Reflection For thevideomathtutor.com
By Luis Anthony Ast
Basic
Mathematics 4
PROPERTIES
OF NUMBERS
There are so many ways to introduce mathematics. An
example is by video tutorial. By this media, students can learn Mathematics
easily. Here is the reflection I made from the video that I got in my English
course several last weeks. Enjoy, please :D
The
Reflexive Property of Equality
A number is equal to itself.
Example:
If
given a number A, then it means that A=A
Then
another example is 2=2, 3=3 and soon.
The
Symmetric Property of Equality
if one value is equal
to another, then that second value is the same as the first.
Example:
1.
If given A=B, so we can move each number
in opposite side become B=A,
2.
Then when we do an algebraic equation
then we find the equation is 3=X. it doesn’t matter. But in the final answer we can write X=3. Cause on
the symmetric property, if we change to another side it will be the same.
The
Transitive Property of Equality
If one value is equal
to a second, and the second happens to be the same as a third, then we can conclude
the first value must also equal the third number.
Example:
1.
If given A=B and B=C, so we can conclude
that A=C.
The
Substitution of Property
If one value is equal
to another, then the second value can be used in place of the first in any
algebraic expression dealing with the first value.
Example:
1.
If given A=B, the we subtract each side
to equal values, for example C,
Then
A-C=B-C
The
Addictive Property of Equality
We can ad equal values
to both sides of an equation without changing the validity of the equation.
Example:
1.
If A=B
Then
A+C=B+C
Or
the other type C+A=C+B
The
Cancellation Low
Example:
1.
The original form is A+B,
Then
add each side by C, A+C=B+C
If
we want to cancel the last addition, we can use this cancellation low.
Become:
A+C-C=B+C-C
The
Multiplication Property of Equality
We can multiply equal
values to both sides of an equation without changing the validity of equation.
Example:
1.
If given A=B, then we multiply each side
to C, so it will always have an equal result. AC=BC.
2.
Then, the form above also have the same
result with the form CA=CB.
The
Cancellation of Multiplication
Example:
1.
The original form is A=B
Then
multiply each side by C, AC=BC
If
we want to cancel the last multiplication, we can use this cancellation low.
Become:
AC/C=BC/C è
A=B
Zero
Factor Property
If two values that are
being multiplied together equal zero, then one of the values, or both of them
must equal zero.
Example:
1.
Let AB=0
From
that, we can expect that it is possible that A=0 or B=0 or both A and B are 0.
The
Law of Trichotomy
For
any two values, only one of the following can be true about these values:
-
They are equals (A=B)
-
The first has a smaller value than the
second (A<B)
-
The first has a larger value than the
second (A>B)
Example:
Given number A and B,
So the possibility is :
a.
A=B
b.
A>B
c.
A<B
The
Transitive Property of Inequalities
If one value is smaller
than a second, and the second is less than a third then we can conclude the
first value is smaller than the third.
Example:
Given A<B and
B<C,
So it means that A<C
Property
of Absolute Value
Example:
1.
|A|≥0, it means that |-A|=|A|
2.
|AB|=|A||B|
3.
|A/B|=|A|/|B|, B≠0
CLOSURE
The
Closure Property of Addition
When you add real
number to other real number, the sum also real number. Addition is a ‘closed’
operation.
Example:
A+B= a real number
The
Closure Property of Multiplication
When you multiply real
number to other real number, the sum also real number. Multiplication is a ‘closed’ operation.
Example:
AB= a real number
COMMUTATIVE
The
Commutative Property of Addition
It doesn’t matter the
order in which numbers are added together.
If given A+B, we can
switch into another side become B+A
The
Commutative Property of Multiplication
it doesn’t matter the
order in which number are multiplied together.
If given form AB, it
will be the same with BA.
ASSOCIATIVE
The
Associative Property of Addition
When we wish to add
three or more numbers, it doesn’t matter how we group them together for adding
purposes. The parentheses can be placed as we wish.
For example, for adding
A+B+C we can modified parentheses into (A+B)+CèA+(B+C). the
result will be same.
The
Associative Property of Multiplication
When we wish to
multiply three or more numbers, it doesn’t matter how we group them together
for adding purposes. The parentheses can be placed as we wish.
