Senin, 21 Mei 2012
Minggu, 15 April 2012
11313244012
International Mathematics Education 2011
Lesson: Introduction to Division
Hello and welcome to this video, introduction to division.
What we will do is take a look for some division problems and give you an explanation of the concept.
Here we have a problem,
18 : 2 = 9
18 is called the dividend, this number is being divided into.
2 is called the diviser, this is a number that exactly divide into the divident
9 is called quotient, this a result.
Lets take a look two more word that have to do with division,
1. Divisible. It means can be divided into.
We can say that 18 is divisible by 2 or 9.
2. Factor. Factor is when one number divide exactly into another number.
We can say 2 and 9 is the factor of 18
Example 1
15 : 3 =
15 as a divident
3 as a diviser
and we have to find the quotient
how many times the divise going to divident?
how many times this three going to 15?
we know 3 goes to 15, is five times, so the result is 5
Remember that divisions is the opposite operation of the multiplication operation.
So, when you learning on times tables, its also helping you to learn the division.
4 x 8 = 32
so, 32 : 8 = 4
32 : 4 = 8
It all works together.
Algebra and Its Application part 1 (Basic)
11313244012
International Mathematics Education 2011
From Marsigit's book (MATHEMATICS for Junior High School)
Chapter 1
Algebra and Its Application
Do you still remember the meaning of algebraic expression? Let see the following illustration.
Suppose Nanda is going to buy 5 books and 4pencils. If one book and one pencil are priced x rupiah and y rupiah, how much money that have to bring by Nanda?
Nanda have to bring 5x - 4y rupiahs.
The form of 5x + 4y from the above illustration is an algebraic expression in which:
5x and 4y are called terms,
x and y are variables
5 is the coefficient of 5x
4 is the coefficient of 4y
We can conclude that Algebraic expression is a statement consisting meaningful of coefficients and variables.
The Operations of Algebraic Expression.
Addition and Subtraction
In algebraic expression, we can only add and subtract the similar terms or like terms. The like terms contain the same variable with the same exponent.
There are two steps to add or subtract the algebraic expression.
1. group the like terms.
2. operate each group by adding or subtracting.
Multiplication Operation
1. Multiplication of one term and two terms of algebraic expressions.
this operations follow the distributive characteristic.
a(x+y)=ax+ay or (x+y)a=ax+ay
a(x -y)=ax-ay or (x-y)a=ax-ay
2. Multiplications of two terms and two terms algebraic expressions.
these multiplication can also be done using the distributive characteristics or using multiplication scheme.
(x+y)(a+b)= x(a+b)+y(a+b) = xa+xb+ya+yb
Exponential Operation
1. Understanding the Exponential
Exponential is a recur multiplication of a number. You can expand p^n as follow.
p^n= p.p.p.p.p} n term
example:
2^2 = 2.2 = 4
(3^2)^3 = 3^2 . 3^2 . 3^2 = 3.3 . 3.3 . 3.3 = 3^6
Divisions
1. Divisions of Algebraic expresions containing one terms
In the division of algebraic expressions is known two key terms:
- divisions with similar terms, such as 4x : x
- divisions with different terms, such as x^2 : x
Example
(x^3+3x) : x = (x^3 : x) + (3x : x)
= x^2 + 3
Solving Linear Equation part 1
11313244012
International Mathematics Education 2011
An Equation is a statement that two expression on quantities are equal.
An equal sign (=) is always a part of an equation.
Equality can be true, false, or neither.
the example:
3+5=8, this equation is true
8-2=8, this equation is false
now lets take a look an equation that a neither,
x+4=9, so this is neither true or false.
because I don't know what the value of x is?
if x=2, what we get?
2+4=9, so this equation is false
now lets change, if x=5
5+4=9, is true
the goal of this lesson is to find all the values of variable that would make an equation true.
- a solution is a value that when substituted in place of a variable, makes an equation true
- the solution set is the set of all solutions, SS = {5}
Example 1
Determine whether x=1 is a solution of the equation 2x+2=4
what should we do?
