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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 tree0.333…

3. The variables. Any letter that represents a number. We usually use x or ybut it can be any other letter Pine tree, ior 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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