For example, for
multiplying A,B, and C we can modified
parentheses into (AB)CèA(BC).
IDENTITY
The
Identity Property of Addition
There exist a special
number, called the ‘addictive identity’. When added to any other number, then
that other number will still ‘keep its identity’ and remain the same.
if given number A, then
add to 0, so the result is the number A itself. Symbolically we can write A+0=A.
or we can also change
the form into 0+A=A. And the result will be same.
The
Identity Property of Multiplication
There exist a special
number, called the ‘multiplication identity’. When multiplied to any other number, then that other number
will still ‘keep its identity’ and remain the same.
For example if we have
number A, then we multiplied to 1, so the result is number A itself.
Symbolically we can write A.1=A
or we can also change
the form into 1.A=A. And the result will be same.
From identity, we can
conclude that:
-
0 is a unique number
in addition
-
1 is a unique number in multiplication
INVERSE
The
Inverse Property of Addition
For every real number,
there exists another real number that is called its opposite, such that,
when added together, we will get the
addictive identity (the number zero).
For example the number
is A. if we add A with the opposite number of A, that’s –A, so the result will
be 0. Symbolically we can say A+(-A)=0
Or we can change the
form into (-A)+A=0, and the result will be same.
The
Inverse Property of Multiplication
for every real number,
expect zero, there is another real number that is called its multiplication
inverse, or reciprocal, such that, when multiplied together, we will get the
multiplicative identity (the number one).
Example: A.1/A=1
1/A.A=1
DISTRIBUTION
Distributive
Law of Multiplication Over Addition
Multiplying a number by
a sum of numbers is the same as multiplying each number in the sum
individually, then adding up our product.
Formula:
If given A(B+C), how to
solve it? We can distribute it. A goes to times by B, then A also goes to times
by C. or symbolically we can say in the form
A(B+C)=AB+AC.
Or for another form we
can write into (A+B)C=AC+BC. It
doesn’t matter because the result will be same.
Example:
1.
If given 5(7+3), using distributive law,
determine the result.
Solution:
5(7+3) =5(10)
=50,
Or
5(7+3) =5(7)+5(3)
=35+15
=50
The
Distributive Law of Multiplication Over Subtraction
Formula:
A(B-C)=AB-AC.
That formula means if we have A(B-C), we can distribute it, A times B subtract
A times C.
The
General Distributive Property
In general distributive
property, we have the general formula:
a(b1+b2+b3+…+bn) = a
b1+a b2+a b3+…+a bn
for example:
2(1+3+5+7) = 2.1+2.3+2.5+2.7
= 2+6+10+14
= 32
The
Negation Distributive Property
If you negate (or find
the opposite) of a sum, just ‘change the signs’ of whatever is inside the
parenthesis.
Formula:
-(A+B)=(-A)+(-B)=
-A-B
QUIZ
1. Find the inverse of the number
bellow
a. -5 = 5
b. 2/3 = -2/3
c. -1 = 1
d. 0 = 0
2. Do this question using the property
above
a. –u+u = 0
b. 8x7 = 7x8
c. 5(w-y) = 5.w-5.y
d. -3+(6+2) =(-3+6)+2
e. Z = Z
f.
a≤/b, a≠b, therefore a˃b
g. m(1/m) = 1
h. since
root of 3 and e are real number, so if root of 3 subtract e, the result will be
a real number.
i.
The form 2+x2 have the same
result with the form x2+2.
j.
(Z+7)+2=z+(7+2)
k. (y)(1) = y
l.
If x=y and y=5, so the value of x=5
m. 2+0 = 2
n. –(x+2) =
-x-2
o. (ab)c = a(bc)
p. [2+(x-1)]y = 2y+(x-1)y
q. (1/x2+4)(
x2+4) = 1
r.
(x+y)+z =
z+( x+y)
s. (1)
(1) = 1
t.
5+w+(-w) =
5
u. (2a)(bc) = 2(ab)c
v. |-2/3| = |-2|/|3| = 2/3
w. 1.(y-z) = y-z
x. X+5 = 5+x
y. pq = qp
z. 2y+8 = 8+2y
aa. 2-ab = ab-2
bb. 3+(w+z) = (3+w)+z
cc. -2(x+3) = (-2.x)+(-2.3)=-2x-6
dd. –(2y-9) = -2y+9
