms: 2x and 3y.

Click on a term to view the definition.

A coefficient is any multiplicative factor in a term. A coefficient can be numerical or literal. A numerical coefficient is the constant part of the term (the number) and the literal coefficient is made up of the variables and their exponents (the symbols).

In the term:

3x

the numerical coefficient is 3, and the literal coefficient is x.

In the term:

x squared

The numerical coefficient is 1, and the literal coefficient is x squared.

In the algebraic expression:

3x cubed plus 2x squared minus x minus 4.The numerical coefficients are 3, 2, and -1(negative 1) and the literal coefficients are x cubed, squared, and x.

Source: "Coefficient - opens in a new window" by David E. McAdams, All Math Words Encylopedia - opens in a new window is licensed under CC BY-SA 4.0 - opens in a new window / A derivative from the original work - opens in a new window

A common factor is a number, variable, or expression that is a factor of two or more terms.

Find the common factors of 4 and 6.

Both numbers are divisible by 2, so 2 is a common factor of 4 and 6.

In the expression:

6x squared plus 3x. Both terms 6x squared and 3x are divisible by 3x, so 3x is the common factor of 6x squared plus 3x.

Source: "Common Factor - opens in a new window" by David E. McAdams, All Math Words Encylopedia - opens in a new window is licensed under CC BY-SA 4.0 - opens in a new window / A derivative from the original work - opens in a new window

A composite number is a natural number (positive integer) that is not prime. A composite number has factors other than itself and one.

6 is not a prime number.

6 is evenly divisible by both 2 and 3, so 6 is a composite number.

Definition source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

Example source: "Prime Number - opens in a new window" by David E. McAdams, All Math Words Encylopedia - opens in a new window is licensed under CC BY-SA 4.0 - opens in a new window

A constant is a value that does not change.

In the expression:

y+2

the 2 is a constant value.

Source: "Constant - opens in a new window" by David E. McAdams, All Math Words Encylopedia - opens in a new window is licensed under CC BY-SA 4.0 - opens in a new window / A derivative from the original work - opens in a new window

Click on a term to view the definition.

A decimal is a fraction (non-integer) whose denominator is a power of 10.

0.2 is (two tenths) or (one fifth) in lowest terms.

0.75 is (75 hundredths) or (three fourths) in lowest terms.

The denominator is the bottom number of a fraction.

In the fraction:

b is the denominator.

A dividend is a quantity or expression that is divided by another quantity or expression.

In the equation:

12 is the dividend.

In the expression:

x minus 3 is the dividend.

A divisor is a quantity or expression that divides another quantity or expression.

In the equation:

12 divided by 3 equal 4

3 is the divisor.

In the expression:

2x is the divisor.

Definition source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

Example source: "Prime Number - opens in a new window" by David E. McAdams, All Math Words Encylopedia - opens in a new window is licensed under CC BY-SA 4.0 - opens in a new window

Click on a term to view the definition.

When two quantities or expressions have the same value, we say they are equal and connect them with an equal sign.

In the statement:

a=b

a is equal to b

In the statement:

3x+4=13

3x+4 is equal to 13.

Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith All Math Words Encylopedia - opens in a new window is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

An equation is a mathematical statement that indicates two expressions are equal to each other.

Also, an equation expressed in words will form a complete sentence.

n+5=2

is an equation because it contains an equals sign, and it can be expressed in words as a full sentence: A number increased by 5 equals 2.

y minus 2 equals x plus 1is an equation because it contains an equals sign, and can be expressed in words as a full sentence: A number less 2 equals another number plus 1.

Source: "Equation - opens in a new window" by David E. McAdams, All Math Words Encylopedia - opens in a new window is licensed under CC BY-SA 4.0 - opens in a new window / A derivative from the original work - opens in a new window

To evaluate an expression, values are substituted for variables, and the expression is simplified.

Evaluate the expression

3+2x when x=5

Step 1 | Substitute 5 in for x. | 3 plus 2 times 5 |
---|---|---|

Step 2 | Multiply 2 by 5 | 3+10 |

Step 3 | Add 3 and 10 | 13 |

Therefore, the value of the expression 3+2x is 13 when x is equal to 5.

Source: "Evaluate - opens in a new window" by David E. McAdams, All Math Words Encylopedia - opens in a new window is licensed under CC BY-SA 4.0 - opens in a new window / A derivative from the original work - opens in a new window

To expand, or distribute, an expression is to multiply through parentheses using the distributive property.

