Term | Things to know... | variable | A letter used to represent numbers. Sometimes we use a variable to represent a single value that is unknown. At other times, you may find that many different numbers can be tested in a variable that produce a satisfactory result. For example, how many numbers satisfy the statement: "x is less than 3" | constant | A numerical value that is what it is: 12 is 12; 3 is 3. Constants can still use letters though; like "p » 3.14159" But there's really no mystery to them... You won't wake up one day to find that p changed its value to 42 or something. Why do variables have all the fun? | expression | Does not contain an equal sign. You do not "solve" an expression. You may simplify or evaluate an expression, however. | simplify | Use whatever legal math moves you can think of to make an expression "simpler." (i.e. add like terms, reduce fractions, etc.) | evaluate | If you know the values of all the variables in an expression, you can plug them in and simplify the expression to a single number! Wow! | equation | Uses an equal sign, which means that both sides are balanced or equivalent. We often solve equations to find specific values for the variables that would make the statement true. Typically we put an expression on each side of an equal sign. | exponent | The tiny number written in the upper right corner. It tells you how many times to multiply the base by itself. | base | This is the letter or number which is written larger when compared to the exponent. Example: x³ = x x x; x is the base, and 3 is the exponent. | Order of
Operations | 1) Parentheses 2) Exponents 3) Multiplication / Division (performed in order of appearance) 4) Addition / Subtraction (also performed in order of appearance) |
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Term | Things to know... | natural
numbers | The numbers you use to count with:
1, 2, 3, 4, 5, 6, 7, etc... | whole
numbers | The same as the natural numbers, except now you get to use ZERO:
0, 1, 2, 3, 4, 5, 6, 7, etc... | integers | The same as the whole numbers, but now you get to use the negative numbers too:
... -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 ... | rational
numbers | These include all the integers, but now you get to add in all those pesky fractions and decimal numbers that lie in between. Examples include: ½, ¾, -15 ½, 211.33, -0.001, 5.333333333, etc. | irrational
numbers | These are the all the other numbers that we haven't mentioned yet. These are the rogue numbers; the black sheep of the number line; the radicals; the outlaws; the non-conformists. They can never be written as a fraction. They exist in decimal form, but they refused to be pinned down to a specific value, never ending, and never repeating their trail; they avoid being predictable, and never have a pattern, yet they are still incedible useful to us: p » 3.141592653589..., Ö2 » 1.41421356237..., Ö3» 1.732..., etc. | real
numbers | The real numbers include all of the number groups we have listed above; even the irrational numbers. The real numbers include every number on the number line! | opposite
numbers | Everybody has an evil twin; even numbers. Here are some opposites: 3 and -3, 6.86 and -6.86, p and -p, Ö2 = -Ö2,etc. | absolute value | The distance on a number line from a number to zero:
|4| = 4, |-3| = 3, |p| = p, , |-p| = p, etc. | terms | The parts of an expression that get linked together by plusses and minuses.
Example: 2x³ + 3xy -8y² + 5y - 27
The expression above has 5 terms: 2x³, 3xy, -8y², 5y, -27 | coefficient | The number that is multiplied by the variables in a term.
Example: 2x³ + 3xy -8y² + 5y - 27
The coefficients in the above expression are: 2, 3, -8, and 5 | constant
terms | A term with a number part, but no variable part.
Example: 2x³ + 3xy -8y² + 5y - 27
The constant term in the above expression is -27 | like
terms | Terms that have exactly the same variable patterns.
Example: -6y² + 5 -12y² + 4xy - 27
In the above expression: -6y² and -12y² are like terms.
So are 5 and -27. |
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