8th Grade Pre-Algebra Help

Help with 8th Grade Algebra

Radicals and Exponents

In 8th grade algebra, you'll work with equations containing radicals and exponents, which you can think of as being opposites. An exponent (the small number) tells you to multiply the base (the big number) a certain number of times. For example, 3^2 tells you to multiply three twice (3^2 = 3 x 3 = 9).

Radicals ask you to find the integer that you have to multiply a given number of times to get a certain number. For instance, (square root of 9) = 3 because you have to square three to get nine (3^2 = 9).

Cube roots are similar, but they ask you to find the number that you have to cube (multiply three times) to produce a certain other number. For example, (cube root of 27) = 3 because 3^3 = 3 x 3 x 3 = 27.

Proportional Relationships

You'll also learn that linear equations, which are expressed as straight lines on a graph, represent proportional relationships. In a proportional relationship, one quantity changes by a certain amount for every unit of change in another quantity.

For example, if a car is traveling steadily at 60 miles per hour (mph), it will cover 60 miles in one hour, 120 miles in two hours and 180 miles in three hours. This is a proportional relationship because for every hour, the distance traveled increases by the same amount (60 miles).

Solving Linear and Simultaneous Equations

In 8th grade pre-algebra, you'll also solve equations with one variable, including those that require you to use the distributive property, a(b + c) = ab + ac. Additionally, you'll learn to solve equations by collecting like terms. For instance, in 6x + 3x = 18, the terms 6x and 3x both have the same variable (x), so you can combine them by adding the coefficients (six and three). This gives you 9x = 18. Then, you can divide both sides by nine to get x = 2.

Functions

A function is a special type of equation that specifies how two variables are related. Some functions are linear, so they are represented by straight lines on the graph. The linear equations we discussed earlier are examples of linear functions.

If the graph of a function increases from left to right, then it represents an increasing function. For instance, the distance traveled by the car in the example above is represented by an increasing function because the distance traveled grows larger over time. A function representing a car that is slowing down would produce a graph that decreases from left to right, so this function would be decreasing.