Approaches to Problem Solving

Introduction to approaches to problem solving:-

In this article we are going to see the important approaches to problem solving. Algebra is a cluster of math, we use script like a, b, x and y to denote numbers. In Algebra we execute count, division, increase, allotment, extraction of roots and substituting. Variables and numbers used as real numbers, algebra is unique, importance and computational skills we obtain what are called algebraic expressions.

Simple approaches to solving- Example problems:-

Approaches to solving- Example problem1:-

Solve - 2 (x + 3) = - 10

Solution:-

Solving algebraic equation

- 2 (x + 3) = - 10

-2x – 6 = -10

-2x = - 10 + 6

-2x = - 4

x = 2.

Approaches to solving- Example problem2:-

5 ( x + 2 ) + 3 ( x – 2 ) = 10

Solution:-

Solving algebraic equations

5 ( x + 2 ) + 3 ( x – 2 ) = 10

5x + 10 + 3x – 6 = 10

5x – 3x + 10 - 6 = 10

2x + 4 = 10

2x = 10 – 4

2x = 6

x = 6/2

x = 3.

Approaches to solving- Example problem3:-

-2( x + 4 ) + 3 ( x + 2 ) = 4x + 20

Solution:-

Solving algebraic equation

-2( x + 4 ) + 3 ( x + 2 ) = 4x + 20

-2x – 8 + 3x + 6 = 4x + 20

-2x + 3x - 8 + 6 = 4x + 20

x - 2 = 4x + 20

x - 4x = 2 0+ 2

- 3x = 22

x = -22/3.

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Approaches to solving- practice problems:-

Problem 1:-

Solve 3x -2(2x - 5) = 2 (x + 3) - 8

Answer:-

x=4.

Problem 2:-

3 (x - 3) = 5(2x+1)

Answer:-2.

Problem 3:-

Solve 15 (m - 4) - 2 (m - 9) + 5 (m + 6) =0

Answer:-

2/3.

Math Children Computer

Introduction to math children computer:

Math children computer is the help through computer to the children in math. Chidren when they solve math homework problems they come across lot of difficulties as the online tutoring websites help children in solving their problems. Tuotr vista is one of the best online tutoring website that help in math shildren in online through computer. Here in this article let us see sample problems solved from tutorvista  for math children computer.

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Math children computer:


Basic algebra problems:

Example 1 :
What is the sum of 7 and 8? Express this statement by using place holder.
Solution :

We can write this statement, in short, as
7 + 8 = ?.

The answer for this problem would be 7 + 8 = 15.

Example 2 :
What number added to 10 will give 15?
Solution :
It is 10 + x = 15

Example 3 :
Rabi has 18 rupees. She buys vegetables for 8 rupees. Find the remaining amount she will have in her hands.
Solution :
We can write it as 18 – 8 = ?

The answer for this problem would be 18 - 8 = 10.

Example 4 :
Find the product of 5 and 12
Solution :
5 × 12 =?

The answer for this problem would be 5 × 12 = 60.

Example 5 :
When a number is multiplied by 4, the product is 116
Solution :
x × 4 = 116.

x = `116 / 4` = 29.

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Math children computer:


Example 6:
What is the sum of 9 and 10? Express this statement by using place holder.
Solution:

We can write this statement, in short, as
9 + 10 = ?.

The answer for this problem would be 9 + 10 = 19.

Example 7:
What number added to 12 will give 17?
Solution:
It is 12 + x = 17
The answer would be x = 17 - 12 = 5.

Example 8:
Rabi has 28 rupees. She buys vegetables for 12 rupees. Find the remaining amount she will have in her hands.
Solution:
We can write it as 28 – 12 = ?

The answer for this problem would be 28 - 12 = 16.

Example 9:
Find the product of 6 and 12
Solution:
6 × 12 =?

The answer for this problem would be 6 × 12 = 72.

Example 10:
When a number is multiplied by 4, the product is 84
Solution:
x × 4 = 84.

x = `84 / 4` = 21.

Basic Mathematics Solving Online

Introduction to learn for solving online basic mathematics

Mathematics is used in many fields like, engineering, science, and medicine. Through online we can easily solving the problems quickly. Through online student can get help and learn at any time. In basic math the students can receive first level of math education called primary education. Through online students can get more help and easily understand the problems. In this article we shall discuss to learn for solving basic mathematics example problems.