2( )+2=4
and we want x=1, so I wanna replace the x to 1
2(1)+2=4
we haven't know whether this equation is true or false until we continue until the operations is end
2+2=4
4=4 (reflexive property)
we get the equation is true, so SS={1}
Minggu, 11 Maret 2012
PYTHAGOREAN THEOREM IN DAILY LIFE
Good morning all, my name is Nanda Putri Amalia from the International class of Mathematics Education.
Let me explain to you about the Pythagorean Theorem in daily life.
Open the Marsigits book page 153, look at the exercise.
- The recommended distance to watch the television is 6 times of the length of the diagonal of the television. Determine the exact distance to watch a 20 inch television!
Answer:
We know that the 1 inch television means that the length of the diagonal of the television is 1 inch or 2. 54 cm .
The 20 inch television means that the diagonal is 20 times 2 .54 is 50. 8 cm.
So, the recommended distance to watch a 20 television is 50. 8 times 6 is equal 3098 cm.
2. Amron and Cathy are playing a kite. The length of the string is 50 m. Cathy is standing below the kite and making a 30 m distance with Amron. Determine the exact height of the kite!
Answer:
We assume that the length of the string as the hypotenuse (c), the distance between Cathy and Amron as the base of triangle (a) and the hight of the kite as the upright side of triangle (b). So, we can use the phytagorean theorem.
a = 30 m
c = 50 m
b = ...?
c2 = a2 + b2
we exchange the position of b,
c2 - b2= a2
502 – 302 = a2
2500 – 900 = a2
the root of 1600 = a
a = 40 m
so, the exact high of the kite is 40 m.
3. Joni is swimming across a river of 12 meters width. Just before he is reaching the opposite of the river, an unexpected wave is taking Joni further as far 5 meters. Determine the distance between the first place and his place now!
Answer:
We assume that 12 meters as the upright side of triangle and 5 meters as the base of triangle.
hypotenuse = the root of = the root of = the root of 169 = 13 meters
so, the distance between the first place and his place now is 13 meters.
4. A 4 meter steel bar is leaning on a vertical wall and making 60° angle with ground.
a. Determine the exact distance of A and C!
b. Determine the exact distance of B and C!
Answer:
To solve this problem, we have to know about the ratio of lengths of sides of a right triangle that has 60° angle. The ratio of the lengths of a right ABC triangle with c as the hypotenuse and has 60° angle is a : b : c = 1 : the root of 3: 2.
We was know the ratio. Now, we use the comparison to know the exact distance that we're looking for.
a. b/the root of 3= c/2
b = [(the root of 3) times 4] divided by 2
b = 2 times the root of 3
b. a/1= c/2
a = (4 . 1) divided by 2
a = 2
so, the exact distance of A and C (b) is 2 times the root of 3 m and the exact distance of B and C (a) is 2 m.
5. A triangle is made by three bars of steel. The lengths of two bars are 20 cm and 48 cm.
a. Determine the length of the third bar thus forming right triangle!
b. If the length of the third bar is less than 48 cm, what kind of triangle formed?
c. If the length of th third bar is more than 52 cm, what kind of triangle formed?
Answer:
a. If we want to form the right triangle (c as the hypotenuse), so we use the theorem:
"If c2 = a2 + b2, then ΔABC is a right triangle"
so, the length of the third bar to form the right triangle is:
c2 = 202 + 482
c2 = 400 + 2304
c = the root of 2704
c = 52 cm
b. If the length of the third bar is less than 48 cm (c as the hypotenuse), we use the theorem:
"If c2 < a2 + b2, then ΔABC is an acute triangle"
c2 < 482 + 202
c < the root of 2704
c < 52 cm
based on the theorem above, if the length of the hypotenuse is less than 48 cm, the kind of triangle formed is acute triangle.
c. If the length of the third bar is more than 55 cm (c as the hypotenuse), we use the theorem:
"If c2 > a2 + b2, then ΔABC is an obtuse triangle."
so, the length of the third bar is:
c2 > 482 + 202
c > the root of 2704
c > 52 cm
based on the theorem above, if the length of the hypotenuse is more than 55 cm, the kind of triangle formed is obtuse triangle.
Ok friends, I hope that you have understand about the Pythagorean theorem in daily life.
Thank you for your attention.
Wassalamu'alaykum wr.wb.