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# Learning Portal -Math: Glossary

Glossary

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 eBook.

## Glossary

Base

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

Example:

In the exponential expression:

b is the base and x is the exponent.

Binomial

A binomial is a polynomial with two terms.

#### Example:

The expression:

2x + 3y

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

Coefficient

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).

Example 2:

In the term:

3x

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

Example 2:

In the term:

The numerical coefficient is 1, and the literal coefficient is x².

Example 3:

In the algebraic expression:

The numerical coefficients are 3, 2, and -1(negative 1) and the literal coefficients are x³, x², and x.

Common Factor

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

Example 1:

Find the common factors of 4 and 6.

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

Example 2:

In the expression:

Composite Number

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

Example:

6 is not a prime number.

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

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

Constant

A constant is a value that does not change.

Example:

In the expression:

y+2

the 2 is a constant value.

Decimal

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

Example 1:

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

Example 2:

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

Denominator

The denominator is the bottom number of a fraction.

Example:

In the fraction:

b is the denominator.

Dividend

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

Example 1:

In the equation:

12 is the dividend.

Example 2:

In the expression:

x - 3 is the dividend.

Divisor

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

Example 1:

In the equation:

12÷3=4

3 is the divisor.

Example 2:

In the expression:

2x is the divisor

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

Equality

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

Example 1:

In the statement:

a=b

a is equal to b

Example 2:

In the statement:

3x+4=13

3x+4 is equal to 13.

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

Equation

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.

Example 1:

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.

Example 2:

is 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.

Evaluate

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

Example:

Evaluate the expression

3+2x when x=5

 Step 1 Step 2 Substitute 5 in for x. 3+2(5) Multiply 2 by 5 3+10 Add 3 and 10 13

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

Expand

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

Example:

In the expression:

3(x−4)

 Step 1 Step 2 Expand by multiplying each term in the brackets by 3. 3•x−3• 4 Simplify 3x−12

Exponent

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

Example:

The expression:

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

Expression

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.

Example 1:

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

Example 2:

x²−2x+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

Factor

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.

Example:

Find all the positive factors of 24

• 1 × 24 = 24

• 2 × 12 = 24

• 3 × 8 = 24

• 4 × 6 = 24

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

Fraction

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.

Example 1:

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

Example 2:

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

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

Greatest Common Factor (GCF)

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

Example 1:

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.

Example 2:

In the expression:

18x²+12x

The greatest common factor is 6x because it is the largest factor of both 18x² and 12x.

Improper Fraction

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

Example:

In the term:

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

Inequality

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

Example:

In the statements:

 Statement 1 Statement 2 a ≠ b a is not equal to b a < b a is less than b a > b a is greater than b a ≤ b a is less than or equal to b a ≥ b a is greater than or equal to b

Integer

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.

Example:

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

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

Irrational Number

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.

Example:

The following numbers are irrational:

• 3.605551275…

• 0.94729...

Least Common Denominator (LCD)

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

Example 1:

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.

Example 2:

In the fractions:

The smallest quantity that can be divided evenly by both 3x² and 4x is 12x². Therefore, the LCD of 3x² and 4x is 12x².

Least Common Multiple (LCM)

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

Example:

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" by Lynn Marecek & Mary Anne Anthony-Smith is licensed under CC BY 4.0 / A derivative from the original work

### Like Term

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.

#### Example:

In the expression:

2x²y³ + 14x³ + 24 + 12x²y³ + 3x³ + 77

The terms:

2x²y³ and 12x²y³

are like terms because they have the same literal coefficients: x²y³.

The terms:

3x³ and 14x³

are like terms because they have the same literal coefficient: x³.

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:

14x²y³ + 17x³ + 101

Mixed Number

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

Example:

In the fraction:

2 is the whole number and  is the fraction.

Multiple

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

Example:

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

• 1 × 3 = 3

• 2 × 3 = 6

• 3 × 3 = 9

• 4 × 3 = 12

• 5 × 3 = 15

• 6 × 3 = 18

Natural Numbers

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

Example:

N = Natural Numbers = {1,2,3,4,5,6…}

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

Numerator

The numerator is the top number of a fraction.

Example:

In the fraction:

a is the numerator.

Polynomial

A polynomial is an expression with one or more terms.

Example:

The expression:

3x² + 2x + 4

is a polynomial with three terms:

3x², 2x, and 4

Power

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

#### Example 2:

Prime Factor

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

Example:

Take the number 6.

We know that 2 × 3 = 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.

Prime Number

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

Example 1:

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

Example 2:

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

Product

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

Example 1:

In the multiplication statement:

7 × 4 = 28

The product of 7 and 4 is 28.

Example 2:

In the expression 2x(x+3)In the expression 2x open brackets x plus 3 close brackets

Quotient

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

Example:

In the expression:

12 ÷ 4

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

Example:

In the expression:

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

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

Rational Number

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.

Example:

• 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.

Reciprocal

The reciprocal of the fraction  is  where a ≠ 0 and b ≠ 0 . A number and its reciprocal have a product of 1.

Example:

Given the fraction:

The reciprocal is:

The product of the fraction and its reciprocal is:

Set

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

Example 1:

The following is a set of whole numbers:

W = whole numbers = {0,1,2,3,4,5,6…}

Example 2:

The following is a set of natural numbers:

N = natural numbers = {1,2,3,4,5,6…}

Simplify

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.

Example:

Simplify the expression:

4x − 3 − 3x + 12

Step

Result

Collect the like terms −3x and 12

x + 9

Collect the like terms −3

x − 3 + 12

Therefore, the simplified expression is x + 9.

Solve

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.

Example 1:

Solve for x in the equation:

2x + 3 = 7

 Step 1 Step 2 Subtract 3 from both sides. 2x + 3 − 3 = 7 + 3 Divide both sides by 2. State the solution. x = 2

Example 2:

Solve for y in the equation:

4x = 2y + 6

 Step 1 Step 2 Subtract 6 from both sides. 4x − 6 = 2y + 6 − 6 Divide both sides by 2. State the solution. y = 2x − 3

Sum

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

Example 1:

2 + 6 = 8

the sum of 2 and 6 is 8.

Term

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.

Example 1:

Some examples of terms are 7, y, 5x², -9a, and 13x.

Example 2:

In the expression:

2x + y − 3

There are three terms: 2x, y, and − 3

Trinomial

A polynomial with exactly three terms.

Example:

The expression:

x² − 5 + 8

is a trinomial because there are three terms:

x², −5, 8

Variable

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.

Example 1:

In the equation:

22 + 17 = a

The variable 'a' represents an unknown quantity.

Example 2:

In the equation:

3 + 2x = 13

The variable ‘x’ represents an unknown quantity.

Whole Numbers

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

Example:

W = Whole Numbers = {0,1,2,3,4,5,6…}

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