Learn Number, Learn Math

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+…+b_n)     =          a b₁+a b₂+a b₃+…+a b_n

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