Algebra/Arithmatic Flashcards
(neg)x(pos)
(neg)
-l-4l
Absolute value ignores the + or - sign because it describes how far number is from 0. Therefore the answer is -4. The Equation can also be seen as -1x4=-4.
Numerator
The top half of a fraction.
Solution Set
Set of solutions
Denominator
Bottom half of a fraction
1-(-5)=
6 or comes out to be 1+5.
(pos)/(pos)
(positive)
(pos)/(neg) or (neg)/(pos)=
(neg)
(neg)x(neg)
(positive) In order for the multiplication of positive and negative numbers to be consistent with everything i’ve constructed in math so far. The product of this equation must be positive and make sense to me intuitively.
(neg)x(pos)=
(negative)
Commutative property
(a)+(b)=(b)+(a)
(a)x(b)=(b)x(a)
Think about the distance between your home and job being the same distance both ways.
Intuition
The ability to understand something immediately without the need for conscience reasoning.
(pos)x(pos)=
(positive)
(-)/(-)
(positive)
Improper fraction
When the numerator is wither greater than or equal to the denominator.
What do fractions need in common in order to be able to add them together?
They must have common denominator.
Constant
A constant is a number on its own or sometimes a letter such as a,b orc to stand for a fixed number.
For example, a general quadratic function is commonly written as:
a x^2 + b x + c + 9 =
where a, b, c and 9 are constants (or parameters), while x is the variable, a placeholder for the argument of the function being studied. A more explicit way to denote this function is
Like Terms
Like terms are terms that have the same variables or powers. The coefficients don’t need to be the same.
Distributive Property
Property of algebra that allows us to distribute a multiplied value across a polynomial.
6(2 + 4x)
The Distributive Property tells us that we can remove the parentheses if the term that the polynomial is being multiplied by is distributed to, or multiplied with each term inside the parentheses.
This definition is tough to understand without a good example, so observe the example below carefully.
6(2 + 4x)
now by applying the Distributive Propery
6 * 2 + 6 * 4x
The parentheses are removed and each term from inside is multiplied by the six.
Now we can simplify the multiplication of the individual terms:
12 + 24x
Another example is presented on the next page.
Variable
Is a letter that represents a number.
Foil
First Outer Inner Last
Example: (x + 2)(x + 5) = x·x + x·5 + 2·x + 2·5
First Outer Inner Last = x2 + 7x + 10
Polynomial
A polynomial is a monomial or the sum or difference of two or more polynomials.
Each monomial is called the term of the Polynomial.
Evaluating Expression
You evaluate an expression by replacing a variable with the given number and performing indicated operation.
Algebraic expression
Algebraic Expression- Is a number, variable or combination of the two connected by some mathematical operation like addition,subtraction, multiplication ect.
Order of operations
When you do have more than one mathmatical operation you need to use the order of operations.
PEMDAS (Please,Excuse,My,Dear,Aunt,Sally)
P: Parenthesis/Grouping symbols E: Exponents (radicals) M: Multiplication/Division always solved from left to right D: ^ A: Addition/Subtraction S:^
Addition Terms/
For word problems
Sum,Increased,More
The sum of five and x: 5+x
A number increased by 5: n+5
5 more than a number: n+5
Opposite of addition
Subtraction
Multiplication terms/
For word problems
Product, Times, or one fifth of a number
The product of 5 and a number: 5n
5 times a number: 5n
one fifth of a number: 1/5n
opposite of multiplication
Division
Division terms/
For word problems
Quotient, Divided
The Quotient of a number and 5: n/5
A number divided by 5: n/5
Distance travled (Constant rate)
(Distance) = (Rate)(Time)
Perimiter
(Perimeter) = 2(Length)+2(Width)
Area of a rectangle
(Area) = (Length)(Width)
Prime number
A whole number that has two distinct factors.
Ex. 2 is 1 and 2
Equivalent Expression
Expression that looks different but has the same value.
Ex. 5*12=60 and 5(10+2)=60
Product
When two or more numbers are multiplied together.
6*3 = 18
factors product
Qoutient
The answer you get after you divide one number by another.
Dividend / Divisor = Qoutient
Prime factorization
When you rewrite a number as a product of prime numbers.
Ex: 12 = (2)(6) = (2)(2)(3)
Fundamental principle of fractions
(a)(c)/(b)(c) = (a)/(b) In other words if you divide out the same factor in both the numerator and denominators then you will end up with an equivalent expression.
Mixed number
Is a whole number and fraction combined.
Term
Is either a single number or variable or a number and variable multiplied together.
Common factor
When you find the factors of two or more numbers and then you look to see which factors are the same. Ex: 12 and 30 Factors of 12 are 1,2,3,4,6,12 Factors of 30 are 1,2,3,5,6,10,15,30 Common factors are 1,2,3,6.
Word problem rule of thumb
Always assign the first variable for the quantity for which you have the least amount of information.`
Cost
C=(n)(p)
Grouping symbol
A device such as parenthesis or brackets used to enclose an expression that should be simplified first.
Reciprocal
ax(1/a)
When a does not equal zero.
just turn the constant or number (a) into a fraction and flip it upside down.
You can change divisional fraction into a multiplication problem by using the reciprocal of the divisor.
Least common denominator
Is the smallest number divisible by all denominators.
Nested Grouping symbols
When you have more than one grouping symbol in the same expression.
Value of expression
The result that you get after evaluating the expression. doesn’t always have to be the correct answer.
Equation
Two expressions set equal to each other.
Solution
A value such that when you replace the variable with it, it makes the equation true.
What is any number divided by 0?
Undefined
Domain
Set of numbers that a variable may represent.
Subtraction
The difference between a number and 5. (n-5)
A number decreased by 5. (n-5)
5 less than a number. (n-5)
5 minus a number. (5-n)
Exponential notation
An exponent tells you how many times you write a base in a product.
Ex.4x4x4x4 = 4^3
Expression
A finite combination of symbols that is well formed according to the rules that depend on context.
Formulas
The definition of a formula is a group of mathematical symbols that express a relationship or that are used to solve a problem, or a way to make something.
Rules for multiplying and dividing like terms.
That the base in both polynomials must be the same.
Ex a^2 x a^3 = a^5
How do you make an exponent in a fraction positive?
(a^-1)/1
The problem was simplified by just changing its exponent to the opposite sign (from negative to positive) and moving it to the bottom of a fraction.
a^-2 = (1)/ a^2
Take the negative exponent and move it by itself to either the top or bottom to make it positive.
Definition of like terms through addition and subtraction.
Need to be the same variable with the same exponent.
The understood (x)
Means that (x) is not just (x) but instead 1x^1/1 this lets us know that we can apply the coefficient exponent or denominator wherever we want.
Difference between (-3)^2 and -3^2
(-3)2 has a base which means the equation looks like this -3x-3.
-3^2 has a base which means the equation looks like this 3x3.