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Learn for solving online basic mathematics example problems


Example:

Solve the expression 6x + 12y - 4 + 3x + 5y + 10

Solution:

• +6x and +3x are like terms, and combined to get +9x,

• +12y and +5y combine the like terms to get +17y, and

• -4 and +10 combine the like term and get +6

So after simplify, the expression:

9x + 17y + 6

Example:

The cost of 8 fruits is `$` 120; find the cost of 15 fruits.

Solution:

Step 1:

Consider the given problem as if the 8 fruits cost is `$` 120. Find the cost of 15 fruits?

Step 2:

8 fruits cost =120

15 fruits cost = 15/8 x120

=225

Answer:

Therefore the cost of 15 fruits is `$` 225

Example:

Solve the equations 6x-12=3x+6

Solution:

Step 1:

Given equation

6x-12=3x+6

Step 2:

Add 12 on both side of the equation

6x-12+12=3x+6+12

6x=3x+18

Step 3:

Subtract 3x on both side of the equation

6x-3x=3x-3x+18

Step 4:

Simplify the x value

3x=18

x=`18/3`

Answer:

Therefore x=6

Example:

The length of the rectangle is 140 cm and breadth is 60cm find the area of the rectangle.

Solution:

Rectangle length, l         = 140 cm

Rectangle breadth, b     = 60 cm

Area of the rectangle = l x b

Therefore 140 x 60 = 8400 sq.cm

The area of the rectangle is 8400 sq.cm

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Learn for solving online basic mathematics practice problems


Problem:

Solving the expression 6x + 12y - 4 + 2x + 3y + 8

Answer:

8x + 15y + 4

Problem:

Solving the equation 10x – 36 = 6x + 4

Answer:

x =10

Problem:

The cost of 6 fruits is `$` 120; find the cost of 20 fruits.

Answer:

Cost of 20 fruits is `$` 400

Word Problems in Math

Introduction to word problems:

Word Problems are the main chapter in 2nd grade math. These 2nd grades math involves basic arithmetic word problems. The basic arithmetic operations are add, subtract, multiply and divide. In this topic we have to seen about the addition and subtraction and multiplication and division word problems. Usually word problems are difficult here these 2nd grade math problems are very simple to study.

Example Word Problems in 2nd grade math

Example 1:

If the cost of 2 cakes is Rs.6 and the cost of one milk shake is Rs.20. Calculate the total price of cake and milk shake.

Solution:

The cost of 2 cakes = Rs.6

The cost of one milk shake = Rs.20

The total price of cake and milk shake = 6 +20.

Here + is the addition operation that is used for adding purpose.

Total price = Rs.26.

Example 2:

Ram has 5 pieces of pizza. He shares to 2 pieces of pizza to his sister. Calculate the remaining number of pizza.

Solution:

Total number of pieces = 5

Left out pieces = 2

Remaining number of pieces = 5 – 2

That is 3.

Here - is the subtraction operation that is used for subtracting purpose.

Example 3:

If the price of one ball is 20 dimes. Find the price of 5 balls.

Solution:

The price of one ball = 20 dimes

Therefore the price of 5 balls = 5 x 20

That is 100 dimes.

Here X is the Multiplication operation that is used for multiplication purpose.

Example 4:

If the rate of 10 bobby dolls is 100. Calculate the rate of 1 bobby doll.

Solution:

The rate of 10 bobby dolls = 100

We have to calculate the rate of 10 bobby dolls. For this we can do the division.

Therefore, the rate of one bobby doll = 100 / 10

Here / is the division operation that is used for dividing purpose.

These are the main types of word problems in 2nd grade math.

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Practice Problems


1. There are 5 apples and 15 jack fruits.  Find the total number of fruits.

Answer: 20 fruits

2. One bun costs 7 dimes Find the rate of 15 buns.

Answer : 105 dimes

3. The cost of 1 kg of carrots be dollar 12 find the cost of half kg of carrots.

Answer : 6 dollars

Equivalent Definition Math

Introduction to equivalent definition math:

The equivalent is the term in the mathematics. It defines the equivalent definition fractions math and the equivalent ratio for the numbers. The fraction of the two numbers has the equivalent fraction for the fraction of other two numbers. Here we are going to see about the equivalent fraction for the two numbers.The equivalent fraction may be find by the common multiplication or the division of the common number in both numerator and also the denominator. I like to share this Derivatives Table with you all through my article.


