Smart Math OPEN SENTENCE IN MATH Easy Methods

SMART MATH  >> Open Sentence in Math
1. Statement Smart Math
In everyday life we often see a variety of the following sentences.
a. Jakarta is the capital city of Indonesia.
b. Mount "Merapi" in Central Java.
c. 8> -5.
The third sentence above is a sentence that is true, because every person recognizes the truth of the sentence.
 

Then consider the following sentences. 

a. "Monas" is located in Jogjakarta.
b. 2 + 5 <-2
c. Sunset in the east.

The third sentence is a sentence that is false, because everyone does not agree with the sentence.
Sentences that can be determined truth value (true or false) statement is called.

Now consider the following sentences.
a. Apple fruit taste sweet.
b. Eat nutritious foods.
c. Learn diligently so you go up a class.
Can you determine the truth value of the sentence - the sentence above? Do you think the sentences are not statements? Why?

2. Open Sentences & Sentence Completion Association open Smart Math.

Can a sentence to answer the question "Indonesia is located on the continent of x". If x is replaced Asia then the sentence is true. As for if x is replaced Europe then the sentence is false. Sentences such as "Indonesia is located on the continent of x" is called open sentence.
a. 3 - x = 6, x member of the set of integers.
b. 12 - y = 7, y member of the set of natural numbers.
c. z * 5 = 15, z member of the set of natural numbers.

Sentence 3 - x = 6, x integer members would be true if x is replaced -3 and will be worth one if x is replaced numbers other than -3. Furthermore, x is called a variable, while the 3 and 6 are called constants.

Try to determine the variables and constants of sentence 12 - y = 7 and z * 5 = 15 in the above example.
Open sentence is a sentence that contains a variable and unknown truth value.

A variable is a symbol (symbol) on the open sentence that can be replaced by any member of the set that has been specified.
The constant is a fixed value (s) contained in an open sentence.
Now consider the sentence x2 = 9. If the variable x is replaced by -3 or 3 sentences then x2 = 9 will be true. In this case x = -3 or x = 3 is the completion of an open sentence x2 = 9. Thus, the completion of the sentence set x2 = 9 is {-3, 3}.
Completion of an open set is the set of all sentences replacement of variables in open sentences so that the sentence is true. That is SMART MATH Open Sentence in Math.

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Smart Math Quick Summary Algebra

Smart Math Quick Summary Algebra
 

1. Variables, constants, factors, as well as similar and not similar rates.
- A variable is a symbol that substitutes a number
its value is not known clearly.
- Constants are parts of an algebraic form
such as number and no load variable.
- The tribes are the kind that has a variable rate and
the rank of each variable are the same.
- Interest is not a type that has a variable rate and
the rank of each variable are not the same.
 

2. On the algebra, addition and subtraction operations
can only be done on similar tribes.
 

4. Multiplication between the two forms is expressed algebraically as follows.
(ax + b) (cx + d) = acx² + (ad + bc) x + bd
(ax + b) (cx² + dx + e) = acx³ + (ad + bc) x² + (ae + bd) x + be
(x + a) (x - a) = x² - a²

 

3. Multiplying a constant number k with the algebra
parts one and two tribes expressed as follows.
k (ax) = kax
k (ax + b) = kax + kb 

the two forms is expressed algebraically as follows.
(ax + b) (cx + d) = acx² + (ad + bc) x + bd
(ax + b) (cx² + dx + e) = acx³ + (ad + bc) x² + (ae + bd) x + be
(x + a) (x - a) = x² - a²
 

5. On the powers of the algebra of the two tribes, tribal tribes coefficient
determined by Pascal's triangle.
(a + b) ¹ = a + b
(a + b) ² = a² + 2ab + b²
(a + b) ³ = a³ + 3a²b + 3ab² + b³
and so on
 

6. Value of an algebraic form can be determined by
substituting any number on the variables
The algebraic form.
 

7. A fraction simplest form of algebraic say if
numerator and denominator have no factors fellowship
except 1 and the denominator is not equal to zero.
 

8. Results of operations of addition and subtraction on fractions
algebra obtained by equating the denominator,
then summing or subtracting the numerator.

 

That is there are 8 item Smart Math Quick Summary Algebra.

