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39 Cards in this Set

  • Front
  • Back
  • 3rd side (hint)
How does one multiply fractions?
(i.e. a/b * c/d)
Multiply the numerators and denominators straight across.
(a*c/b*d)
Think simple. REALLY simple.
How does one divide fractions?
(i.e. a/b / c/d)
You invert the divisor (the second number), and then multiply!
(a/b * d/c)
They call him Flipper, Flipper, faster than liiiightning...
How does one add fractions of the same denominator?
(i.e. a/b + c/b)
Add the numerators!

(a+c/b)
(no hint. this is pretty obvious.)
How does one add fractions of different denominators?
(i.e. 2/5 + 3/7)
Find a common denominator, and multiply the numerators by said denominator. Then add the numerators and put it over the common denominator.
(common denominator = 35.
35/5 = 7 and 35/7 = 5, so 2*7 = 14 and 3*5 = 15...
SO, 14 + 15 = 29
...and our final answer is 29/35!!
Gee, I wish they had some common ground...
What if there are common factors in the numerator and the denominator?
(i.e. ab/cb)
Cancel out the common factors. It basically gets divided by itself, therefore disappearing from the problem altogether.
(ab/cb = a/c)
What if two fractions are set equal to one another?
(i.e. a/b=c/d)
Cross multiply.

(if a/b=c/d, then ad=bc)
What is the relation between division and the inverse of a number?
Dividing a number by something is the same as multiplying it by 1 over that number.
(i.e. a/b = a*1/b)
What is set builder notation?
Set-builder notation is written like:
A={x|x is an integer and 0<x<7}
It is then read as "A is the set of all x such that x is an integer and 0<x<7."
What is the union of two sets and how is it notated?
A union is the set that consists of all elements that are in S OR T. Basically, it is the set that contains the entirety of both S and T. The two are joined in union. Like a mathematical marriage. A mathemarriage, if you will.

The notation then is shaped like a U. (i.e. A U B)
What is the intersection of two sets and how is it notated?
The intersection of two sets is the set that contains all elements common to both sets. It is the "overlap" section.

The notation is shaped like an upside down U, or an arc. (which unfortunately isn't on the keyboard)
What is an open interval and how is it notated?
An open interval (a,b) is the set of all number between a and b but EXCLUDING the endpoints a and b themselves.

It is obviously notated (a,b).
What is a closed interval and how is it notated?
A closed interval [a,b] is the set of all numbers between AND INCLUDING a and b themselves.

It is obviously notated [a,b].
What is the definition of absolute value?
Absolute value is the distance from a number to zero, so there is an |a| greater than or equal to 0 for every number a. The absolute value of a number is always positive or zero.
How do we define the distance between two points a and b on the real number line?
The distance between a and b is the absolute value of b minus a.

d(a,b)=|b-a|
What if we are multiplying two different powers of the same number?

a^m*a^n
If two integers of two different powers are being multiplied, we just add the exponents.

a^m+n
What if there is a number a with a negative exponent?

a^-x
A negative exponent is the same is 1 over a to the positive of that exponent.

1/a^x
What if a number has the exponent 0?
Any number raised to the power of zero is then equal to 1.
What if we are dividing two different powers of the same number?

a^m/a^n
If two integers of two different powers are being divided, we just subtract the exponents.

a^m-n
What if we raising something with an exponent to a new power?

(a^m)^n
Multiply the old and new powers.

a^mn
What if two numbers inside parentheses are being raised to one power?

(ab)^m
Distribute the power within the parentheses.

a^m*b^m
What if we are raising a quotient(a.k.a. fraction) to a power?

(a/b)^m
Distribute the power into both the numerator and the denominator.
(a^m/b^m)
What if we are raising a fraction to a negative power?

(a/b)^-n
The negative power flips the fraction into its reciprocal, and the power then becomes positive.

(b/a)^n
What if the numerator and the denominator of a fraction are being raised to two different negative powers?

a^-n/b^/m
The negative powers flip the fraction to its reciprocal, and both powers become positive.

a^m/b^n
What is the definition of an nth root?
The nth root of an integer a is equal to b^n=a. Therefore, taking the nth root of a number a is equal to raising a^1/n.

To reiterate, the nth root of a = a^1/n.
What if we take the nth root of a^n, if n is ODD?
The nth root of a^n when n is ODD is equal to a.
What if we take the nth root of a^n, if n is EVEN?
The nth root of a^n when n is EVEN is equal to |a|.
What is a rational exponent, and how do we raise a number a to one?
A rational exponent is also called a fractional exponent. It is merely a fractional power.
What is the degree of a polynomial?
The degree of a polynomial is simply the highest power of any of the terms.
Special Product Formula:
(A-B)(A+B)
= A^2-B^2
Special Product Formula:
(A+B)^2
= A2 + 2AB + B^2
Special Product Formula:
(A-B)^2
= A^2 - 2AB + B^2
Special Product Formula:
(A+B)^3
= A^3 + 3A^2B + 3AB^2 + B3
Special Product Formula:
(A-B)^3
= A^3 - 3A^2B + 3AB^2 - B3
What is factoring?
Factoring is the process by which we reverse expanding. For each set of like terms, find a common factor. Then, combine those factors to find the greatest common factor of the whole expression.
Difference of Squares:
A^2-B^2
= (A-B)(A+B)
Perfect Square:
A^2 + 2AB + B^2
or
A^2 - 2AB + B^2
= (A+B)^2
or
= (A-B)^2
Difference of Cubes:
A^3-B^3
= (A-B)(A^2 + AB + B^2)
Sum of Cubes:
A^3+B^3
= (A+B)(A^2 - AB + B^2)
How can one recognize a perfect square?
A perfect square is recognizable if the middle term (2AB or -2AB) is plus or minus twice the product of the square roots of the outer two terms.