Math

prime factor

A factor that is a prime number.

scientific notation

A mathematical method of writing numbers using powers of ten.

monimial

A number, a variable, or a product of a number and one or more variables

Complex fraction

Complex fraction A complex fraction is a fraction where the numerator, denominator, or both contain a fraction. Example 1: is a complex fraction. The numerator is 3 and the denominator is 1/2. Example 2: is a complex fraction. The numerator is 3/7 and the denominator is 9.

Even numbers

Even numbers always end with a digit of 0, 2, 4, 6 or 8. 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30 are even numbers.

Exponent

Exponent The exponent of a number says how many times to use that number in a multiplication. It is written as a small number to the right and above the base number. In this example: 82 = 8 × 8 = 64 (The exponent "2" says to use the 8 two times in a multiplication.) Another example: 53 = 5 × 5 × 5 = 125 Other names for exponent are index or power.

fraction

How many parts of a whole: • the top number (the numerator) says how many parts we have. • the bottom number (the denominator) says how many equal parts the whole is divided into

improper fraction

Improper Fraction A fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). So it is usually "top-heavy". Example: 5/3 (five thirds) and 9/8 (nine eighths) are improper fractions. Improper fractions are NOT bad.

Odd numbers

Odd numbers always end with a digit of 1, 3, 5, 7, or 9. 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31 are odd numbers.

proper factor

Proper Factor Any of the factors of a number, except 1 or the number itself. All positive factors of 12: 1,2,3,4,6,12 Proper positive factors of 12: 2,3,4,6

Real Number-

Real Number The type of number we normally use, such as 1, 15.82, −0.1, 3/4, etc. Positive or negative, large or small, whole numbers or decimal numbers are all Real Numbers. They are called "Real Numbers" because they are not Imaginary Numbers.

greatest common factor

The largest factor that two or more numbers have in common.

common monomial factor

To factor a polynomial, we look first for the greatest common monomial factor, that is the greatest monomial that is a factor of each term of the poly- nomial. For example: 1. Factor 4rs + 8st. There are many common factors of 4rs and 8st such as 2, 4, 2s, and 4s. The greatest common monomial factor is 4s

Divide Polynomials

divide each term of the dividend by the monomial divisor

look at percentages in accuplacer guide

p

Product

the answer to a multiplication problem

numerator

the top number in a fraction

solution set of an equation

the value or values of the variable that make the equation true

difference between two squares

x^2 - y^2 = (x+y)(x-y)

"radical" equation

A "radical" equation is an equation in which the variable is hiding inside a radical symbol (in the radicand).

double inequalities

A double inequality is an inequality where there are two signs, as opposed to one. Ex: an inequality could be 3x < 15 A double inequality could be 3x < 15 < x + 20

Polynomial

A monomial or a sum or difference of monomials

Irrational Number

A real number that can NOT be made by dividing two integers (an integer has no fractions). Its decimal goes on forever without repeating. Example: π (the famous number "pi") is an irrational number, as it can not be made by dividing two integers. See: Rational Number pi is irrational

Composite Number

Composite Number A whole number that can be made by multiplying other whole numbers. Example: 6 can be made by 2 × 3 so is a composite number. But 7 can not be made by multiplying other whole numbers (except 1×7, but we said to use other whole numbers), so is not a composite number, it is a prime number. All whole numbers above 1 are either composite or prime.

PEMDAS "Order of Operations"

Parenthesis Exponents Multiply/Divide Add/Sub

Denominator

The bottom number in a fraction. Shows how many equal parts the item is divided into. (The top number is the numerator and shows how many parts we have.)

Absolute inequalities

The math symbol used for absolute values is a set of straight vertical lines on either side of the value, like |x|. Our absolute values can never be negative, so problems such as |x| = -4 cannot be solved. An absolute value inequality is an absolute value problem with inequalities.

empty set

an equation that has no true solution

quadratic formula

n elementary algebra, the quadratic formula is the solution of the quadratic equation. There are other ways to solve the quadratic equation instead of using the quadratic formula, such as factoring, completing the square, or graphing. Using the quadratic formula is often the most convenient way. The general quadratic equation is a x 2 + b x + c = 0. {\displaystyle ax^{2}+bx+c=0.}

degree of a polynomial

the greatest degree of any term in the polynomial

Base-10 system

• our everyday number system is a Base-10 system. • the Base-10 number system is known as the decimal system and has 10 digits to show all numbers 0,1,2,3,4,5,6,7,8,9 using place value and a decimal point to separate whole numbers from decimal fractions.

rational number

a divided by b A number that can be made by dividing two integers (an integer is a number with no fractional part). The word comes from "ratio". Examples: • 1/2 is a rational number (1 divided by 2, or the ratio of 1 to 2) • 0.75 is a rational number (3/4) • 1 is a rational number (1/1) • 2 is a rational number (2/1) • 2.12 is a rational number (212/100) • −6.6 is a rational number (−66/10) • etc But π (pi) is not a rational number, it is an "Irrational Number".