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Smart Math Methods "Algebra Arithmetic Operations" Easy way

Smart Math Methods algebra arithmetic operations 

1. Addition and reduction Algebra Shape On the algebra, addition and subtraction operations can only be performed on similar tribes. Totalizing or subtract the coefficients on similar tribes.Determine the sum and subtraction algebraic form following.a. -4ax + 7axb. (2x2 - 3x + 2) + (4x2 - 5x + 1)c. (3a2 + 5) - (4a2 - 3a + 2)Smart Math Solution:a. 7ax-4ax + = (-4 + 7) ax = 3ax 
b. (2x2 - 3x + 2) + (4x2 - 5x + 1) = 2x2 - 3x + 2 + 4x2 - 5x + 1= 2x2 + 4x2 - 3x - 5x + 2 + 1 = (2 + 4) x2 + (-3 - 5) x + (2 + 1)= 6x2 - 8x + 3c. (3A2 + 5) - (4A2 - 3a + 2) + 5 = 3A2 - 4A2 + 3a - 2= 3A2 - 4A2 + 3a + 5-2 = (3-4) a2 + 3a + (5-2) =-a2 + 3a + 32. 

Multiplication You need to recall that the integer multiplication effect / distributive properties of multiplication of the sum, ieax (b + c) = (axb) + (axc and distributive properties of multiplication the reduction, the ax (b - c) = (axb) - (axc),for any integers a, b, and c. This also applies to the nature of the algebra multiplication.a. Multiplying constants with the algebra of multiplication of a constant number k with the tribes and tribal algebraic form two stated as follows.k (ax) = kax k (ax + b) = kax + kb Hypotenuse angled triangle are (2x + 1) cm, while the length of the side of the elbow (3x - 2) cm and (4x - 5) cm. Find the area of ​​the triangle. Describe the following algebraic form, and then simplify it.a. 4 (p + q)b. 5 (ax + by)c. 3 (x - 2) + 6 (7x + 1)d. -8 (2x - y + 3z)

 Smart Math Solution:a. 4 (p + q) = 4p + 4Qb. 5 (ax + by) = 5ax + 5byc. 3 (x - 2) + 6 (7x + 1) = 3x - 42x + 6 + 6 = (3 + 42) x - 6 + 6 = 45xd. -8 (2x - y + 3z) =-16x + 8y - 24z

 b. Multiplication between two forms of algebraic as a constant multiplication by algebraic form, to determine the product of the two forms of algebra we can use the distributive properties of multiplication to addition and multiplication distributive nature of the reduction.Besides this way, to determine the product of the two forms of algebra, can use the following method.Note the multiplication of the algebra of two parts with the following two parts.(ax + b) (cx + d) = ax X cx + d + cx + b X b X d = acx2 + (ad + bc) x + bd

The above problem is to describe some of the workings of arithmetic operations in the form of algebraic subtraction, addition and multiplication, the ways solving already elaborated on smart math methods.

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Smart Math Quick Method "FORM AND ALGEBRAIC ELEMENTS"

SMART MATH Quick Method Form and Algebraic Elements

Consider the following illustration.
Many of her dolls more than 5 Rachel Angel doll. If a lot
Rachel stated stuffed with so many dolls Angel x expressed by x + 5. 

If Rachel doll 4 pieces then Angel doll as much as 9 pieces.
Forms such as (x + 5) is called the algebra.
The algebra is a mathematical form in presentation contains letters to represent numbers not yet known.

Algebraic form can be used to resolve Smart Math Quick Method
problems in everyday life. Things that are not known as much fuel it takes a
buses in each week, the distance covered in a certain time, or the amount of forage required within 3 days, can be found using algebra.
Examples of other forms like algebra :

2x,-3p, 4y + 5, 2x2 - 3x +7, (x + 1) (x - 5), and-5x (x - 1) (2x + 3). 

The letters x, p, and y on the algebra is called a variable. Furthermore, there is a form of algebra elements algebra, including variables, constants, factors, similar tribes, and tribal not similar.

In order for you to be more clear about the elements of the form algebra, study the following descriptions.
 

1. Variables, Constants, and Factor
Note the algebraic form 5x + 3y + 8x - 6y + 9.
On the algebraic form, the letters x and y are called variables.
A variable is a symbol that has not a substitute for a number known values ​​clearly.