Example problems for equivalent definition math:


Example 1 for equivalent definition math:

Find the equivalent fraction for `2/5` .

Solution:

The given fraction is `2/5` .

We have to find the equivalent triangle, for that we multiply or divide the numerator or the denominator by the common number to get the equivalent fraction.

Multiply the above fraction by 5 on the denominator and also numerator

`2/5`  `xx` `5/5` = `10/ 25`

Multiply the given fraction by 3 also we get the equivalent fractions.

`2/5`  `xx` `3/3` =` 6/ 15`

Divide the given fraction by 4 to get the equivalent fractions.

`2/4``-:` `5/4`= (`2/4` )/ (`5/4` )

`2/4``-:` `5/4`   = `2/5`  `xx` `4/4`

`2/4``-:` `5/4`   = `8/20`

Divide the given fraction by 8 to get the equivalent fraction.

`2/8``-:` `5/8`  = (`2/8` ) / (`5/8` )

`2/8``-:` `5/8` =` 16/40`

The equivalent fractions of `2/5 ` are `10/ 25` ,` 6/ 15` , `8/20` and `16/40` .


Example 2 for equivalent definition math:

Find the equivalent fraction for `4/7` .

Solution:

The given fraction is `4/7` .

We have to find the equivalent triangle, for that we multiply or divide the numerator or the denominator by the common number to get the equivalent fraction.

Multiply the above fraction by 2 on the denominator and also numerator.

`4/7` `xx`` 2/2` =` 8/ 14`

Multiply the given fraction by 5 also we get the equivalent fractions.

`4/7` `xx`` 5/5` = `20/ 35`

Divide the given fraction by 3 to get the equivalent fractions.

`4/3``-:` `7/3` = (`4/3` )/ (`7/3` )

`4/3``-:` `7/3` = `4/7`  `xx` `3/3`

`4/3``-:` `7/3` = `12/21`

Divide the given fraction by 9 to get the equivalent fraction.

`4/9``-:` `7/9`  = (`4/9` ) / (`7/9` )

`4/9``-:` `7/9` = `36/63`

The equivalent fractions of `4/7 ` are `8/ 14` , `20/ 35` , `12/21` and `36/63` .

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Practice problem for equivalent definition math:


Find the equivalent fraction for `1/7` .
Answer: `2/14` , `4/28` , `5/ 35` .

Basic Subtraction Fraction

Introduction-basic subtraction fraction:

Study fraction math (from the Latin fractus, broken) is a number that can represent part of a whole. The earliest fractions were reciprocals of integers: ancient symbols representing one part of two, one part of three, one part of four, and so on. A much later development were the common or "vulgar" fractions which are still used today (`1/2`, `5/8`, `3/4`, etc.) and which consist of a numerator and a denominator in study fraction math.

Source: Wikipedia

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Definition-basic subtraction fraction:


Fractions are frequently used in mathematics, science and the world impressive like us. They have been used by human sovereign whereas the time of the new Egyptians and are still used by public to solve problems in their day-by-day lives.

Fraction math came into regular use in the 16th century. Look at this study fraction math:

`25/50`

Solve subtraction of fraction with same denominators:

Just as we subtract fractions, we can take off numbers with same denominator.

Example:

`5/2`-`3/2`=?

Solution:

= `5/2`-`3/2`

=`(5-3)/(2)`

=`2/2`

=1

Solve subtraction of fraction with different denominators:

Just as we subtract fractions, numbers also can be taking from with unlike denominators. The common denominator is realized by finding out the LCM.

Example:

`4/2`-`5/3`=?

Solution:

=`4/2`-`5/3`                                              (we need to take LCM of 2 and 3)

=`(12-10)/(6)`                                         (we need to perform subtraction operation)

=`2/6`                                                 (divided by 2, both the numerator and denominator)

=`1/3`                                                 (then, we get result)

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Example- basic subtraction fraction:


Example 1:

If Sam get `$15` in a day and pay out `$10` , what part of his weekly pay did he keep?

