Another math Christmas blog

Hi Another blog on Christmas !!:D



see that ? ^.^

today's question is : How do we add and subtract rational expressions?

so lets start lets say you get an expression like :

4b2-12 + b+3
  b +3      b+3

Step 1:
find the common denominator for the non siplified part of the expression.
therefore ;

4b2-12
Greatest number is b and 4 
so :
4b(b-3)

Step two: connect it back to the full expression :

4b(b-3) +  b+3
b+3           b+3

Step three.: you cross out the variables that are identical. 


4b(b-3) +  b+3
b+3           b+3


4b(b-3) +  b+3
b+3           b+3



4b(b-3) + 1  
 b+3

 Step four: combine what is left
4b(b-3)+1
 b+3


Works cited
Picture :http://img.spikedmath.com/comics/124-christmas-puns.png

Exponents i think..

HELLO !!  math people ^.^
I'm a bit late..well i'm really late because of some technical difficulties:(.

so lets get started with a math-christmas photo since its CHRISTMAS!!
and like a total nerd im doing a blog xP
oh well,  here the picture:

       
I dont know if HO3, is a chemistry component or a math picture but what ever I think the bear is super dupper cute 
>.<.

now that the picture is over, we are going to solve the question of the day :

How do we simply expressions with rational exponents?

so lets start with a simple, and easy expression like:

x4

                                                                                                          x-6
because we cannot have a negative exponent in the bottom of the bar we have to switch the negative exponent along with the x and flip it to the opposite side. 

For example: 

given expression : 

x4

                                             x-6
change the negative exponent to the opposite side of the bar. Therefore: 

x4 x6

                                              1
from there,we can say we are multiplying both x's. when we multiply, the exponents are added therefore :

x4x6 :  4+6 

x10

lets try more problems:
x3x(2/4)x-3  = 
Step one : add all exponents 
3+(2/4)+(-3)
3+(-3) =0
0+(2/4) = (2/4)

Step two : combine the answers 
 X(2/4)

Another problem: 
 (X15 Y25 )(1/5)

Step one: first multiply the outside exponent to the inside exponents. 
 (X15 Y25 )(1/5) :
(15)(1/5)
multiply straight across so it would be :
X:   15 x 1  = 15 = 3  
       1      5      5

Y:   25 x 1 =  25 = 5
       1      5      5

Step Two:  combine the exponents to its appropriate variable.
X3Y5


NOW YOU TRY :D

X-3
X2

X (-9/18)
X3

Works cited :
picture : http://i1.cpcache.com/product/180766012/ho_ho_ho_christmas_math_humor_teddy_bear.jpg?height=150&width=150

Radicals

안녕하세요 (annyeonghaseyo)

meaning hello ^.^

thank god its the weekend  I AM EXHAUSTED !!!!!!

Well today is another BLOG DAY:) !!!YAY!!!!! NOT REALLY !!!!! :P

Lets gets started with a picture that gets me through the day :) :

Isn't this a perfect collaboration of both FOOD and MATH ^.^ 

This is my FAVORITE math picture so far :)

Now onto our question of the day ......

How do we rationalize a denominator ?

 we only rationalized the denominator when we are dealing with radicals at the bottom of the expression. We rationalize the denominator to obtain a solid number that can make the fraction be true. 

For Example this is our expression :

   -10  

 10-√2

 

Lets start,

First Step : multiply both the numerator and 

denominator by the conjugate of the denominator.The 

conjugate means to just flip the middle sign.

Example:

  -10      (10+√2)

(10-√2) (10+√2)

Numerator :

First part = -10(10√2)

-10(10√2) = -100√2  -> radicals do not change 

unless you multiply a radical by a radical.

Denominator :

10*10=100

(10)(√2) = 10√2

(-√2)(10) = 10 -√2 ( negative times a positive is 

negative)

(-√2)(+√2) = -√4 (radical times radical equals 

radical.)

Second Step : unite all parts together.

                                      -100√2          

                         100  10√2  10-√2 -√4

Step Three: Combine like terms

-100√2  = no like terms so we leave it as it is.

100 10√2 10-√2 -√4 :

both (10√2) and (10-√2)  cancel each other because 

one is positive and the other is negative. 

we are then left with : 100 -√4 

The square root of (√4)  is 2, therefore it would turn 

to -2. 

so.. 100-2 = 98.

Step four : Unite both parts for a final answer. 

YAY !!! ^.^

-100√2

98 

Now you try :D

Solve :

    4   

-9-√3

    9    

10+√5

                             Final picture :

This is me after so much math,hopefully you feel the 

same as i do :P

                               안녕히 가세요 (annyeonghi gaseyo)

                               meaning GOODBYE ^.^

Works cited:

Food and math picture: http://img.math-

fail.com/images-old/math-cereal.jpg

Woman running away:

http://121lml.files.wordpress.com/2010/07/projectcompletion01.jpg

Another just simple math blog :)

Hi there, its another MATH blog :).

i thought of starting with a random picture,so that the math blog wont be so mathy >:P

Today pic :D

this is a pretty picture ^.^,it makes me feel like i'm in a spy movie:)

well on today's math blog our aim today is:(tan-tan-tan)

How do we Factor by grouping?

when we factor a equation, we use the cubic equation
like:
2x3+ 4x2+25x+10= 0 

because this equation is a cubic equation we cannot use the diamond problem to find the factors. 

lets get started :
Step 1: we separate this equation in half like : 2x3+4x2
Step 2: we find the greatest common factor of 2x3+4x2.
 in this case 2x2 is their common factor,because both 2 and 4 are divisible by 2 and both of them have x's.

