Integers:

Any counting number including negative numbers.

-Whole numbers

-Ex: -3, -1, 2, 7... but not 2.5)

-Whole numbers

-Ex: -3, -1, 2, 7... but not 2.5)

Real Numbers:

Numbers that appear on the number line including pi, the square toot of 2, etc.

-One that is not imaginary

-One that is not imaginary

Order of Operations: PEMDAS

1. Parentheses

2. Exponents

3. Multiplication/Division

4. Addition/Subtraction

2. Exponents

3. Multiplication/Division

4. Addition/Subtraction

PEMDAS Example:

2 + 6/2 x (5-1)^2 = _______

2 + 6/2 x (5-1)^2 = _______

= 2 + 6/2 x 16

To get the number 16...

(5-1)^2

= (4)^2

=(4)(4)

= 16

= 2 + 48 = 50

To get the number 48...

6/2 x 16 = 48

To get the number 16...

(5-1)^2

= (4)^2

=(4)(4)

= 16

= 2 + 48 = 50

To get the number 48...

6/2 x 16 = 48

You can also remember PEMDAS as...

Please Excuse My Dear Aunt Sally

The Commutative Property:

a + b = b + a,

a x b = b x a

a x b = b x a

The Associative Property:

(a + b) + c = a + ( b + c),

(a x b) x c = a x (b x c)

(a x b) x c = a x (b x c)

The Distributive Property:

a x (b + c) = ab + ac,

a x (b - c) = ab - ac

a x (b - c) = ab - ac

The Commutative and Associate Properties DO NOT WORK WITH...

Subtraction or division

Prime Number:

Is one that is divisible only by itself and 1.

-In other words, a positive integer with exactly positive divisors.

-This includes 2, 3, 5, 7, and 11

-NOT 9 because 3 x 3 = 9

-In other words, a positive integer with exactly positive divisors.

-This includes 2, 3, 5, 7, and 11

-NOT 9 because 3 x 3 = 9

What number is not a Prime Number?

1

What is the smallest Prime Number and the only even Prime Number?

2

Memorize all Primes below 60...

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59

Factorization:

If X can be multiplied by Y to get Z, assuming all of these are positive integers, then X and Y are considered factors of Z

Prime Factorization of a number is...

Dividing it into its constituent primes...

-For 20... this is 3 x 7;

-For 60... 2 x 2 x 3 x 5.

-For 7644...

2 x 2 x 3 x 7 x 7 x 13

-For 20... this is 3 x 7;

-For 60... 2 x 2 x 3 x 5.

-For 7644...

2 x 2 x 3 x 7 x 7 x 13

To find the Prime Factorization of 60...

You can use...

60 = 30 x 2 = 15 x 2 x 2 = 5 x 3 x 2 x 2

60 = 30 x 2 = 15 x 2 x 2 = 5 x 3 x 2 x 2

16 has Five Positive Divisors:

1, 2, 4, 8, 16

40 has Eight Positive Divisors:

1, 2, 4, 5, 8, 10, 20, 40

Divisibility 3:

Sum of digits divisible by 3

Divisibility 4:

The last two digits of number are divisible by 4

Divisibility 5:

The last digit is either a 5 or a 0

Divisibility 6:

Even number and sum of digits is divisible by 3

Divisibility 8:

If the last three digits are divisible by 8

Divisibility 9:

Sum of digits is divisible by 9

Absolute Values:

The absolute value of a number is its distance from the number line.

|x| = x

|-x| = x

|x| = x

|-x| = x

"Percent" =

Per 100;

19% = 19/100

0.43% = 0.43/100

= 43/10000

19% = 19/100

0.43% = 0.43/100

= 43/10000

To find what percent some part is of a whole, use...

part/whole = percent/100

Ex: If 120 people of 800 people in town smoke, then...

120/800 = percent/100

So...

120 divided by 800

= 0.15

= 15/100

= 15% of the townspeople smoke

So...

120 divided by 800

= 0.15

= 15/100

= 15% of the townspeople smoke

Percent Change:

% change =

change/original value

change/original value

Example:

If the price of something goes from $40 to $52, the percent change is...

If the price of something goes from $40 to $52, the percent change is...

(52-40)/40 =

12/40

= 3/10

= 30/10

= 30%

The price increased 30%

12/40

= 3/10

= 30/10

= 30%

The price increased 30%

From the example... this can also be written as...

(change x 100)/ original value

(52-40) x 100

---------------

40

= 1200/40

= 30%

(52-40) x 100

---------------

40

= 1200/40

= 30%

Ratios:

Ratios let us compare the proportions of two quantities

If there is a 2:5 ratio of boys to girls at a school, that means...

That for every 5 girls, there are 2 boys.

SO there could be 2 boys and 5 girls,

20 boys and 50 girls

200 boys and 500 girls, etc.

SO there could be 2 boys and 5 girls,

20 boys and 50 girls

200 boys and 500 girls, etc.

Ratios are given by...

x:y

x to y

or

x/y

(Ratios can also be x:y:z)

x to y

or

x/y

(Ratios can also be x:y:z)

Ratios can be simplified like fractions...

3:6 is the same as 1:2