Solution:

Step 1: Numerator: amount saved=15-10=5

Step 2: Denominator: salary = $15

Step 3: Part or fraction

=`(15-10)/(15)`                                             (we need to perform subtraction operation)

= `(5)/(15)`                                                  (divided by 5, both the numerator and denominator)

=`1/3`                                                     (then, we get result)

Answer is `1/3`

Example 2:

`12/4`-`2/3`=?

Solution:

=`12/4`-`2/3`

=`6/2`-`2/3`                                                    (we need to take LCM between 2 and 3)

=`(18-4)/(6)`                                                  (we need to perform subtraction operation)

=`(14)/(6)`                                                       (numerator and denominator are divided by 5)

=`7/3`                                                         (then, we get result)

Answer is `7/3`

Inequality Math

Introduction to inequality in math:

In mathematics, an inequality is a statement about the relative size or order of two objects or about whether they are the same or not. (Source : Wikipedia).In inequality we are using many number of mathematical symbol and each one represent the particular operation. I like to share this Compound Inequality Solver with you all through my article.

>  greater than symbol

<  less than symbol

>=  greater than or equal to

<= less than or equal to

=  equal to

!= not equal to

Here we are going to study about how solve the inequality problems and its example


Math example problems:


Example: 1

Solve the following inequality equation.

4x+3+2x +5 < 2x+4

Solution:

In the left hand side combine the like term first

4x+3+3x +5 < 2x+4

7x + 8 < 2x + 4

Add both sides -4 we get

7x + 8 - 4 < 2x + 4 - 4

In right hand side 4 - 4 will be cancelling

7x+ 4 < 2x

Add both sides -2x

7x -2x + 4 < 2x -2x

5x + 4 < 0

Add both sides -4 we get

5x + 4 -4 < -4

5x < -4

Divide both sides 5 we get

(5x / 5) < - `(4/5)`

x < - `(4/5)`

Therefore the x value less than - `(4/5)`

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math example : 2


Solve the following inequality 2x - 23 > x - 4

Solution:

First we have to solve the x value

Add both sides +4 we get

2x - 23 +4 > x + 4 – 4

In right hand side 4 - 4 will be canceling

2x - 19 > x

Add both sides 19 we get

2x + 19 -19 > x + 19

2x > x+19

Add both sides –x we get

2x – x > x-x +19

x > +19

Here the greater than symbol represent the x value greater than 19 that is 20, 21, 22 ……

Learning Basic Statistics Problems

Introduction to learning basic statistics problems:

Learning Statistics is making good use of numerical data to groups of individuals or experiments. To obtain more information about the propensity of the data to deviate about a particular value, there are certain procedures which characterize the entire data. These procedures are called the Measures of Central Tendency namely, mean, median, mode and range. I like to share this Calculate Median with you all through my article.

Learning Basic statistics problems-Formula

Learning Basic Statistics Mean

The mean is the average of the set of values. The average is calculated by arrange the values from the set in a particular way ascending or descending order and computing a single number as being the average of the set.

Basic Statistics mean formula

Mean or average= sum of elements / total number of elements

Learning Basic Statistics Median

The median is the number in the middle of the given series. To find the median, to arrange the values in order from ascending order or descending order, and then find the number that is exactly located in the middle

Basic Statistics median formula

When total number of data is odd then median = n/2

When total number of data is even then median = n/2 and n/2+1

Learning Basic Statistics Mode

The mode is the value that occurs most often in the given data.

Basic Statistics Range Formula

Range is calculated by subtracting the smallest value (sample lowest) from the highest value (sample highest) in the set of raw data values.

Range = Upper (maximum) value – Lower (minimum) value.

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learning basic statistics problems-examples

Mean problems

The scores are: 100, 78, 93, 84, 91, 100, 82, and 79.

The mean of the scores is

Mean = (100+78+93+84+91+100+82+79) / 8

= 88.375

Median problems

The median of the scores is "the number in the middle"

100, 100, 93, 91, 84, 82, 78, 79

Since there is an even number of values, the medians between these two, an even number of score there is no number in the middle so the two numbers in the middle are averaged:

Median = (91 + 84)/2 = 87.5

Mode problems

The mode of a set of numbers is the number that occurs more times.

The scores are: 100, 78, 93, 84, 91, 100, 82, and 79.

