Direct and inverse variation refers to two values that are proportional to one another depending on a particular constant, or k: Direct variation multiplies the constant to one of the values. Inverse variation divides the constant by one of the values. To determine which variation to use, look closely at the words used in [...]

Absolute value, represented as a vertical line on either side of the value, refers to a number or variable’s distance from zero on the number line. There are always two numbers that share the same distance from zero: a positive number and its negative counterpart. The absolute value for a variable will usually result [...]

The idea of the equation shouldn’t be new to you. We’ve already covered several concepts where an action results in a specific value. If you recall, there is always an equal sign between the action and the result, which is a statement that one expression is equal to the other. Since algebraic expressions can [...]

Since we can multiply algebraic expressions we can factor them out. While the process of factoring is different than using a factor tree, the concept is the same. You are looking for what parts make up the whole algebraic expression. Think of factoring as the reverse of multiplying algebraic expressions. Factoring out algebraic expressions [...]

Algebraic expressions are not solely made up of coefficients and a single variable. Algebraic expressions can be made up of multiple terms, which are either added or subtracted from each other. These terms can include several distinct variables, their coefficients, and known quantities called constants. Depending on their number of terms, algebraic expressions can [...]

Investment word problems involve simple and compound interest. In these problems, an individual deposits a specific amount of money, called the principal, into a bank account that has a particular interest rate. The account accrues interest over a period of time, which is money paid into your account by the bank. Basically, the bank [...]

You’ve ridden in a car enough times to know it travels a specific rate, such as miles per hour, to reach its destination. You’ve also seen the speed limit signs designating the maximum rate allowed for a particular stretch of road. If you look up directions to a place you want to go, then [...]

While the fundamental counting principle, permutations, and combinations deal with all possible combinations that can occur, probability deals with the likelihood of a specific event occurring. For example, you know that when you toss a penny it is just as likely the penny will land heads up as it will land tails up. The [...]

Combinations, another variation of the fundamental counting principle, come into play when the order of the selected elements from the single set does not matter. For example, the ice‐cream store has a special for a cup of ice‐cream with five flavors (no toppings), but you cannot choose the same flavor again for any of [...]

Permutations are a variation of the fundamental counting principle except that you are determining a certain number of combinations from a single set. More importantly, the order in which you choose elements from the set matters. For example, you would use permutations when making a password (123 is not the same as 321). Also, [...]