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P.MATEMATIKA INTERNASIONAL

English Assignment  (Reflection)

Reflection of Video "Basic Mathematics Lesson 4"

by Luis Anthony Ast

I explain property. I would use variable ABC, to present my number and variable expression.

E. Commutativity

1.    The Commutative Property of Addition

It does not matter the order in which numbers are added together.

Example :

A plus B is the same thing as B plus A.

F.    Associativity

1.    The Associative Property of Addition

When we wish to add three ( or more ) numbers. It does not matter how we group them together for adding purpose. The parantheses can be placed as we wish.
Example :

( A + B ) + C same with A + ( B + C ). All the associative property addition I can associate the group together I can associate different ways, we can move the paratheses on the any place. I can put (A+(B+C), so the result is A + ( B + C ).

2.   The Associative property o Multiplication

When we wish to multiply three ( or more ) numbers, it does not matter how we group them together for multiplication porpose. The paratheses can be placed as we wish.
Example :

( A .B ). C same with A. ( B . C ), because the assosiative disposition. It's same thing with multiply, the first two term, and the result time the third or I can associate indifferent way, the third times second term and the result times by the first. In any case it same at all, by the way, associative property doesn’t cover substraction and division.

G.   Identity

1.    The Identity Property of Addition

There exists a special number, called the “additive identity”, when added to any other number. Then that other number will still “keep its identity” and remain the same.
Example :

A + 0 = A

A ( anyy number ) plus 0. So the result is A.

2.    The Identity Property of Multiplication

There exixts a special number, called the “ multiplicative identity”, when multiplied to any other number, then that other number will still “keep its identity” and remain the same.
Example:
A.1=A
When we calculate a times I, so the result is A. It is same with 1.A=A.

A Special Note

0 is unique for the addition.

1 is the unique for the multiplication.

H.    Inverse

1.    The inverse property of addition

For every real number, there axis another real number that is called its opposite, such that when added together. You get the additive identity(The number zero).

Example:
A+(-A)=0
(-A)+A=0
Symbolically A is the number and we add the inverse is equal to zero, and when we turning the result is same, the opposite number plus the number and the answer is zero.

2.    The inverse Property of Multiplication

For every number, except zero. There is another real number that is called its multiplicative inverse, or reciprocal, such that, when multiplied together, you get the multiplicative identity ( the number one).

Example:
A.1/A=1
1/A.A=1
Symbolically we can say, the number is times multiplicative identity one position round, the multiplicative inverse, times the number is one. By the way finally there is one number doesn’t have multiplicative number is zero, why? Because I divided by zero, this is undifined, so zero has no multiplicative number .

I.     Distributivity

1.    The 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 products.

Example : 1. 5 (7+3)

First, we must addition the number on the brackets 5.

5 ( 10)

Then, we get 5 times 10, so the result is 50.

If we have another case,

2. 5(7) + 5(3)

First, we multiply 5 and 7 and we multiply 5 and 3. And we get 35 + 15 = 50

The answer is the same with the first example. From the first and second example, we get A(B+C)=AB+AC. A times the B plus A times the C is equal to AB+AC. So A goes times to B then A times the C. We have (A+B)C=AC+BC. I can distribute like this, C times A is AC and C times B is BC. So it is easy.

2.    The Distributive Law of Multiplication Over Subtraction

You can symbolic like this, A(B-C)=AB-AC. A times B is equal to AB and A times C is equal to AC, so you can subtract it.

A( B-C) = AB-AC

This video is dealing with logarithms. the first rule that you should remember is about log b of x equals y. basically, b is called the base and then u can rewrite in other formula that is b y equals x.

Logarithm sometimes does not make senses but i gonna make it sense with making some notations.

The notations is that if you have a log base ten of x, u can only write it with log x. it's just th same. likewise with log base 'e' (some irrational number, just like phi) of x, we can only write it with lnx (l n of x) or we can say it with natural logarithm. so natural logarithm is just thesame with lnx.

So, we have a couple problem here and we will finish this using the first property with the expanantial form. if we want to evaluate log base ten of one hundred equals x, we have to notice the first pattern, the base raises to the power so b raises to the y equals x. so we have the same pattern for this problem (log 10 of 100=x), ten raises to the x equals 100. so dont say x equals 100 because x is the exponent, so u should say ten squared equals 100 that means x value is 2. so all that means is that log base ten of one hundred is equals the number of two.

The same way in the problem log base two of x equals 3 , and we will find the value of x. so u should invert the form becomes two third power equals x meaning 8 equals x. and finally we can find that log of two of eight equals three.

Move the next example, suppose we have log of seven of one over forty nine is some number called x. so i will rewrite it using exponent. so we can write 7 raises to the x power being equals to one over fortinine. seven squared is 49 but we dont need that, we need one over 49 so it becomes one over seven square.

And we can find seven power of x equals seven power of minus two because we should change the sign of the exponent.

And finally find the power should be equals meaning that x equals to negatif two.

Now move to the some properties u should know, suppose we have log base b of m times n with the rule log base b of M plus log base b of N because product (perkalian) turns into addition.

The next one says that log b of M divided by N so it becomes log base b of M minus log base b of N.

And the last but not least is about exponent rule, suppose u have log base b of x raises to the n power, it becomes n times log base b of x.

We have an example here.

We have log base 3 of squared times y plus one over z cubed. so use the middle property, it is the division property.