In this case, since there are 2 100's, the mode is 100.

Range problems

Data: 2, 3, 4, 5, 6, 6, 6, 7, 7, 8, 9.

Upper value 9

Lower 2

Range= 9 - 2 = 7

Imaginary Complex Number

Introduction:

We will discuss about imaginary number. An imaginary number is a number in the form bi where b is a non-zero, real number and i, defined by i2 = − 1, is known as imaginary unit.An imaginary number bi can be added to real number a to form a complex number of the form a + bi,a and b are called , "real part" and "imaginary part" .Imaginary numbers can thought of complex numbers where real part is zero.


Applications of Imaginary Numbers


Real numbers (or even rational numbers) propose a satisfactory portrayal of data.
Fraction such as ⅔ and ⅛ are worthless to a personality including stones, but fundamental to a person compare the size of poles apart collection of gravel.
Pessimistic numbers such as −3 and −5 are insincere when measure the mass of an object, but essential when keeping track of pecuniary debit and credit.
Complex Imaginary numbers have indispensable physical application in a variety of sciences and allied areas such as signal processing, control theory, fluid dynamics, quantum mechanics, cartography, and trembling analysis.
In the complex number demonstration the same apparatus are referred to as real and invented. When the complex number is with the sole purpose make-believe, such as a real part of 0 and an imaginary part of 120. Understanding Number Sense is always challenging for me but thanks to all math help websites to help me out.

Control theory


In control theory, systems are often misshapen from the time domain to the regularity domain using the Laplace transform.
The system pole and zeros are then analyzed in the intricate seaplane.
In the root locus method, it is more than increasingly important whether the pole and zeros are in the omitted or right half hydroplane, i.e. have real part superior than or a reduced amount of than zero.
In the right half plane, it will be unbalanced.
All in the left half plane, it will be stable,
On the pretend axis, it will have unimportant immovability..
If a system has zeros in the right half plane, it is a minimum phase system.

Solve Basic Probability Problems

Introduction:

Probability is one of the important topic in intermediate and college mathematics. Probability plays an important role in the day to day life. It is way of expressing that an event will occur or has occurred. It is also defined as the possible outcomes to the total number of events.

A probability of an event A occurred is represented by a real number in the range from 0 to 1 and written as P(A), p(A) or Pr(A). The probability of impossible event is given as 0, and a certain event has a probability of 1. However, the conversations are not always true: probability 0 events are not always impossible, nor probability 1 events certain. Basic proabbility problems are easy to solve. When the concept of basic probability is understood very well, then it is easy to solve those problems.

Examples problems for basic probability:

Basic probability Problem 1:

What is the probability of rolling a 3 on a dice?

Solution:

Here the number of possible out comes on the event is 6
The number of outcomes in rolling a dice is 3
Solve for the probability,

number of outcomes in Event
Prob(E) = --------------------------------------------------------------------
Total number of possible outcomes of the event

Prob(E) = 3/6

Prob(E) = 1/2

Basic probability problem 2:

What is the probability of selecting card of hearts from a deck of 52 cards?

Solution:

The total number of cards in a deck is 52
The number of cards of hearts fro a deck of cards is 13
Solve for the probability,

number of outcomes in Event
Prob(E) = ----------------------------------------------------------------------
Total number of possible outcomes of the event

Prob(E) = 13/52

Prob(E) = 1/4

Basic probability problem 3:

What is the probability of selecting number 9 from a deck of 52 cards?

Solution:

The total number of cards in a deck is 52
The number 9 from a deck of cards is 4
Solve for the probability,

number of outcomes in Event
Prob(E) = ----------------------------------------------------------------------
Total number of possible outcomes of the event

Prob(E) = 4/52

Prob(E) = 1/13

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Basic probability problems practice:

What is the probability of rolling a 3 on a dice?

Answer:

The answer is 6/6 = 1

2) What is the probability of selecting two balls from a basket containing 20 balls?

Answer:

The answer is 2/20 = 1/10.

Basic Terms and Definitions

Introduction to basic terms and definitions:

Mathematics is the group of sciences (arithmetic, geometry, algebra, calculus etc) dealing with quantities, magnitudes, and forms and their relationships, attributes etc by the use of numbers and symbols. There are many branches in mathematics. There are several terms and definitions involved in mathematics. Some of the basic terms and definitions involved in mathematics are defined below: Is this topic Translations Math hard for you? Watch out for my coming posts.