In the expression:

3 open bracket x minus 4

Step 1 | Expand by multiplying each term in the brackets by 3. | 3 times x minus 3 times 4 |
---|---|---|

Step 2 | Simplify | 3x minus 12 |

Source: "Distribute - opens in a new window" by David E. McAdams, All Math Words Encylopedia - opens in a new window is licensed under CC BY-SA 4.0 - opens in a new window / A derivative from the original work - opens in a new window

Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

An exponent is used to indicate repeated multiplication. An exponent can also be called a power.

The expression:

2 squared

means base 2 raised to the power of 2, or 2 multiplied by itself 2 times: 2 times 2 equals 4

Source: "Exponent - opens in a new window" by David E. McAdams, All Math Words Encylopedia - opens in a new window is licensed under CC BY-SA 4.0 - opens in a new window / A derivative from the original work - opens in a new window

An expression is a set of variables, numbers, operators, parenthesis and/or functions without any equal sign or inequalities.

When stated in words, an expression forms an incomplete sentence or phrase.

5x+2

is an expression because there is no equal sign, and it forms an incomplete sentence when stated in words: 5 times a number increased by 2

x squared minus 2x plus 3

is an expression because there is no equal sign, and it forms an incomplete sentence when stated in words: A number squared minus 2 times the same number plus 3

Source: "Expression - opens in a new window" by David E. McAdams, All Math Words Encylopedia - opens in a new window is licensed under CC BY-SA 4.0 - opens in a new window / A derivative from the original work - opens in a new window

Click on a term to view the definition.

Factor can act as a verb or a noun.

As a noun, a factor is a number or algebraic expression that divides into another number or algebraic expression evenly (no remainder).

As a verb, to factor is to find all the mathematical objects that divide a mathematical object evenly. When factors are multiplied together they give the original number or expression.

Find all the positive factors of 24

- 1 times 24 equals 24
- 2 times 12 equals 24
- 8 times 8 equals 24
- 4 times 6 equals 24

Therefore, the factors of 24 are all the numbers it is divisible by: 1, 2, 3, 4, 6, 8, 12, and 24.

Source: "Solving Quadratic Equations - opens in a new window" by Boundless - opens in a new window is licensed under CC BY SA 4.0 - opens in a new window / A derivative from the original work - opens in a new window

Source: "Factors - opens in a new window" by Boundless - opens in a new window is licensed under CC BY SA 4.0 - opens in a new window / A derivative from the original work - opens in a new window

A fraction represents a part of a whole, or a numerical quantity that is not a whole number.

A fraction is written as , where a is the numerator and b is the denominator. The denominator is the number of equal parts the whole has been divided into, and the numerator is how many parts have been included.

is a fraction and means that we have 2 parts out of 5.

is a fraction and means that we have 1 part out of 4.

Definition source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

Click on a term to view the definition.

A greatest common factor (GCF) is the largest number, variable or expression that is a factor of two or more numbers or expressions.

In the numbers 8 and 12, the greatest common factor is 4 because it is the largest number that is divisible into both 8 and 12.

In the expression:

18x squared plus 12x

The greatest common factor is 6x because it is the largest factor of both 18x squared and 12x.

Source: "Greatest Common Factor - opens in a new window" by David E. McAdams, All Math Words Encylopedia - opens in a new window is licensed under CC BY-SA 4.0 - opens in a new window / A derivative from the original work - opens in a new window

Click on a term to view the definition.

A fraction is improper if its numerator is greater than or equal to its denominator.

In the term:

The numerator of 10 is greater than the denominator of 6, so the fraction is improper.

Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

An inequality is used in algebra to compare two quantities or expressions that may have different values.

In the statements:

Statement 1 | a is not equal to b |
---|---|

Statement 2 | a is less than b |

Statement 3 | a is greater than b |

Statement 4 | a is less than or equal to b |

Statement 5 | a is greater than or equal to b |

Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

Integers are the set of all positive and negative whole numbers including 0. An integer is a whole number having no decimal or fraction part.

**Z** = Integers = {...-3, -2, -1, 0, 1, 2, 3…}

For example: -235, -7, 0, 2, 17, and 2456 are all integers.

Source: "Integer - opens in a new window" by David E. McAdams, All Math Words Encylopedia - opens in a new window is licensed under CC BY-SA 4.0 - opens in a new window / A derivative from the original work - opens in a new window

An irrational number is a number that cannot be written as the ratio of two integers. In other words, an irrational number can not be expressed as a fraction, and its decimal form does not stop and does not repeat.

The following numbers are irrational:

- 3.605551275…
- 0.94729...

Click on a term to view the definition.

