817 Math Blog

We Learned 4 diffferent ways to nathematical use fractions, adding ,subtracting, multiplying, and dividing.


Adding

Adding fractions is really simple. First you have to find the lowest common denominator (the lowest number that both denominators go into), then add both numerators using the lowest common denominator. If it is a mixed fraction, you convert it to a improper fraction. To convert it, you multiply the denominator with the whole number, then add the numerator. You then place that number over the numerator; the improper fraction should have a numerator that is larger than the denominator, hence the name improper fraction. Alternatively, you can add the whole numbers, and simply add the fractions, then you put both of them together. This way is recommended when adding, it is a lot simpler.




Subtracting


Subtracting fractions is almost just as simple. Instead of adding, you subtract. You find the lowest common denominator and subtract the numerators, and often, you simplify at the end. If it is a mixed fraction, subtract the whole numbers, and fractions, if possible. If it isn't possible to subtract the fractions, subtract one, from the first mixed number, then add the numerator and denominator, and use the sum of that to replace the first numerator in the fraction; now it is a improper fraction. Finally, subtract normally.



Dividing


Probably the most confusing of all, is division. There are two ways to divide, using a ratio table, or using the reciprocal, the ratio table is easier in my opinion. To use the ratio table, we place the fraction that is being divided on the left side of the table, and the divisor fraction on the right side of the table. Here, we focus mostly on the divisor fraction. Using division and multiplication, make that divisor fraction into a whole. What you do to the divisor fraction, you must do to the fraction that is being divided. Your answer will be the results of the fraction being divided. To use the reciprocal, all you do is turn the second fraction upside down, and multiply.



Multiplication


Multiplying fractions is a bit easier. You simply multiply the numerators and denominators, then simplify. To multiply mixed numbers, convert them to improper fractions, then multiply, then convert them back to mixed numbers.

Today we learned how to divide Fractions and some of it's differences from multiplying fractions.

Such as, what the two different math types say.
eg. 6 / 1/2 = this division question would say, how many groups of 1/2 are in 6
6 * 1/2 = this multiplication question would say 6 groups of 1/2

Homework:
We had 3 questions for our homework and we`d have to show how to do all of them 2 ways,
I`ll show photos on how to do the last 2 questions.

6 / 2/3 ,
1/2 / 1/4 ,

2 / 3/4 ,

Sometimes when subtracting fraction you first have to turn them into improper factions, you can also borrow from the fractions.

A good time to switch to improper factions first is when you find out you can't subtract the numerators and the fractions are small. ,
2 1/2 - 1 3/4 =
2 2/4 - 1 3/4 =
= ?

You can't subtract 3 from 2 so you have to start the question with improper factions,
2 1/2 - 1 3/4 =
5/2 - 7/4 =
10/4 - 7/4
=3/4
These questions are an example of when you need to do switch to start with improper fractions.

A good time to borrow when subtracting fractions is when the fraction are huge,
625 1/2 - 100 3/4 =
625 2/4 - 100 3/4 =
= ?

When the question ends up with 2 subtracted by 3 is a good time to borrow,
625 1/2 - 100 3/4 =
625 2/4 - 100 3/4 =
(624 + 4/4 + 2/4)
624 6/4 - 100 3/4=
= 624 9/4
The question is now solved by borrowing fractions.

You can do any subtracting question now, you can do it normally, you can borrow, or you can use improper fractions

Today was our video project day, we were supposed to prove the Pythagoras theorem. The 6 and 8 are the legs and the hypotenuse is 10 of the whole right angle triangle,below is a video of the proof.






The video below you is how to do the equation and how it works.



This video is the proof of the equation and how it all works together.




For the next scribe i choose Liem if he already did one then kevin

Last week we were all given an assignment about a Greek mathematician named Pythagoras , and his theorem the "Pythagorean Theorem"



Pythagoras: The greatest genius ever lived. An "uber" smart mathematician, he was a Greek geek. It's not for sure that he really existed. Because all the information was from one of his students(so called).