Basic terms and definitions:


Arithmetic:

It is a branch of mathematics that deals with the study of number specially with regard to basic operations such as addition, subtraction, multiplication and division etc and their applications to solution of problems.

Algebra:

Algebra, like arithmetic is a branch of the science of calculation. In arithmetic, however, we calculate by means of figures only, whereas in algebra, we use symbols also to denote quantities.

Algebraic equation:     It refers to any equation that contains only algebraic expressions and signs of operations.

Algebraic expression: It consists of various algebraic terms connecting with the help of signs of operations.

Algebraic function: Any function that involves only algebraic expressions and  signs of operations.

Geometry:

A branch of mathematics concerned with the properties of lines, curves, and surfaces usually divided into pure, algebraic, and differential geometry in accordance with the mathematical techniques utilized.

Calculus:

It is a branch of mathematics that deals with differentiation (differential calculus) and integration (integral calculus) of functions. It finds applications in different areas of natural, physical and social sciences.

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Additional basic terms and definitions:


Trigonometry:

Trigonometry includes the measurement of triangles and includes the relation between the angles, sides, and triangles.

Trigonometric equation: Equations whose variables are the argument of trigonometric functions are the trigonometric equations

Trigonometric identities: Identities involving trigonometric function are called as trigonometric functions.

Probability:

The Numerical measure of the likelihood of an event to occur is referred as probability.

Statistics:

Statistics is the science of making effective use of numerical data relating to groups of individuals or experiments. In other words, Statistics is the numerical data collected systematically, summarized, and tabulated.

Definition of Algebra

Definition of algebra:

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. -Source from Wikipedia.

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Simple problems On Algebra:


Example 1:

Solve the algebraic expression X-3= 12

Solution:

We need to find the value of x

Step 1: X-3+3=12+3 (we need to add 3 on both the sides)

Step 2: X=15.

Example 2:

Solve the algebraic expression 3a-9=63

Solution:

We need to find the a value

Step 1: 3a-9+9=63+9 (first we need to add 9 on both the sides)

Step 2: 3a=72 (Now we divide using 3 on both the sides)

Step 3: a=24

Example 3:

Solve the algebraic expression 10+B+1=2(B+1)

Solution:

Step1 :( 11+B)=2B+2

Step 2: 11+B-B=2B-B+2 (subtract B on both the sides)

Step 3: 11=B+2

Step 4: 11-2=B+2-2 (Subtract 2 on both the sides )

Step 5: 9=B.

Example word problems:

Word Problem 1:

Marissa spent `$` 42 for shoes.  This was `$` 14 less than twice what she spent for a dress.  How much was the dress?

Solution:

Step 1: Let assume x be how much she spent for the dress.

Step 2: So, 2x-14=42

Step 3: 2x+14-14=42+14 (Here we need to add 14 ob both the sides)

Step 4: 2x=56(Now we divide using 2 on both the sides)

Step 5: x=56/2

Step 6: x= 28

So the dress cost is $28.

Word Problem 2:

The sum of two numbers is 84, and one of them is 12 extra than the other.  What are the two numbers?

Solution:

In this problem, we need to find two numbers. So, let x be one of them.  Let x be the first number.

We know that the other number is 12 more, x + 12.

Here the sum is 84:

So it can be written as x+x+12=84.

Now we need to solve this:

So, x+x+12=84.

Step 1:  2x+12 =84

Step 2: 2x-12+12=84-12 (subtract 12 on both the sides)

Step 3: 2x=72 (now we need to divide using 2 on both the sides)

Step 4: x= 36 .So the first number is 36

Now we need to find another number:

x+12 =36

So, 36+12 = 48.The another number is 48

(The sum of 36+48 is 84)

Basic Geometry Test

Introduction:

Geometry is used to learn all kinds of shapes and their properties. There are two main classifications in geometry. Basic geometry is the straight edge in every side of a figure completely lies in the same plane. Basic geometry learns about all shapes such as lines, circles, etc. The term geometry means learn of properties of figures and shapes and the relationship between them. Please express your views of this topic What is a Straight Angle by commenting on blog.