Step 3:  using the common factor we can make a factor of 2x3+4x2
for example:
     2x3+4x2    (original part)
     2x2(x+2) (undistributed part ) 
Step 4: then we find the common factor of the second part of the equation.
For example: 25x+10
5(x+2) 
5 = the greatest common factor
(x+2)= is the factor of 25x+10

Step5:  connect the parts together.

2x2(x+2) + 5(x+2)

Step 6:  finishing up by grouping it.
For example: 
2x2(x+2) + 5(x+2)

(2x2+5) = connect both the 2x2+5 into one parenthesis.
(x+2)= stays the same. 

Final answer:
(2x2+5)(x+2)

Now you try :

6.

7.

3.

LAST PICTURE:
                                                     
This is how I feel after doing math blogs :)

Problems: http://www.regentsprep.org/Regents/math/algtrig/ATV1/RevFactPractice.htm
First Picture: http://cdn.c.photoshelter.com/img-get/I0000XMSl1tB.tzg/s/650/650/jiufen-taiwan-chinese-lanterns-night-002.jpg
Last picture:http://www.regentsprep.org/Regents/math/algtrig/ATV1/revFactorGrouping.htm

Another blog

Aim: How do we calculate quadratic inequalities?

Hi :) again, another math blog.

what are quadratic inequalities?
quadratic inequalities are similar to quadratic equations the only difference is the inequality signs are added.

A sample of a quadratic inequality is :
x2+10x+25≤ 0

lets use this quadratic inequality to solve it :

STEP 1: Foil the quadratic inequality as a quadratic equation.

x2+10x+24 =  (x+6)(x+4)

STEP 2: Find  X by equaling the expressions to zero.

     x+6=0                                              x+4=0
        -6=-6                                               -4=-4
         x=-6                                                x=-4

STEP 3: Plot points back to the equation to know what way the arrow will be going.

Ex: (0,0)
0^2+10(0)+24 ≤ 0
0+0+24≤ 0
24 ≤ 0

This is not true because 24 is greater than 4, therefore the (-4) will not go in the direction that the zero is at.

Ex: (-10,0)
-10^2+10(-10)+24 ≤ 0
100+(-100)+24≤ 0
 24≤ 0

Because 24 is greater than 0 the closest number to -10 ,(-6) will not go in the direction of -10. 

With the new found information we will now use it and correctly plot the points in a graph.

STEP 4: GRAPH 
(Remember )
≤   Less than or equal to signs have a closed circle when graphed.

YOU TRY NOW :

1.

Using a number line,  graph the solution set of

2.

Solve algebraically:

Works Cited:

Regents prep Problems: http://www.regentsprep.org/Regents/math/algtrig/ATE6/quadinequalpractice.htm

Graph pic: It was made by me 

The Late BLOG :'(

Aim : How do we use complex conjugates to divide imaginary numbers?

So ... we are on a brand new math journey ....



when dealing with imaginary numbers,things can get a bit complex.

For example we can get a question like =
Express your answer in a, a+ bi form :

3-4i          
3+i

We know,from our previous knowledge that an i in the denominator  wont satisfy the answer because it does not  provide a real answer. To correctly answer this question we need to use the conjugate.

A conjugate, is the opposite of the expression.If the expression has a positive sign we switch it to a negative sign to make it a conjugate.                                 

For Example: 
Initial expression:                                     Conjugated expression:
 24+i                                                                     24-i
 30- i                                                                     30+i

MOVING ON TO THE FIRST EXAMPLE~

Express your answer in a, a+bi form:
3-4i
3+i 

STEP 1: Find the conjugate of the denominator and multiply it to the top and bottom of the expression.
                              
3-4i  =  (3-4i)(3-i)                            
3+i   =  ( 3+i)(3-i)

STEP 2: Distribute the expressions. (try to do one part at a time ) 

(3-4i)(3-i)  =  9-3i-12i+4i2                    (remember the imaginary numbers rule)
                  =  9-15i+4(-1)
                  = 9-15i -4                      (combine like terms)
                  = 5-15i 

(3+i)(3-i)   = 9-3i+3i-i2 
                            = 9-i2                                                           (imaginary number rule)
              = 9-(-1)   (a negative number multiplied by a negative number produces a positive number)
              =9+10
              = 19
Step 3: Combine both answers of the both to have a final answer.
     
