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

In the previous article in this series, I covered the arithmetic concepts needed to understand algebra. In this article, we’ll go over some of the terminology needed to understand the basic concepts of algebra.

1. **Order of operations**. This was covered in the arithmetic article. It’s just as 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, *ft*0.333…

3. **Variables.** Any letter that represents a number. We usually use *X* or *there*but can be any letter other than *ft*, *I*or *e.* (These are actually constants, meaning they each have a specific value that cannot change.)

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

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

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

6. **Similar terms**. Have identical variable parts, but which can vary by coefficients. 3xyz and 6xyz are “like terms”. 5xyz and 5xya and NOT “similar terms”.

7. **Exhibitor**. Small raised number which is shorthand for repeated multiplication. (It’s one of those things that Ezine can’t write, so I have to use the ^ symbol.) So xxxx = x^4. A single variable, like y, has an “included” exponent of 1.

8. **Phrases**. Combinations of terms using only + or -. Examples: 2x + 3a or 5a + 2b – 3c

9. **Polynomials**. Expressions of a variable number of terms,

**Monomial** – a 1-term polynomial, like 3x

**Binomial** – a polynomial of 2 terms, like 3x – 4y

**Trinomial** – a polynomial of 3 terms, like 3x – 4y + 6

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

3x – 4 = 6 or x + y = 6

11. **Inequality**. Statements that say things are NOT equal. 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 over the variables. x^2y^3 has degree 5. Degree becomes important when we start plotting a graph.

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

14. **Fractional** **exhibitors**. This is also difficult to explain without the correct symbols. Fractional exponents are another way to write radicals (square roots, cube roots, etc.)

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

Don’t expect to understand all of this now. Just skim through it, then come back to it as we come to the appropriate topics.

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