Basic geometrical concepts:


Point
Line
Ray
Line segment
Plane
Point:

In basic geometry test, place a dot with the sharp tip of your pencil or with a pin on a sheet of paper. Learn about dot gives you an idea of a point. The point represents a particular location. Thus we say that a point has an exact position. Point does not contain length, breadth or thickness.

Line:

In basic geometry test, two points are joined in any direction. It has no height and thickness. It is a straight one dimensional figure. It can extend in both directions infinitely.

Ray:

In basic geometry test, we learn that the sun is emitting rays of light. We can also see the rays of light in the torch light. A ray of light originates from a point in the sun or from the torch light and extends endlessly in one direction.

Line segment:

In basic geometry test, a line segment is a part of the line consisting of two end points on it.

Plane:

In basic geometry test, a plane is a flat surface which extends endlessly in all directions. No boundaries are present in the plane. A plane cannot be drawn of our own. But a branch of a plane can be drawn on any flat surface. Is this topic 2 Parallel Lines hard for you? Watch out for my coming posts.


Basic Geometry example


Example 1:

Let XY be a ray.

(1) What is the starting point of the ray?

(2) May Y be the starting point of the ray?

(3) Where does the point Y lying on the ray?

(4) Are the ray XY and YX different?

Solution:

1) Starting point is X.

2) No.

3) Y can be marked anywhere on the ray in order to name the ray.

(4) XY and YX are different because they are in different directions.

Learning Basic Algebra Free

Introduction to learning basic algebra free:

Algebra, a branch of mathematics deals with the expressions of various order, their operations, relations and construction and concepts of expressions.Algebra is the combination of numerical numbers, alpha-numeric variables, expressions and etc., the basic aim of the algebra is balancing the algebraic equations on both sides.In learning basic algebra free, you can learn about the various expressions and order of expressions, with their standard forms.In this article for learning basic algebra free we shall discuss about the basics of algebra. Is this topic Improper Fractions to Mixed Numbers hard for you? Watch out for my coming posts.


Basics of Algebra – learning basic algebra free:


Adding and Subtracting ,
Multiplication of algebra ,
Division of algebraic and
Solving Equations.


Adding and Subtracting Algebraic Expressions:

This shows how to solve the addition and subtraction in algebraic expression.

eg:

Addition:

2a^2 + 2b + 5a^2= 7a^2 +2b.

Subtraction:

15a^2 – 31b -10a^2 = 5a^2 – 31b.

Multiplication of algebra expressions:

This shows how to solve the Multiplication in algebraic expression.

eg:

multiplication:

2(a + 3b) = 2a +6b.

Division of algebraic expressions:

This shows how to solve the Division on in algebraic expression.

Eg:

Division:

12ab2 / 31ab2

Solving Equations:

This shows how to solve the system of algebraic expression.

Eg:

Solve:

5 - (x + 2) = 0.

-5x + 10 = 0

-5x = -10

x = 2

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Example for solving algebra - learning basic algebra free:


Solve the following linear equations: x + 2y + 3z = 14, 3x + y + 2z = 11, 2x + 3y + z = 11.

Solution:

x + 2y + 3z = 14 (1)

3x + y + 2z = 11 (2)

2x + 3y + z = 11 (3)

Consider the equations (1) and (3)

(1) ? x + 2y + 3z = 14

(3) × 3 ? 6x + 9y + 3z = 33 (subtracting)

–5x – 7y = –19

5x + 7y = 19 (4)

Consider the equations (2) and (3)

(2) ? 3x + y + 2z = 11

(3) × 2 ? 4x + 6y + 2z = 22 (subtracting)

–x – 5y = –11

x + 5y = 11 (5)

Consider the equations (4) and (5)

(4) ? 5x + 7y = 19

(5) × 5 ? 5x + 25y = 55 (subtracting)

–18y = –36

? y = 2

Substitute y = 2 in (5) we get

x + 5(2) = 11

x + 10 = 11

x + 10 - 10 = 11 - 10

? x = 1

Substitute x = 1, y = 2 in (3) we get

2(1) + 3(2) + z = 11

2 + 6 + z = 11

8 - 8 + z = 11 - 8

? z = 3

The solution is x = 1, y = 2, z = 3.