1.Legs: These are connected to create the right angle of the right angle triangle a.k.a sides "A" and "B". They are also smaller than the hypotenuse.

2.Hypotenuse: The hypotenuse is the longest side of the right angle triangle, its the opposite side of the right angle also.

3. R.A.T: The starting of the words Right Angle Triangle.

4.Greek : A person that originated from ancient and or modern Greece.

5.Theorem: A theoretical proposition, statement, or formula embodying something to be proved from other propositions or formulas.

There were other artifacts besides the definitions.



One of the artifacts is the Pythagorean Theorem. Pythagorean Theorem:

The Pythagorean Theorem is the sum of the areas of the two squares on the legs, (which is a and b) equals the area of the square on the hypotenuse (which is c)


This artifact is known as a right triangle, or R.A.T (Right Angle Triangle) The right triangle has a 90 degree angle, which is the little square inside the triangle corner. All in all the triangle is 180 degrees.











In this artifact, this is just a plain square. The lines on each sides shows that each of those sides are equal to the others. The square has 2 right triangles, that looks like the first artifact. This square has four 90 degree angles which means that angles equal 360 degrees, and to get that you times 90 degrees by 4 which equals 360 degrees.

Bob: Hey, i'm bob.
Borock Obama: Hey, i'm borock Obama.
Bob: May i ask you a question Borock Obama.
Borock Obama: Sure, I guess, but what is the question about ?
Bob: it's about Math.
Borock Obama: okay.
Bob: What is n+3-5n+12.
Borock Obama: negative 6n+15 .
Bob: Wrong, the answer is -4n+15
Borock Obama: How so ?
Bob: The first "n" means positive 1, and the second "n" is negative 5n. The positive and the negative integers cancel each other out leaving negative 4n . Canceling out the positive integer and the negative integer was your mistake.
Borock Obama: I see. Give me another question please, i'll get it correct.
Bob: okay, 2 + 4 bracket 3n+8 bracket .
Borock Obama: 12n + 10, i'm sure of it.
Bob: That's wrong again, the real answear is 6n + 32.
Borock Obama: How , i was so sure it was 12n + 10 .
Bob: You didn't use Distributive Property.
Borock Obama: Seriously !
Bob: Yea.
Borock Obama: Well i have to leave now , BYE !
Bob: Nice talking to you Borock Obama. Bye !

Adding Integers (Haiku):

Adding Integers,

2 numbers equal the sum,

Easy thing to do.

Subtracting Integers (Cinquain):

Subtraction

Negatives, Minus.

Reducing, diminishing, less than.

Take away.

Partative Division (Free Verse):

How many equal parts are in 5 go into 10?

When you look at your barn doors you'll have an answer!

Quotative Division (Free Verse)

Quotative Divison is very easy,
if you don’t know the trick it will make you go crazy
the trick is how many of this goes into that,
after you know this you’ll be ready for combat.

Rules for multiplying integers (Free Verse):

When brackets kiss they multiply,

The numbers will grow sky high,

Or grow the opposite to fall and die,

It`s so easy when you try.

Today in class we talked about multiplying integers again.

We made a theory for these integers

1.(-)(-)= 5.(+)(-)=

2.(-)(-)(-)= 6.(+)(-)(-)=

3.(-)(-)(-)(-)= 7 .(+)(-)(-)(-)(-)=

4.(-)(-)(-)(-)(-)= 4(+)(-)(-)(-)(-)(-)=

1. When you multiply an even amount of negative integer the product is a positive integer.

2. When you multiply an odd amount of negative integers the product is a negative integer.

So after those rules it would be.

1.(-)(-)= (+) 5.(+)(-)= (+)

2.(-)(-)(-)= (-) 6.(+)(-)(-)= (-)

3.(-)(-)(-)(-)= (+) 7 .(+)(-)(-)(-)(-)= (+)

4.(-)(-)(-)(-)(-)= (-) 4(+)(-)(-)(-)(-)(-)= (-)

One of the questions we did during class was

(-1)(-2)(-2)(-1)=

You can’t multiply nothing so you needed to add “Zero Pairs”. How I did the question I split the whole question in 2 parts.

eg. (-1)(-2) = 2

(-2)(-1) = 2

Together is would be (+2) (+2) now, this question would say 2 groups of +2.

