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Algebra: GED Test Prep (page 2)

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Updated on Mar 9, 2011

Percent

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.

Examples

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?

Like Terms

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.

Example

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.

Example

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.

Example

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.