Rational Expression

an algebraic fraction whose numerator and denominator are polynomials

equivalent fractions

having the same value

interger or whole number

integer (pronounced IN-tuh-jer) is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14, .09, and 5,643.1.

look at proportions in guide

l

Power

more ... Power The power of a number says how many times to use the number in a multiplication. It is written as a small number to the right and above the base number. In this example: 82 = 8 × 8 = 64 (Other names for power are index or exponent)

Multiply Polynomials

multiply each term in one polynomial by each term in the other polynomial add those answers together, and simplify if needed

common denominator

A denominator that is the same in two or more fractions.We can add and subtract fractions only when they have a common denominator. To get common denominators we can multiply both top and bottom of a fraction by the same amount. Example: we can't add 1/3 and 1/2 as they are. • But when we multiply 1/3 by 2/2 we get 2/6 • And when we multiply 1/2 by 3/3 we get 3/6 • Now they have a common denominator! • We can now add 2/6 and 3/6 to get 5/6

decimal point

A point (small dot) used to separate the whole number part from the fractional part of a number. Example: in the number 36.9 the point separates the 36 (the whole number part) from the 9 (the fractional part, which really means 9 tenths). So 36.9 is 36 and nine tenths.

prime number

A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole numbers that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. Numbers that have more than two factors are called composite numbers. The number 1 is neither prime nor composite.

mixed number

A whole number and a fraction combined into one "mixed" number. Example: 1½ (one and a half) is a mixed number. Also called a Mixed Fraction.

Decimal numbers

Decimal numbers are used to represent numbers that are smaller than the unit 1.Decimals are written to the right of the units place separated by a period. That is the say: Hundreds Tens Units . Tenths Hundredths Thousandths

Division

Division Division is splitting into equal parts or groups. It is the result of "fair sharing". Example: there are 12 chocolates, and 3 friends want to share them, how do they divide the chocolates? Answer: They should get 4 each. We use the ÷ symbol, or sometimes the / symbol to mean divide: 12 ÷ 3 = 4 12 / 3 = 4 See division in action here. Notice that there is often an amount left over called the "remainder":

Least Common Multiple

Least Common Multiple The smallest positive number that is a multiple of two or more numbers. Example: the Least Common Multiple of 3 and 5 is 15, because 15 is a multiple of 3 and also a multiple of 5. Other common multiples include 30 and 45, etc, but they are not the smallest (least). (Also called Lowest Common Multiple)

Order of Operations (PEMDAS)

Order in which you solve a math expression: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction

Completing the Square

Say we have a simple expression like x2 + bx. Having x twice in the same expression can make life hard. What can we do? Well, with a little inspiration from Geometry we can convert it, like this: As you can see x2 + bx can be rearranged nearly into a square ... ... and we can complete the square with (b/2)2 In Algebra it looks like this: x2 + bx + (b/2)2 = (x+b/2)2 "Complete the Square" So, by adding (b/2)2 we can complete the square. And (x+b/2)2 has x only once, which is easier to use.

Negative Exponents

Search Negative Exponents Exponents are also called Powers or Indices Let us first look at what an "exponent" is: 8 to the Power 2 The exponent of a number says how many times to use the number in a multiplication. In this example: 82 = 8 × 8 = 64 In words: 82 can be called "8 to the second power", "8 to the power 2" or simply "8 squared" Example: 53 = 5 × 5 × 5 = 125 In words: 53 can be called "5 to the third power", "5 to the power 3" or simply "5 cubed" In general: an tells you to use a in a multiplication n times: exponent definition But those are positive exponents, what about something like: 8-2 That exponent is negative ... what does it mean? Negative Exponents Negative? What could be the opposite of multiplying? Dividing!

Discriminant

The discriminant is the part of the quadratic formula underneath the square root symbol: b²-4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.

radicand

The value inside the radical symbol. The value you want to take the root of. In √x, "x" is the radicand

Parentheses

Used in mathematics as grouping symbols for operations. When simplifying an expression, the operations within the parentheses are performed first.

Solve a Quadratic Equation by Factoring

Well, suppose you have a quadratic equation that can be factored, like x2+5x+6=0. This can be factored into (x+2)(x+3)=0. So the solutions must be x=-2 and x=-3. Note that if your quadratic equation cannot be factored, then this method will not work.

percentages

When we say "Percent" we are really saying "per 100 "100% means all. 50% means half. A Percent can also be expressed as a Decimal or a Fraction Example: Calculate 25% of 80 25% = 25 100 And 25 100 × 80 = 20 So 25% of 80 is 20xample: 15% of 200 apples are bad. How many apples are bad? 15% = 15 100 And 15 100 × 200 = 15 × 200 100 = 15 × 2 = 30 apples 30 apples are bad Example: A Skateboard is reduced 25% in price in a sale. The old price was $120. Find the new price. First, find 25% of $120: 25% = 25 100 And 25 100 × $120 = $30 25% of $120 is $30 So the reduction is $30 Take the reduction from the original price $120 − $30 = $90 The Price of the Skateboard in the sale is $90