Understanding Algebra

A variable without a coefficient really has a coefficient of 1

"M" really means 1M, and "K" really means "1K"

algebra

In algebra, we use symbols, usually letters such as x, y, or z, to represent unknown numbers. The part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations

descending order

In order from the highest value to the lowest. e.g. 9-1 or Z-A.

like terms

Terms that contain the same variables raised to the same power.

dependent variable

The other variable that you solve for is called the dependent variable. a variable (often denoted by y ) whose value depends on that of another.

Evaluation

The process of simplifying a mathematical expression by first substituting (replacing) a variable with a number, and then solving the expression using order of operations. Example, evaluate 3y-6 when y=8. Because we know y=8, we substitute y with 8. Then, we follow order of operations: In this case, we multiply first.

independent variable

The variable that you are substituting for is called the independent variable

Algebraic expression

A collection of numbers, variables, operational symbols, and grouping symbols

expression

A mathematical phrase that contains operations (such as + or -), numbers, and/or variables.

equation

A mathematical sentence that contains an equals sign. To solve an equation, we find the missing number, or variable, that makes the sentence true. This number is called the solution.

Coefficient

A number multiplied by a variable in an algebraic expression. For example, in the expression 6x + 4, the coefficient is 6.

constant

A number that stays fixed in an expression (it stays constant). For example, in the expression 6x + 4, the constant is 4. A value that does not change, a term without a variable

Properties

A set of math rules that are always true. They often help us to solve equations. Some important ones are. . . Identity property of addition Identity property of multiplication Commutative property of addition Commutative property of multiplication Associative property of addition Associative property of multiplication Distributive property of multiplication Distributive property of multiplication over subtraction

Variable

A symbol that is used to represent a number Letters or symbols used in place of a quantity we don't know yet.

term

A term is a number by itself or the product of a number and a variable (or more than one variable). Each term is separated by an addition calculation symbol. In the expressions 6x + 4, there are two terms: 6x and 4. An expression is made up of one or more terms. In an expression, terms are separated by an addition calculation, which may appear as a positive or negative sign. an expression that is a number, a variable, or the product of a number and one or more variables

combining like terms

Combine like terms to simplify an expression. Rewrite the expression so that it contains fewer numbers, variables, and operations. Basically, you make it look more simple. If two terms do NOT have the exact same variable, they cannot be combined. In order to combine like terms, the variables have to be exactly the same. So, 4y cannot combine with 3y squared because 3y squared really means 3 x y x y, so the terms are not alike.

Operators

These symbols tell us what to do. Addition (+), subtraction (-), multiplication (x), and division (/) are the most common operators. Word problems that deal with expressions use words instead of operators. Sum means addition Difference means subtraction Product means multiplication Quotient means division The symbols with which you can specify the type of calculation you want to perform such as + or -

isolate the variable

To get a variable alone on one side of the equation in order to solve the equation. Often we are not given a number to substitute for the variable. This is when we must solve for the unknown, or solve for x