The least common denominator (LCD) of any fractions is the least common multiple (LCM) of their denominators.

In the fractions:

The smallest number that can be evenly divided by both 3 and 6 is 6. Therefore, 6 is the least common denominator of 3 and 6 is 6.

In the fractions:

The smallest quantity that can be divided evenly by both 3x squaredand 4x is 12x squared. Therefore, the LCD of 3x squared and 4x is 12x squared.

Example Source: "Least Common Denominator - opens in a new window" by David E. McAdams, All Math Words Encylopedia - opens in a new window is licensed under CC BY-SA 4.0 - opens in a new window / A derivative from the original work - opens in a new window

A least common multiple (LCM) is the smallest expression that is evenly divisible by two or more expressions or integers.

Take the integers 2 and 5.

The smallest number that is evenly divisible by both 2 and 5 is 10.

Therefore, 10 is the least common multiple of 2 and 5.

Source: "Least Common Multiple - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

Terms are like terms if they have the same literal coefficients, which means they have the same variables raised to the same exponents. Like terms can be collected together by adding and/or subtracting their numerical coefficients to simplify an expression or equation.

In the expression:

2x squared y cubed + 14x cubed + 24 + 12x squared y cubed + 3x cubed + 77

The terms:

2x squared y cubed and 12x squared y cubed

are like terms because they have the same literal coefficients: x squared y cubed

The terms:

3x cubed and 14x cubed

are like terms because they have the same literal coefficient: x cubed.

The terms:

24 and 77

are like terms because they are both constants; they both have no variables or exponents

Therefore, by combining the numerical coefficients of the like terms this expression can be simplified to:

14x squared y cubed + 17x cubed + 101

Source: "Like Terms - opens in a new window" by David E. McAdams, All Math Words Encylopedia - opens in a new window is licensed under CC BY-SA 4.0 - opens in a new window / A derivative from the original work - opens in a new window

Click on a term to view the definition.

A mixed number consists of a whole number followed by a fraction.

In the fraction:

2 is the whole number and is the fraction.

A multiple of a number is the product of the number and a natural number.

A multiple of 3 would be the product of a natural number and 3. Below are the first six multiples of 3.

- 1 times 3 equals 3
- 2 times 3 equals 6
- 3 times 3 equals 9
- 4 times 3 equals 12
- 5 times 3 equals 15
- 6 times 3 equals 18

Click on a term to view the definition.

Natural numbers are the set of positive integers starting at 1, also known as the counting numbers.

**N** = Natural Numbers = {1,2,3,4,5,6…}

For example:, 1, 22, 345, and 4763 are all natural numbers.

The numerator is the top number of a fraction.

In the fraction:

a is the numerator.

Click on a term to view the definition.

A polynomial is an expression with one or more terms.

The expression:

3x squared plus 2x plus 4

is a polynomial with three terms:

3x squared, 2x and 4

Source: "Polynomial - opens in a new window" by David E. McAdams, All Math Words Encylopedia - opens in a new window is licensed under CC BY-SA 4.0 - opens in a new window / A derivative from the original work - opens in a new window

A power is made up of a base and an exponent.

2 cubed

x cubed

Source: "Polynomial - opens in a new window" by David E. McAdams, All Math Words Encylopedia - opens in a new window is licensed under CC BY-SA 4.0 - opens in a new window / A derivative from the original work - opens in a new window

A factor of a given integer that is also a prime number.

Take the number 6.

We know that 2 times 3 equals 6 so 2 and 3 are both factors of 6.

,Also note that 2 and 3 are prime numbers, because each is divisible by only 1 and itself. Therefore, 2 and 3 are prime factors of 6.

Source: "Prime Factor - opens in a new window" by Boundless - opens in a new window is licensed under CC BY-SA 4.0 - opens in a new window / A derivative from the original work - opens in a new window

A prime number is a natural number greater than 1 whose only factors are 1 and itself.

13 is a prime number because it’s only factors are 1 and 13.

17 is a prime number because it’s only factors are 1 and 17.

A product is the result of multiplying two or more quantities or expressions together.

In the multiplication statement:

7 times 4 equals 28

The product of 7 and 4 is 28.

2 x open brackets x plus 3 close brackets is the product of 2x and open brackets 3 pus x close brackets

Click on a term to view the definition.

The quotient is the result of dividing two quantities or expressions together.

In the expression:

12 divided by 4

The quotient is 3 because 4 can be subtracted from 12 exactly 3 times.

In the expression:

the quotient is 4x because 8x divided by 2 equals 8x.

