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Integers are

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

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A rational number is

a number that can be expressed as a ratio of two integers

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An irrational number is

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

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The most important irrational numbers for the PSAT

√2, √3, π

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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

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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

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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

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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

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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

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To count consecutive integers

Subtract the smallest from the largest and add 1

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Count the number of integers from 13 through 31

Subtract: 31-13=18

Add 1: 18+1=19

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Elements/Members are

the things in a set

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The union of Set A and Set B is expressed as

A∪B

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

{1,2,3,4}

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The intersection of Set A and Set B is expressed as

A∩B

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

{3}

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Union

set of elements that are in both sets combined

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Intersection

the set of elements common to both sets

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Factors

Positive integers that divide into a number with no remainder

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Multiples

Integers that a number divides into with no remainder

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To Find the Prime Factorization of an integer

Factor until all the factors are prime

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Relative Primes are

Integers that have no common factor other than one

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Determine if two integers are relative primes by

breaking them both down to their prime factorizations

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Are 35 and 54 relative primes?

35=5x7

54=2x3x3x3

They have no prime factors in common, so 35 and 54 are relative primes

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A Common Multiple is

a number that is a multiple of two or more integers

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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

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To find the Greatest Common Factor

Break down the integers into their prime factorizations and multiply all the prime factors they have in common

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GCF of 36 and 48

36=2x2x3x3

48=2x2x2x2x3

They have a 2, 2, and 3 in common

2x2x3=12

12 is the GCF

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An integer is divisible by 2

if the last digit is even

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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

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An integer is divisible by 3

if the sum of its digits is divisible by 3

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An integer is divisible by 9

if the sum of its digits is divisible by 9

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An integer is divisible by 5

if the last digit ends in 5 or 0

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The Remainder is

the whole number left over after division

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To reduce a fraction to lowest terms

factor out and cancel all factors the numerator and denominator have in common

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To add or subtract fractions

find a common denominator and then add or subtract the numerator

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To multiply fractions

multiply the numerators and multiply the denominators

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To divide fractions

invert the second one and multiply

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Percent Formula

Part=% x Whole

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To increase a number by a percent

Add the percent to 100 percent, convert to a decimal, and multiply

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To find the original whole before a percent increase or decrease

set up an equation

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After a 5 percent increase, the population was 59, 346. What was the population before the increase?

Setup: 1.05x=59, 346

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Average Formula

Average=sum of terms/ number of terms

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