aUthOR purple new concepts
O
NOTE fROM
o
welcome to my notes
red important details or to keep in mind
the best of lucks yellow characteristics
imma leave a
blue Kinda important /side note
may be a concept prev studied .
summary of color
coding in the side as per highlighting
to keep in mind . just for visually contrast
TF
#final answer !
MATH 108 NOTES
00
↑ 1. The properties of real numbers
Absolute value :
positive magnitude of any given quantity. Physical distance to zero.
1-3 3 151
=
:
5
distance formula given two points NOTE
between two lines (X , y)(X2 ,
Yz) +b Fa + b
V(X2 No Ma+ 1 + 3 +1
+
d = -
X ) + (yz y )
,
-
,
=
d =
cspythagoreom there so
· (Yc Y -
,
) + (Xc X)2 c -
=
((Yc y ) + (Xc X)"
-
,
-
= c (distance)
Properties of numbers
zero property =
for any values a,
a .
0 = 0
b .
0 =
0
Important for solving equations by Zero FACTOR Theorem
a b 3 = 0x
If a. b = 0
.
+
It has to equal o
↳ Either a= 0 or b = 0
, property of division
=
↳
useful to
simplify complex fractions
-
multiply by reciprocal
-
Why :
-
( you want to
get rid of
fractions , by cancelling
the bottom .
properties of negatives
-
3 .
4= -
12
. (4) =
3 -
12
-
a .
b =
( a) .
b =
a( -
b)
-t == (
operations with fractions (get comfortable with them )
!
②
I + = 109=
=
linson)
-
,=
i 5 =
LCD= S
+
:
9
42
-
LCD =
=
=
<(2) 115) + 3
- 4- + LCD = 10
-
=
=
18
#
#
LCD = S
, P 2
.
Integer exponents
↳ rules for all exponents
zero property of exponents
↳ an exponent is a shorthand way of writting repeated multiplication
X5 = X .
X -
X .
X .
X
x3
+ 3
Xo = 1 x* x3 =
yo =
= 1
Negative exponent property
a
1
-
X =
Xa
X
Ya =
Product rule for exponents
xm yn .
=
xm + n
why ?
2
x x
"
= x5
& 2x
*
x" = 2x
*
(3x3)(5xY) 15x =
(-
4yz)(3y3) = -
12y9
(2x-3)(4x3) = two ways to solve
1)(2x 3)(4x)) 8x += 8x 8(1)
-
= = =
8
di
2)(x 3)(4x3)
2 4x
-
=
.
O
NOTE fROM
o
welcome to my notes
red important details or to keep in mind
the best of lucks yellow characteristics
imma leave a
blue Kinda important /side note
may be a concept prev studied .
summary of color
coding in the side as per highlighting
to keep in mind . just for visually contrast
TF
#final answer !
MATH 108 NOTES
00
↑ 1. The properties of real numbers
Absolute value :
positive magnitude of any given quantity. Physical distance to zero.
1-3 3 151
=
:
5
distance formula given two points NOTE
between two lines (X , y)(X2 ,
Yz) +b Fa + b
V(X2 No Ma+ 1 + 3 +1
+
d = -
X ) + (yz y )
,
-
,
=
d =
cspythagoreom there so
· (Yc Y -
,
) + (Xc X)2 c -
=
((Yc y ) + (Xc X)"
-
,
-
= c (distance)
Properties of numbers
zero property =
for any values a,
a .
0 = 0
b .
0 =
0
Important for solving equations by Zero FACTOR Theorem
a b 3 = 0x
If a. b = 0
.
+
It has to equal o
↳ Either a= 0 or b = 0
, property of division
=
↳
useful to
simplify complex fractions
-
multiply by reciprocal
-
Why :
-
( you want to
get rid of
fractions , by cancelling
the bottom .
properties of negatives
-
3 .
4= -
12
. (4) =
3 -
12
-
a .
b =
( a) .
b =
a( -
b)
-t == (
operations with fractions (get comfortable with them )
!
②
I + = 109=
=
linson)
-
,=
i 5 =
LCD= S
+
:
9
42
-
LCD =
=
=
<(2) 115) + 3
- 4- + LCD = 10
-
=
=
18
#
#
LCD = S
, P 2
.
Integer exponents
↳ rules for all exponents
zero property of exponents
↳ an exponent is a shorthand way of writting repeated multiplication
X5 = X .
X -
X .
X .
X
x3
+ 3
Xo = 1 x* x3 =
yo =
= 1
Negative exponent property
a
1
-
X =
Xa
X
Ya =
Product rule for exponents
xm yn .
=
xm + n
why ?
2
x x
"
= x5
& 2x
*
x" = 2x
*
(3x3)(5xY) 15x =
(-
4yz)(3y3) = -
12y9
(2x-3)(4x3) = two ways to solve
1)(2x 3)(4x)) 8x += 8x 8(1)
-
= = =
8
di
2)(x 3)(4x3)
2 4x
-
=
.
