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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 arithmetic concepts essential to understanding algebra. In this article we will review some of the terms needed to understand the basic concepts of algebra.

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

2. **stability**. As the name implies, constants do not vary in value. Any number is constant: 5, -2.3, 3/8, *pi*0.333…

3. **variables.** Any letter that stands for a number. We usually use *x* or *y*But can be any letter except *pi*, *i*or *e* (These are actually constants – meaning they each have a specific value that cannot be changed.)

4. **period**. Any combination using a single number, a single variable, or both *Multiply and/or divide*. Examples of terms: x, 5, 3a, 7abxy, 3/(xy)

5. **coefficient**. A number before the verse explaining how many there are.

3x is a factor of 3. y has an “understood” coefficient of 1. The coefficient of (4x)/(5y) is 4/5.

6. **Terms like**. have the same variable parts, but the coefficients may differ. 3xyz and 6xyz are “like terms”. 5xyz and 5xya and not “like terms.”

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

8. **Expressions**. Combining terms using only + or -. Examples: 2x + 3y or 5a + 2b – 3c

9. **polynomials**. expression of various 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 with equal signs (complete idea).

3x – 4 = 6 or x + y = 6

11. **Inequalities**. Statements that things are not equal. Example: x + y > 10. In terms x plus y is greater than 10.

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

13. **Negative** **exponents**. It’s hard to explain without the right symbols. Negative exponents are another way of writing fractions. x^(-1) is the same as 1/x

14. **partial** **exponents**. It is also difficult to explain without the correct symbols. Partial exponents are another way of writing radicals (square roots, cube roots, etc.).

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

Don’t expect to understand it all right away. Just scan through it, and then come back to it when we get to the appropriate topics.

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