Unit 1

Variable

"Like terms" are terms whose variables (and their exponents such as the 2 in x2) are the same. In other words, terms that are "like" each other. Note: the coefficients (the numbers you multiply by, such as "5" in 5x) can be different

like terms

"Like terms" are terms whose variables (and their exponents such as the 2 in x2) are the same. In other words, terms that are "like" each other. Note: the coefficients (the numbers you multiply by, such as "5" in 5x) can be different

Irrational Number

A number that cannot be expressed as a ratio between two integers and is not an imaginary number. If written in decimal notation, an irrational number would have an infinite number of digits to the right of the decimal point, without repetition. Pi and the square root of 2 (√2) are irrational numbers.

Perfect Cube

A perfect cube is the result of multiplying a number three times by itself. a · a · a= a³ We can also say that perfect cubes are the numbers that have exact cube roots. 1, 8, 27, 64, 125, 216, 343, 512, 729, 1,000, 1,331, 1,728, 2,197, 2,744, 3,375...

equivalent expressions

An algebraic expression is a string of numbers, variables, mathematical operations, and possibly exponents. For example, 4x + 3 is a basic algebraic expression. Or, we could get a little more complex with 3x(2x^2 + 2x - 5) + 6y. ... Also notice that there's no equal sign in an algebraic expression.

Exponent

An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.

Integer

An integer (pronounced IN-tuh-jer) is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14, .09, and 5,643.1.

Power to Power Rule

Below is List of Rules for Exponents and an example or two of using each rule: Zero-Exponent Rule: a0 = 1, this says that anything raised to the zero power is 1. Power Rule (Powers to Powers): (am)n = amn, this says that to raise a power to a power you need to multiply the exponents.

term

In Algebra a term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or − signs. See: Variable. Algebra - Definitions.

Rational Number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number

Zero Exponent Rule

Let's first define some terms as they relate to exponents. When you have a number or variable raised to a power, the number (or variable) is called the base, while the superscript number is called the exponent, or power. ... The zero exponent rule basically says that any base with an exponent of zero is equal to one.

expression

Math Term Definition. Algebraic Expression. An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables (like x or y) and operators (like add,subtract,multiply, and divide). Here are some algebraic expressions: a + 1

Negative Exponet Rule

Negative Exponent Rule: , this says that negative exponents in the numerator get moved to the denominator and become positive exponents. Negative exponents in the denominator get moved to the numerator and become positive exponents.

Quotient Rule of Exponet

Quotient Rule: , this says that to divide two exponents with the same base, you keep the base and subtract the powers. This is similar to reducing fractions; when you subtract the powers put the answer in the numerator or denominator depending on where the higher power was located

Radical Symbol

Radical expression involving roots, also known as an Nth root. Radical symbol (√), used to indicate the square root and other roots.

Rational Approximation

Rational Approximation. If is any number and and are integers, then there is a rational number for which. (1) If is irrational and is any whole number, there is a fraction with and for which. (2)

Cude Root

Real numbers. For any real number y, there is one real number x such that x3 = y. ... For real numbers, we can define a unique cube root of all real numbers. If this definition is used, the cube root of a negative number is a negative number.

Scientific Notation

Scientific notation is the way that scientists easily handle very large numbers or very small numbers. For example, instead of writing 0.0000000056, we write 5.6 x 10-9.

Cude Root Symbol

The Cube Root Symbol. This is the special symbol that means "cube root", it is the "radical" symbol (used for square roots) with a little three to mean cube root. You can use it like this: (we say "the cube root of 27 equals )"

Coefficient

The coefficients are the numbers that multiply the variables or letters. Thus in 5x + y - 7, 5 is a coefficient. It is the coefficient in the term 5x. Also the term y can be thought of as 1y so 1 is also a coefficient. Like terms are terms that contain the same variable raised to the same power.

Decimal Expansion

The decimal expansion of non-negative real number x will end in zeros (or in nines) if, and only if, x is a rational number whose denominator is of the form 2n5m, where m and n are non-negative integers.

Product Rule of Exponets

The exponent "product rule" tells us that, when multiplying two powers that have the same base, you can add the exponents. In this example, you can see how it works. Adding the exponents is just a short cut! The "power rule" tells us that to raise a power to a power, just multiply the exponents.

Square Root

a number that produces a specified quantity when multiplied by itself.

linear expression

noun, Mathematics. 1. a first-order equation involving two variables: its graph is a straight line in the Cartesian coordinate system. 2. any equation such that the sum of two solutions is a solution, and a constant multiple of a solution is a solution.

Perfect Square

the product of a rational number multiplied by itself. the product of a polynomial multiplied by itself.