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
