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Explaining Variables and Terms Study Guide (page 2)

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Updated on Oct 3, 2011

Algebra Vocabulary

A sentence, whether it contains variables or not, is made up of terms. A term is a variable, constant, or product of both, with or without exponents, and is usually separated from another term by addition, subtraction, or an equal sign. While a variable can have different values in different situations, a constant is a term that never changes value. Real numbers are constants. The sentence x + 4 = 5 contains 3 terms: x, 4, and 5.x is a variable, and 4 and 5 are constants.

The sentence 3x – 5 = 11 also contains 3 terms: 3x –5, and 11.3x is a single term, because 3 and x are multiplied, not added or subtracted. In the same way, – = 2 also has only three terms, because is a single term.

The numerical multiplier, or factor, of a term is called a coefficient. In the term 3x, 3 is the coefficient of x, because 3 multiplies x. In the term 9y, the coefficient of y is 9. In multiplication, the order in which one value multiplies another does not matter: 4×5and 5×4 both equal 20. The order in which 3 and x are multiplied does not matter, either, but we typically place the constant in front of the variable. The constant is considered the coefficient, and the variable is considered the base. Because the coefficient is one factor of the term, the base is the other factor. If a variable appears to have no coefficient, then it has a coefficient of 1: 1x = x.

Tip:

Division can be rewritten as multiplication. x divided by 5 is the same as x multiplied by The coefficient of x in the term is because can be written as

In algebra, the base of a term is often raised to an exponent. An exponent is a constant or variable that tells you how many times a base must be multiplied by itself. Exponents are small numbers (superscripts) that appear above and to the right of a base. The term x2 is equal to x multiplied by x. The term y6 means (y)(y)(y)(y)(y)(y). If a variable appears to have no exponent, then it has an exponent of 1: x1 = x.

Like and Unlike Terms

If two terms have the same base raised to the same exponent, then the two terms are called like terms. For instance, 2a2 and –6a2 are like terms, because both have a base of a with an exponent of 2. Even though the terms have different coefficients, they are still like terms. If two terms have different bases, or identical bases raised to different exponents, then the two terms are unlike terms. 7m and 7n are unlike because they have different bases. 7m4 and 7m5 are also unlike terms. Even though they have the same base, the exponents of the bases are different. In the next lesson, we will see why recognizing terms as like or unlike is so important.

Find practice problems and solutions for these concepts at Explaining Variables and Terms Practice Questions.

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