Integers are
whole numbers; they include positive and negative numbers and zero, but not fractions or decimals

A rational number is
a number that can be expressed as a ratio of two integers

An irrational number is
a real number that can't be expressed precisely as a fraction or decimal

The most important irrational numbers for the PSAT
√2, √3, π

To add a positive and a negative
Ignore the signs and find the positive difference between the number parts. Then attach the sign of the original number with the larger number part

Add 23 and -34
Ignore the negative sign and find the positive difference between 23 and -34~which is 11. Then attach the sign of the number with the larger number part- in this case it's the minus sign from the -34. So the answer is -11

To multiply and/or divide positives and negatives
treat the number parts as usual and attach a minus sign if there were originally an odd number of negatives

Multiply -2, -3, and -5
Multiply 2 x 3 x 5 = 30. Go back and note that there were three-an odd number- negatives, so the product is negative: (-2) x (-3) x (-5) = -30

PEMDAS
Parentheses, Exponents, Multiplication and Division (left to right), and Addition and Subtraction (left to right)
*Remember Please Excuse My Dear Aunt Sally, she limps from Left to Right

To count consecutive integers
Subtract the smallest from the largest and add 1

Count the number of integers from 13 through 31
Subtract: 31-13=18
Add 1: 18+1=19

Elements/Members are
the things in a set

The union of Set A and Set B is expressed as
A∪B

If Set A={1,2} and Set B={3,4}, then A∪B=
{1,2,3,4}

The intersection of Set A and Set B is expressed as
A∩B

If Set A={1,2,3} and Set B={3, 4, 5}, then A∩B equals
{3}

Union
set of elements that are in both sets combined

Intersection
the set of elements common to both sets

Factors
Positive integers that divide into a number with no remainder

Multiples
Integers that a number divides into with no remainder

To Find the Prime Factorization of an integer
Factor until all the factors are prime

Relative Primes are
Integers that have no common factor other than one

Determine if two integers are relative primes by
breaking them both down to their prime factorizations

Are 35 and 54 relative primes?
35=5x7
54=2x3x3x3
They have no prime factors in common, so 35 and 54 are relative primes

A Common Multiple is
a number that is a multiple of two or more integers

To find the Least Common Multiple
Check out the multiples of the larger integer until you find one that's also a multiple of the smaller

To find the Greatest Common Factor
Break down the integers into their prime factorizations and multiply all the prime factors they have in common

GCF of 36 and 48
36=2x2x3x3
48=2x2x2x2x3
They have a 2, 2, and 3 in common
2x2x3=12
12 is the GCF

An integer is divisible by 2
if the last digit is even

An integer is divisible by 4
if the last two digits form a multiple of 4
Ex. 562 is not divisible by 4 because the last two digits 62 do not form a multiple of 4

An integer is divisible by 3
if the sum of its digits is divisible by 3

An integer is divisible by 9
if the sum of its digits is divisible by 9

An integer is divisible by 5
if the last digit ends in 5 or 0

The Remainder is
the whole number left over after division

To reduce a fraction to lowest terms
factor out and cancel all factors the numerator and denominator have in common

To add or subtract fractions
find a common denominator and then add or subtract the numerator

To multiply fractions
multiply the numerators and multiply the denominators

To divide fractions
invert the second one and multiply

Percent Formula
Part=% x Whole

To increase a number by a percent
Add the percent to 100 percent, convert to a decimal, and multiply

To find the original whole before a percent increase or decrease
set up an equation

After a 5 percent increase, the population was 59, 346. What was the population before the increase?
Setup: 1.05x=59, 346

Average Formula
Average=sum of terms/ number of terms

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