Source: "Division - opens in a new window" by David E. McAdams, All Math Words Encylopedia - opens in a new window is licensed under CC BY-SA 4.0 - opens in a new window / A derivative from the original work - opens in a new window

Source Example: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window / A derivative from the original work - opens in a new window

Click on a term to view the definition.

A rational number is a number that can be written as a ratio of two integers. A rational number can be written as a fraction.

- 3 can be written as
- −8 can be written as
- 0 can be written as
- 7.3 can be written as

Therefore, these are all rational numbers.

The reciprocal of the fraction is where a cannot equal 0 and 0 b cannot equal 0. A number and its reciprocal have a product of 1.

Given the fraction:

The reciprocal is:

The product of the fraction and its reciprocal is:

Click on a term to view the definition.

A set is a collection of elements, such as numbers or distinct objects.

The following is a set of whole numbers:

**W** = whole numbers = {0,1,2,3,4,5,6…}

The following is a set of natural numbers:

**N** = natural numbers = {1,2,3,4,5,6…}

Source: "Addition - opens in a new window" by David E. McAdams, All Math Words Encylopedia - opens in a new window is licensed under CC BY-SA 4.0 - opens in a new window / A derivative from the original work - opens in a new window

In general, to simplify an expression means to do all the math possible and to put the expression into a form that makes it easier to work with. This may involve several steps, and what you need to do to simplify an expression depends on what you start with.

Simplify the expression:

4x minus 3 minus 3x plus 12

Step | Result |
---|---|

Collect the like terms negative 3 and 12 | x plus 9 |

Collect the like terms negative 3x | x minus 2 plus 12 |

Therefore, the simplified expression is x + 9.

To solve a problem is to find the answer to the question.

To solve an algebraic equation means to find the values of the variable(s) that make the equation a true statement.

Solve for x in the equation:

2x + 3 = 7

Step 1 | Subtract 3 from both sides. | 2x + 3 minus 3 equals 7 minus 3 |
---|---|---|

Step 2 | Divide both sides by 2. | |

Step 3 | State the solution. | x = 2 |

Solve for y in the equation:

4x equals 2y plus 6

Step 1 | Subtract 6 from both sides. | 4x minus 6 equals 2y plus 6 minus 6 |
---|---|---|

Step 2 | Divide both sides by 2. | |

Step 3 | State the solution. | y equals 2x minus 3 |

Source: "Solve - opens in a new window" by David E. McAdams, All Math Words Encylopedia - opens in a new window is licensed under CC BY-SA 4.0 - opens in a new window

The sum is the result of the addition of two or more quantities.

In the addition statement:

2 plus 6 equals 8

the sum of 2 and 6 is 8.

Source: "Addition - opens in a new window" by David E. McAdams, All Math Words Encylopedia - opens in a new window is licensed under CC BY-SA 4.0 - opens in a new window / A derivative from the original work - opens in a new window

Click on a term to view the definition.

Algebraic expressions are made up of terms. A term is a constant or the product of a constant and one or more variables.

A term is a part of an expression that is separated from other terms by addition or subtraction.

Some examples of terms are 7, y, 5x squared, negative 9a and 13x)

In the expression:

2x plus y minus 3

There are three terms: 2x, y, and negative 3

Source: "Term - opens in a new window" by David E. McAdams, All Math Words Encylopedia - opens in a new window is licensed under CC BY-SA 4.0 - opens in a new window / A derivative from the original work - opens in a new window

A polynomial with exactly three terms.

The expression:

x squared minus 5x plus 8

is a trinomial because there are three terms:

x squared, negative 5x, 8

Click on a term to view the definition.

A variable represents a value that can change (vary). A variable can be a letter or another symbol that stands for an unknown in an equation or expression.

In the equation:

22 plus 17 equals a

The variable 'a' represents an unknown quantity.

In the equation:

3 plus 2x equals 13

The variable ‘x’ represents an unknown quantity.

Source 1: "Mathematical Vocabulary - opens in a new window" by OER Commons - opens in a new window is licensed under CC BY-NC 4.0 - opens in a new window / A derivative from the original work - opens in a new window

Source 2: "Variable - opens in a new window" by David E. McAdams, All Math Words Encylopedia - opens in a new window is licensed under CC BY-SA 4.0 - opens in a new window / A derivative from the original work - opens in a new window

Click on a term to view the definition.

The set of numbers that includes the natural numbers and zero.

**W** = Whole Numbers = {0,1,2,3,4,5,6…}

For example: 0, 10, 310 and 1035 are all whole numbers.

Source: "Prealgebra - opens in a new window" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 - opens in a new window