The answer is 4.

We were assigned to do some practice on it. For our practice, we had to page five, questions 19 to 36.

Here are some questions and answers.

36. -12(8) (-5) (0) (-7) =0

The answer would be 0 because it doesn’t matter where the 0 is in the question it will automatically be a 0

22. 3(-5) (4) = (-60)

I split the question to [3(-5)] (4), I did the square brackets first. The question inside says 3 groups of -5 that would be -15.After that the question would look like

(-15)(4)

That question says now remove 15 groups of 4. What’s left when you move 15 groups of 4 from the zero pairs would be -60.

I choose Liem to be the next scribe. HAHAHAHA

Introduction

Have you ever been scared to death, brought back in time, and was lost ?I have I'm Kurosaki my friends, Sora, Yuki, Stark and I. Were walking through the park at night during Halloween. It would be the worst mistake we've ever made. Here it goes.

Chapter 1- The Night of Friends

Today was Halloween and it was after the dance, we were at Sora's house watching a new movie called The Lost. I really like Yuki she was one of my best friends and was the prettiest girl i knew, I was really craving to go to the park, with her and walk the scary dirt trail at night and she would be scared and hide in my arms. I asked if she would come with Sora, Stark and I to the park after the movie. She agreed, I was Extremely exited and happy. Were at the park and i see the dirt trail. It was my chance and i went for it,"Yuki , would you want to come with me though the dirt trail."
She answered,"Um, only if Sora and Stark will come ."
Of course i agreed so we went. I was right she was in my arms most of the way,until we saw an old lady. We got distracted and fell down the side of the trail to and in the lake. But I wasn't wet and it seemed i was in an whole place i was at a plain nothing was in sight except grass and and old house.

Chapter 2 - Kurosaki's Story

I was at the old house and the old lady from before was standing right in front of my face.
She said,"Are you lost boy? "
I said,"Where am I and what did you do to my friends !"
She whispered,"To move to your nearest friend you must answer, (+10)+(-90)+(-20)= ."
What was it that Mr.Harbeck told us about adding multiple integers ? I remember now combining like terms, (-90) and (-20) are both negative numbers, together they would make (-110). So the question would be (+10)+(-110)=. The other thing was, have and owe. So if i have 10$ and but i owe -110$ so i i give 10$ i would owe 100 dollars after.
I answered without hesitation,"(-100)."
She Shouted,"Correct."

Today we had to near 100 questions. We had to do pg.41A, pg.42B and pg.42C.

For Page 41A we had to do the questions in a number line.

For Page 42B, questions for 1-10 were supposed to be done in Owe and Have. For questions 11-15 is supposed to be done in a number line form. Questions 16-24 was your choice, it can be done in anyway but it can’t be done in only answers.

1-10
eg. (+4) + (+3) =+7
Have 4 and Have 3=+7

11-15

16-24

eg. (+4) + (+3) =+7
(+4) + (+3) =+7
Have 4 and Have 3=+7
Number line

For pages 42C, questions for 1-10 were pictoral. Questions 11-75 is choice again you can chose anything you want expect you have to write down the questions.

1-10

11-75

eg. (+4) + (+3) =+7
(+4) + (+3) =+7
Have 4 and Have 3=+7
Number line

Mean

• Arrange the data in ascending order


• The sum of all data divided by the number of data


• with an outlier the mean is less accurrate "average"

Median

• Arrange data in ascending order Find the middle number
  If there are 2 middle numbers you have to find the mean of them


• Great to use if there is an outlier

Mode

• Arrange data in ascending order Find the data that occurs the most


• You can have more than one mode


• You can have no mode

Range

• Arrange data in ascending order


• Subtract the smallest number from the largest number


• Large=Outlier

Here is a video i found about Mean , Median , and Mode