 TA-DA YOUR ANSWER:

    5-15i

     19 

your answer could be shown this way as well as :

  5    -  15i

 19       19

Now YOU try it out :)

Simplify:

Choose:  35/37 + (12/37)i  35 + 12i   35/36 + (12/36)i

Simplify:

Choose:  5 - 2i  3 + 2i   15 + 10i

LAST IMAGE:

Works cited:

people walking : http://walkingfit.ucr.edu/images/Men%20and%20Women%20walking_cropped.jpg

Try it problems: http://www.regentsprep.org/Regents/math/algtrig/ATO6/multprac.htm

I love math cup:  http://rlv.zcache.com/math_lover_mug-p168094805368057360bzq92_210.jpg

Imaginary numbers

 Hi^.^
another math blog for YOU ALL !!!

Today's question is :  How do we operate on imaginary numbers?

So... to get started what are imaginary numbers?

A imaginary number is i , it represents all imaginary numbers. 

For example when we have a negative square root and we say that there isn't a "real world solution" we say that because you cant square a negative number. 

To make those negative square roots have a real answer we use a special number called the: imaginary number represented as = i or 
√-1

For example : 

√-9  =    √-1  √9 

 we use the value of i which equals √-1 and then multiply it 

by the positive square root 9. we then square root the 9. 

And get: 

√-9= 3i


lets say you have a more complicated expression like: i3   Then we have to know the more complicated process of i

i=i

i2=-1
if we already that i2 =-1  
we can then figure out that 13 equals -i because we can multiply the -1*i and get -1

Following this cycle we can say that  i4 equals 1 because 
(-1)(-1) = 1.
(-1)(-1) are used because their exponents i2*i2 give i4

for i5 we multiply (-i)(-1) and it gives us +i

the cycle:
i= i
i2=-1
i3= -i
i4 = 1
i5= +i

Now you try :D

√-25

√-100

i360

i4926

GOODBYE AND REMEMBER :D

works cited:
Just for you:http://worshipsounds.files.wordpress.com/2012/03/just-for-you.gif
Heart math:  http://mentalfloss.cachefly.net/wp-content/uploads/2008/11/math_tee2.jpg        

The weird FIRST time

MY FIRST POST(yay!^.^)

Hello, everyone :D

this is the second blog about math D;

(Yea,yea) we all hate math like typical teenagers, but I have to do it because of my teacher :(

but enough of introductions

its the dreading time (tan,tan,tan)

Trigonometry Time 

Question: 

"Why do we flip the inequality symbol when multiplying by a negative number or solving absolute value inequalities?"

okay, so here we go ^.^ on our foot journey:)...

                           

For example, if we had a statement like: 20 > 12 then it would be true, but lets say that that you are told to multiply both numbers  by a negative number ?

what do we do now ?? :O 

have no fear I will explain :)

In my example,we will multiply each side by -2.

20(-2) < 12(-2)

your outcome will be: 

-40 > -24 and this is false because -40 is lesser than -24

To make it clear I made a number line ---->

In a number line, the positive numbers show amount of value by having the numbers closer to zero value less while the numbers father away from zero have a greater value.

But for the left side of the number line if the numbers are closer to zero then their amount of value higher than the numbers father away from zero.

• therefore if -42 is more farther from zero then it has a lesser value than -24 since it is much more closer.

Back to our problem, if  :  -42 > -24 

it would be incorrect  because like we said before -42 has a lower value than -24 because it is the more farther away than -24.

DO YOU GET IT NOW?

So, we change the sign to number one : have the correct sign when dealing with negative numbers

In absolute inequalities you change the sign for the same reason 

for example :

I2x+1I >6 

you would first make two separate equations 

like: 

2x+1>6  and 2x+1<-6.                       

•  2x+1>6 : 

In this case we are saying that 2x+1 is greater than 6   

• 2x+1<-6

 In this equation we switched the sign and made the 6 negative, because from the previous equation we only had the answer of a full set of positive numbers not the negative numbers .

•  To have  the full amount of possible numbers we have to one keep the equation the same and two, we have the sign switch and make a number negative.

NOW you try:D

-3>6

Do you think it is correct as it is ?

I-3x I> 6

Solve, and also do you switch the sign why or why not ?

HAVE A FANTASTIC DAY WITH MATH !!!!!!

A last math picture ^.^ to make your day :)

Bye~bye ^.^

Works cited:

Trigonometry picture:http://soquelhs.net/home/images/stories/academic/math.jpg

Panda picture:http://www.roflzoo.com/pics/042010/now-what-do-we-do-about-this.jpg

Foot steps picture :http://sibbia.files.wordpress.com/2007/08/footprints.gif?w=3104&h=621

Math pictures:https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjloyUmwj__nc24p95rsmgZjEDyjspS4vMIPjU0amECzf1SMz9sUcRKK6lcW_gks_dVYWb2WofZNPZWfnBmPDVTllb-SKWMKjSfL6gDErJZwRAABNctEH1A9vpu5Kq9hJSZ3vxmJlvPc8s/s1600/IMAG0558.jpg