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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, ft0.333…
3. Variables. Any letter that represents a number. We usually use X or therebut can be any letter other than ft, Ior 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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