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## A Parent’s Guide to Algebra’s Basic Concepts – Basic Algebra Terminology

In the previous article in this series, I discussed the arithmetic concepts needed to understand algebra. In this article we will review some of the terminology needed to understand the basics of algebra.

1. **Order of operations**. This was covered in the arithmetic article. It is equally important in algebra.

2. **constants**. As the name suggests, constants do not vary in value. Any number is a constant: 5, -2,3, 3/8, *Pine tree*0.333…

3. **The variables.** Any letter that represents a number. We usually use *x* or *y*but it can be any other letter *Pine tree*, *i*or *e.* (They are actually constants, meaning each has a specific value that cannot change.)

4. **term**. A single number, a single variable or any combination of both using *multiplication and/or division*. Examples of terms: x, 5, 3a, 7abxy, 3/(xy)

5. **coefficient**. The number in front of a term that tells “how many” there are.

3x has a coefficient of 3. y has an “included” coefficient of 1. (4x)/(5y) has a coefficient of 4/5

6. **Similar terms**. They have identical variable parts, but may vary according to the coefficients. 3xyz and 6xyz are “like terms”. 5xyz and 5xya and NOT “like terms”.

7. **exponent**. Raised small number that is a shorthand for repeated multiplication. (This is one of those things that Ezine can’t type, so I have to use the ^ symbol.) So xxxx = x^4. A single variable, such as y, has an “included” exponent of 1.

8. **expressions**. Combinations of terms that use only + or -. Examples: 2x + 3y or 5a + 2b – 3c

9. **Polynomials**. Expressions of several numbers of terms,

**monomial** – a polynomial of 1 term, such as 3x

**binomial** – a polynomial of 2 terms, such as 3x – 4y

**trinomial** – a polynomial of 3 terms, such as 3x – 4y + 6

10. **Equations**. Algebraic sentences (have a complete thought) with an equal sign.

3x – 4 = 6 x + y = 6

11. **Inequalities**. Statements that say things are NOT the same. Example: x + y > 10. In words, x plus y is greater than 10.

12. **degree**. Basically, the exponent of the variable if there is only one variable. 2x has degree 1. 3y^4 has degree 4. If a term has more than one variable, then the degree is the sum of the exponents of the variables. x^2y^3 has degree 5. Degree becomes important when we start graphing.

13. **negative** **exponents**. This is hard to explain without the correct symbols. Negative exponents are another way of writing fractions. x^(-1) is the same as 1/x

14. **Fractionated** **exponents**. This is also hard to explain without the correct symbols. Fractional exponents are another way of writing radicals (square roots, cube roots, etc.)

15. **Zero as exponent**. In words, anything raised to the 0 power is 1 (except 0^0 which is undefined).

Don’t expect to understand all of this right now. Just scan it and come back to it as we come to the right topics.

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