Variable called variables. Variables are usually denoted with small letters a, b, c, ..., z.
As for the number 9 on the algebra of the above referred constants.
Is the rate constant of a form of algebra in the form numbers and no load variable.

If a number can be converted into a = p X q with a, p, q integers, then p and q are called the factors of a.
On the algebra above, 5x can be described as
5x = 5 X X X 1 or 5x = 5x.
So, the factors of 5x is 1.5, x, and 5x.

As for the meaning of the coefficients are constant factor a tribe in the form of algebra.
Note the coefficient of each term in the algebra
5x + 3y + 8x - 6y + 9. 5x the rate coefficient is 5, the tribe
3y is 3, at 8x rate is 8, and the tribe is-6y -6.

2. It kind of tribe and tribe Similar
a) The rate is variable or constant coefficients along the form of algebraic operations that are separated by a number or a difference.
The tribes are the kind that has a variable rate and the rank of each variable are the same.
Example: 5x and-2x, 3A2 and a2, y and 4y, ...

Tribe is not a type that has a variable rate and the rank of each variable are not the same.
Example: 2x and-3x2,-y and-x3, and 5x-2y, ...

b) the Tribe is a form of algebra that are not connected by sum or difference operations.
Example: 3x, 2a2,-4xy, ...

c) is the algebra of the two parts are connected by a single sum or difference operations.
Example: 2x + 3, a2 - 4, 3x2 - 4x, ...

d) is the algebra of three parts which are connected by two sum or difference operations.
Example: 2x2 - x + 1, 3x + y - xy, ...
Algebraic forms that have more than two parts called many tribes. so we can do with smart math Quick Method

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Smart Math exponential number and Operations powers of integer arithmetic

Smart Math in exponential number.
quadratic terms of a number. Squared or the square of a number is multiplying a number by the number itself.Furthermore, the powers of a number means multiplying repeated with the same number. 
Note the following powers of prime number 2. 

2 ² = 2 x 2 (2 ² read 2 squares or 2 to the power 2)= 42 ³ = 2 x 2 x 2 (2 ³ read 2 to the power 3)= 8 

Smart Math Solution:
a. 9 ² = 9 x 9 = 81b. (-6) ³ = (-6) x (-6) x (-6) = 36 x (-6) = -216c. -5 = - (5 x 5x 5 x 5) = -625d. (-10) 4 = (-10) x (-10) x (-10) x (-10) = 10,000 Properties exponential number.

a. Multiplicative nature of the exponential number Note the following rank of integer multiplication.3 ² x 3 ³ = [3x3] x [3x3 x3]Means [3x3] = 2 factors and [3x3x3] = 3 factors So there are 5 factors add up, so be 3x3x3x3x3 

b.Nature of the distribution of exponential number Note the following integer division rank.
5 ³: 5 ² = [5x5x5]: [5x 5] the meaning [5x5x5] = 3 factors and [5x 5] = 2 factors So there is 1 factor is reduced, so that a 5
Smart Math Operation Count Mixed Integer 
In completing integer arithmetic operations, there are two things to note, that1. sign arithmetic operations;2. brackets.If in a mixed integer arithmetic operations are bracketed, workmanship are in brackets should be done first. 

If in an integer arithmetic operation there is no parentheses, the process is based on the properties of the following arithmetic operations.1. Operations of addition (+) and subtraction (-) as strong, meaning that operations are located on the left side done first.2. Multiplication (x) and division (:) as strong, meaning that operations are located on the left side done first.3.  

Multiplication (x) and division (:) is stronger than the addition operation (+) and subtraction (-), multiplication means (x) and division (:) done first rather than the addition operation (+) and subtraction (-).
Example: 
a. 24 + 56 x 42-384 : 12= 24 + (56 x 42) - (384: 12)= 24 + 2352-32=       2376-32= 2,344 

b. 28 x (364 + 2,875): (9756-9742)= 28 x 3,239: 14= 90 692: 14= 6,478
c. 80: ((11-7) x (-4))= 80: (4 x (-4))= 80: (-16)= -5

d. (-8 + 5) x (36: (6-9))= -3 X (36 (-3))= -3 X (-12)= 36 

Thus example Smart Math exponential number and Operations of integer arithmetic, may be useful for the reader.

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