So it becomes log base 3 of x squared times y plus one minus log base 3 of z cubed. and the next step is to brake up the first part into addition and we will have log base 3 of x squared plus log base 3 of y plus one minus log base 3 of z cubed.

And the last step is we will use the exponent rule, so we have 2 times log base 3 of x plus log base 3 of y plus one minus 3 times log base 3 of z.

So those are the expanssion of the properties.

HOW TO SOLVE PROBLEM?

Word problems can be very challenging to many students and some of the basic things to think about when we trying to solve the word problem is to figure out what about the facts and what is being outs for.

Example:
A college student plans to spend $420 on books for one semester. He also plans to spend $20 per week on pizza. The Fall semester is 18 weeks long. How much will he need for books and pizza?

Solution:
Basically, we have the fact that the student is going to spending some money. He's spending $420 for books and $20 per week on pizza.  And then we know  there is 18 weeks long for this semester.
So, we are going to take $20 he's spending each week and multiply times 18 the number of week.
So he's spending $360 on pizza and $420 on books for this semester.
If we want to know how much he's spend on books and pizza in this semester, we need to add $360 and $420 and get the answer is $780. So, he will need $780 for books and pizza.

this video tells us about how to solve word problem which usually faced by the children. it is also helpful for teacher to help him to teach the students related to solve the word problem.

the 'word problem' related to every single parts of daily life. it related to many things and finally required a math operation to solve the problem.

many students usually get scared of word problem because it consists of many words that makes them confused. in this video, there is a new way to brake up the problem that is the use of 'buck'. buck itself is easy to understand because it closely related to money.

buck consists of four big important parts, they are B- box the information U-underline the information needed C-circle the vocabulary K-knock out the unneeded information because many students usually get confused by too much word.

there is an example there. how to solve the prblem?you can use the BUCK system to SOS: simplify, organize, and solve the problem.

so we can start by  B: box the question, how many t-shirts are sold in a week ?

U: the underlined information are three, 10 minutes and 9am until 9pm everyday.

C:the circle word that needed to aware, they are minutes, everyday, and week.

K: and the unneeded information that may cause a problem are $19.95, 45 , and $24.95.

so the informations needed to solve the problem are:

60 minutes in an hour

12 hours from 9am to 9pm

so we have to multiply 12 times 60=720 minutes per day the shop is open

a t-shirt sold every ten minutes so we will devide 720 devide 10=72 per day

so in week we should multiply 72 times 7=504

and finally we can get the answer that the shop sells 504 t-shirts per week

there is another example that might cause people think that he is not in the end of the problem, so we should pay attention to the question.

so the formula of BUCK are:

B-how much money should maria bring

U- the info i need to know is a pair of shoes, the original price is $ 80.00 and discount of 20%

C-the vocabulary that i need to understand to solve the problem is the meaning of the original and discount.

and the information which do not needed are shoe store and last one week.

so the informations we need to solve the problem are:

the original proce is $80.00

and the discount is 20%, it means that the new price should be smaller than the original price.

so 80.00 times 20% = $16.00

and the new prices comes from the original price $80.00 minus the discount of $16.oo = $ 64.00

so the answer is that maria needs to bring at least at $64.00 with to the shoe store.

finally, what you need to underline when using BUCK when solving word problems are:

Box the question

Underline the information needed

Circle the vocabulary

Knock out information not needed.

there are some new vocabulary in this video which you can learn using your own word, they are:

-original cost

-discount

-measurements----minutes, hours, days, week

This video is going to show how to solve puzzle and riddles (otherwise known as word problems) using two variables.

and there will be two more examples. the first question.

so we need to replace the 1st number with X and the 2nd # with y.

so we can make a formula for those two questions with:

1st #: X x+2y=23

2nd #: Y                2x+y=31

and we can use one of those formula to solve the problem.

let say i will be with the first formula

x+2y=23 ( and i will subtract 2y for both side) so,

 -2y  -2y so,

x=23-2y

so lets move the second formula that is 2x+y=31 and replace the x with the formula above

2x+y=31

2(23-2y)+y equals 31 (so we have one variable here)

46-4y+y equals 31 ( and we can simplify)

  -3y+46 equals 31 ( and i think i will make it positif with adds +3y for both side, and make it simple with subtracts 31 for both number also)

  +3y-31        -31+3y (so the answer will be)

      15=3y so y equals 5.

so lets find the answer of the other formula

x=23-2y ( and subtitute y with 5, so)

 =23-2(5)

 =23-10

x=13

So the number are 13 and 5

Again we have the situation to find the first and the second number. And we write the two equation. The first number is x and the second number is y.

The first number plus 2 more than 3 times the second equation is 18. So, x + (3y + 2) = 18.
We can simplify the second equation to be x+3y= 16. So, we have x+3y=16 and x+y= 16 .
Now, we have to find x and y. We may multiply the second equation with -1. So it will be
x+3y= 16
-x-y= -16. We get 2y=0 and y=0.
Now, we apply y=0 on the first equation. We get x+y= 16
x+0= 16, so x=16.

 Let's check.
For the first equation, 0+16=16. For the second equation, 16+2=18. These are right.

So the numbers are 16 and 0.

Of the song that's math, we know that anything we do is always related to mathematics. As an example when the ball bounced off the wall, or when we calculate how much we owe, even when counting sheep when you can not sleep. It all shows that whatever we do in fact always associated with mathematics , as andrew said that we can not get out of math.