Algebra (The Basics) Vocabulary

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Algebra (The Basics) Vocabulary
2014-01-21 11:15:46
Various terms related to Algebra.
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  1. al·ge·bra
    • noun
    • 1. the branch of mathematics that deals with general statements of relations, utilizing letters and other symbols to represent specific sets of numbers, values, vectors, etc., in the description of such relations.
  2. Operations
    Add, subtract, multiply, divide, squaring, etc. If it isn't a number it is probably an operation.
  3. Order of Operations

    • Do things in parenthesis and brackets First.
    • Exponents (Powers, Roots)
    • Divide and Multiply rank equally (and go left to right)
    • Add and Subtract rank equally (and go left to right)
  4. What is an equation?
    • An equation says that two things are equal.
    • It will have an equals sign "=" like this:


    That equations says: what is on the left (x + 2) is equal to what is on the right (6)

    So an equation is like a statement "this equals that"
  5. Formula
    A special type of equation that shows the relationship between different variables.

    A formula will have more than one variable.
  6. What is a variable?
    A symbol like x or V that stands in for a number we don't know yet.

  7. What is a constant?
    A number on its own is called a Constant.

  8. What is a coefficient?
    • A Coefficient is a number used to multiply a variable (4x means 4 times x, so 4 is a coefficient).
  9. What is an operator?
    An Operator is a symbol (such as +, ×, etc) that represents an operation (ie you want to do something with the values).

  10. What is a term?
    A Term is either a single number or a variable, or numbers and variables multiplied together.

  11. What is an expression?
    An Expression is a group of terms (the terms are separated by + or - signs).

  12. What is the formula for finding the volume of a box?
    V = lwh

    V stands for volume, l for length, w for width, and h for height.
  13. What is Subject of a Formula?
    The "subject" of a formula is the single variable (usually on the left of the "=") that everything else is equal to.
  14. Inequalities
    Mathematics is not always about "equals"! Sometimes you only know that something is bigger or smaller. 

    We call things like that inequalities (because they are not "equal")

    • >  greater than      5 > 2
    • <  less than           7 < 9

    • ≥  greater than or equal to      x ≥ 1
    •           or
    • ≤  less than or equal to          y ≤ 3

    Inequality tells you about the relative size of two values.
  15. What is an exponent?
    The exponent (such as the 2 in x2) says how many times to use the value in a multiplication.

    82 = 8 × 8 = 64
  16. What is a polynomial?
    Polynomial comes from poly- (meaning "many") and -nomial (in this case meaning "term") ... so it says "many terms"

    Example of a Polynomial: 3x2 + x - 2

    A polynomial can have constants, variables and exponents, but never division by a variable.
  17. What are monomial, binomial, trinomial?
    Monomial, binomial, trinomial are special names for polynomials with 1, 2 or 3 terms:

  18. What are like terms?
    Like Terms are terms whose variables (and their exponents such as the 2 in x2) are the same.

    In other words, terms that are "like" each other. (Note: the coefficients can be different)

    • (1/3)xy2                    -2xy2                  6xy2
    • Are all like terms because the variables are all xy2