Algebra: GED Test Prep (page 2)
When you take the GED Mathematics Exam, you will be asked to solve problems using basic algebra. This article will help you master algebraic equations by familiarizing you with polynomials, the FOIL method, factoring, quadratic equations, inequalities, and exponents.
What Is Algebra?
Algebra is an organized system of rules that help solve problems for "unknowns."This organized system of rules is similar to rules for a board game. Like any game, to be successful at algebra, you must learn the appropriate terms of play. As you work through the following section, be sure to pay special attention to any new words you cmay encounter. Once you understand what is being asked of you, it will be much easier to grasp algebraic concepts.
An equation is solved by finding a number that is equal to an unknown variable.
Simple Rules for Working with Equations
- The equal sign separates an equation into two sides.
- Whenever an operation is performed on one side, the same operation must be performed on the other side.
- Your first goal is to get all of the variables on one side and all of the numbers on the other side.
- The final step often will be to divide each side by the coefficient, the number in front of the variable, leaving the variable alone and equal to a number.
5m + 8 = 48
–8 = –8
m = 8
To check an equation, substitute the number equal to the variable in the original equation.
To check the equation you just solved, substitute the number 8 for the variable m.
5m + 8 = 48
5(8) + 8 = 48
40 + 8 = 48
48 = 48
Because this statement is true, you know the answer m = 8 must be correct.
To learn how to work with percentages or proportions, it is first necessary for you to learn how to cross multiply. You can solve an equation that sets one fraction equal to another by cross multiplication. Cross multiplication involves setting the products of opposite pairs of terms equal.
There is one formula that is useful for solving the three types of percentage problems:
When reading a percentage problem, substitute the necessary information into the previous formula based on the following:
- Always write 100 in the denominator of the percentage sign column.
- If given a percentage, write it in the numerator position of the percentage sign column. If you are not given a percentage, the variable should be placed there.
- The denominator of the number column represents the number that is equal to the whole, or 100%. This number always follows the word of in a word problem.
- The numerator of the number column represents the number that is the percent, or the part.
In the formula, the equal sign can be interchanged with the word is.
Finding a percentage of a given number: What number is equal to 40% of 50?
Finding a number when a percentage is given: 40% of what number is 24?
Finding what percentage one number is of another: What percentage of 75 is 15?
A variable is a letter that represents an unknown number. Variables are frequently used in equations, formulas, and in mathematical rules to help you understand how numbers behave.
When a number is placed next to a variable, indicating multiplication, the number is said to be the coefficient of the variable.
8c 8 is the coefficient to the variable c.
6ab 6 is the coefficient to both variables a and b.
If two or more terms have exactly the same variable(s), they are said to be like terms.
7x + 3x = 10x
The process of grouping like terms together performing mathematical operations is called combining like terms.
It is important to combine like terms carefully, making sure that the variables are exactly the same. This is especially important when working with exponents.
7x3y + 8xy3
These are not like terms because x3y is not the same as xy3. In the first term, the x is cubed, and in the second term, the y is cubed. Because the two terms differ in more than just their coefficients, they cannot be combined as like terms. This expression remains in its simplest form as it was originally written.
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