1.2: Properties of numbers

commutative prop of addition: 10 + (-2x) =

(-2x) + 10

what do rational numbers include?

- whole numbers (123) - integers (-12) - terminating decimals (.75) - repeating decimals (.3̅ ) (√36)

associative prop of multiplication: 3(6y) =

6(3y)

associative prop of addition: 16 + (8+m) =

8 + (m+16)

commutative prop of multiplication: 3x·5y·9z =

9z·5y·3x

what is an irrational number?

a number that can be written as a decimal but can't be written as a fraction

identity (addition vs multiplication)

addition >> 0 is the identity ex: a+0 = a = 0 + a multiplication >> 1 is the identity ex: a·1 = a= 1·a

inverse (addition vs multiplication)

addition >> add opposite that'll equal to 0 ex: a + (-a) = 0 = (-a) + a multiplication >> take reciprocal which will equal to 1 ex: a·1/a = 1 = 1/a ·a

whole numbers

all positive numbers from 0 to infinity

natural numbers

all positive numbers from 1 to infinity

what is a rational number?

any number that can be written as a simple ratio (fraction)

3 + (12+4x) = (3+12) + 4x

associative prop of addition

5x + (4 + y) = (5x + 4) + y

associative prop of addition

(-4·10)·8 = -4(10·8)

associative prop of multiplication

10(2x) = (10·2)x

associative prop of multiplication

inverse =

cancel

(10b+8c) + 4d = (8c+10b) + 4d

commutative prop of addition

6(xy) = 6(yx)

commutative prop of multiplication

another name for natural numbers

counting numbers

ax + bx = (a+b)x

distributive prop

3x + 0 = 3x

identity prop of addition

5y(1) + 9 = 5y + 9

identity prop of addition

1(3p-2) = 3p-2

identity prop of multiplication

closure

if you add 2 real numbers, you'll only get a real number (same thing for multiplication)

14 + (-14) = 0

inverse prop of addition

1/y·y = 1

inverse prop of multiplication

commutative =

order

examples of irrational numbers

pi (π) square root of any imperfect square (√3) (√5)

associative =

regroup

identity =

same

commutative property

when you switch the order ex: a+b+c = c+b+a (a+b)+c = (b+a)+c) a·b = b·a

associative

when you switch the order and change what is inside the parenthesis ex: (a+b) + c = a (b+c) (ab)c = a(bc)

integers

whole numbers and their opposites (positives, negatives, and 0)

what is the difference between whole numbers and natural numbers?

whole numbers include 0 and natural numbers don't