Parallelism in Grade V

Today we are going to put some light on the geometry of grade V of ICSE. grade V is the is last class of primary section and in this class you do revision of all the topics that you have learned and with this you learn several new topics. In the last article of the same grade we have discussed about geometry and the very first topic of the same we have discussed construction of the basic geometric figures and today you will learn,  Parallelism, Perpendicularity, and Congruence.

Afore we move to parallelism, first talk about parallel lines. Parallel lines are distinct lines, which lie in the same plane and they never intersect each other. With this, parallel lines also have same slope.

Parallelism is defined as the state of being parallel or corresponding in some way. When two lines or object moves parallel to each other we define it as parallelism.
Now, the next one that is Perpendicularity, do you know what does perpendicular means? Perpendicular means when an object is placed at exactly 90⁰. Perpendicular lines are those lines that intersect each other at a right angle or at 90⁰.  If two lines are perpendicular to each other, then the product of their slopes is always equal to – 1.   Example:              

Perpendicularity is the phenomenon in which a straight line is placed at 90⁰ to given plane, line or surface.  The equation of perpendicularity is given as:
ay – bx + k =0
It represents for different values of k a family of lines perpendicular to the lines ax + by + c = 0.
Now the last topic of today i.e. Congruence,
In this we deal with congruent triangles. What do you understand by congruent triangles, it means having the same measure. Similarly the congruent angles are those angles that have same measure.  You all know equilateral triangles; it has all its angle equal to 60^0. In the same way concurrent triangles also have same measures. Congruent Figures have the same shape and size.

Congruent Segments have the same length.

Example: Line CD bisects another line AB at point P. Name any two congruent angles formed.
Output:
Step 1: When a line bisects another line, four right angles are formed.

Step 2: Two such angles are angle CPB and angle APD.

This is all about the three topics I mentioned above. Geometry is very simple branch of mathematics and in this you have to only deal with figures, shapes and their properties. Geometry is simple if you do practice on daily basis. Learn the topic on the very same day and clear all your doubts. To score good grade do the practice and become master of the subject.

In upcoming posts we will discuss about Fractions in Grade V. Visit our website for information on prime factorization

Math Blog on Grade V

Geometry is full of different figures and designs. If you understand geometry then it is one of the interesting math answers for the problems. In geometry we have basic geometric shapes like circle, triangle, square, rectangle, rhombus, parallelogram, etc. geometry doesn’t end. Here we also have many other advanced level of construction, since analytical geometry problems deals with shapes, its constructions and properties. Each and every geometric shape has its own well defined set of properties. Every construction of geometry problems involve some steps that has to be followed. In this article, we will focus on the very first geometrical topic of Grade V in which you will learn the basic geometrical shapes constructions like line, circle, etc.

Let's first see the construction of line: Line is a basic construction of all figures in geometry. To construct many figures in geometry we join two or more lines. In order to construct line use a ruler. Ruler is a rectangular object helps to measure the length of line in centimeter. Keep the ruler on the paper and move the pencil adjacent to the ruler on the longer side, our line is ready. Here is a diagram of line:

                      A---------------------B
Now, let’s see the construction of the triangle. Before moving to its construction let’s answer a question that what do you understand by triangle. A triangle is a closed three sided plane figure. You can easily construct a triangle with the help of ruler, compass and protractor. Since a triangle has three sides, so it also has three angles. to understand the geometry problems related to construction let's see few examples.
Example: Construct a triangle ABC in which AB = c units, BC = a units, CA = b units.
You can also take any mathematical units in place of variable a, b and c.
Steps for basic geometric construction of triangle are:
    


We are going to draw a triangle with sides a, b and c
1) Draw the line AB = c units with the help of a ruler.
2) Take a compass and measure b units using ruler.
3) With A as center, cut an arc above the line segment AB using compass.
4) Take a compass and measure ‘a’ units.
5) With B as center cut an arc above the line segment AB.
6) Both the arcs cut at a point, say C.
7) Join AC and BC. Now, ABC is the required triangle.
Example: construct atriangle with sides 5,5 and 5.
Construction:



There are several different types of triangles and you can easily construct them without facing any difficulty. If you know construction of one triangle then other can also be constructed.
My dear friends if you love dealing with shapes then no one can beat you in this game of shapes. With a bit concentration and efforts you can become master of the geometry.
In next post we will talk on Parallelism in Grade V. For more information on syllabus of economics for ICSE class 12, you can visit our website

Equations in Grade V

Hello friends as you all know grade V algebra is part of algebra 1, which is the very first step towards the learning of algebra (take help of algebra calculator also). In the previous articles we have learnt several different topics of algebra that you study in grade v. Grade v is generally the last class of primary group. In this article we will discuss the last topic of grade V algebra.  Today I will make you familiar with the interesting algebra topics one is equations and other is inequalities. Equation and inequalities are the basic of algebra and whole algebra moves around both the topics. Not only in grade V but also in higher grades you will learn both the topics.
Equations are defined as the two mathematical statements that are joined together with an equal to symbol. Equal symbol is the main sign by which you can easily identify the equation. In equation we deal with numbers, variables, constant and mathematical operators along with equal to symbol (=). There are several different types of equations which you learn when you move to different grades. Whenever we have to solve any equation, first of all we always try to isolate the variables, so that we can easily and simply get the solution of the problem. Equations are even used when we solve complex words problems also, as it is hard to understand the word problem and solve them. So first we try to take the word problem in form of equations and then put the valid method on the given equation and find the answer or solution of the problem.
Now move towards the principle that we use while solving equations,
1. The addition principle: according to this principle you can say that when a = b,
a + c = b + c for any number c.
Here is an example so that my students can easily understand this concept,
Solve: a + 6 = - 15
Using the above mentioned principle add – 6 to both the sides and try to find the value of the variable.
a + 6 – 6 = - 15 – 6,
The variable is now isolated,
 Thus,  a = - 21.
This is all about the addition principle.
2. The next principle is called as multiplication principle. In this principle is if a = b. and c is any number,
a * c = b * c. this principle is also used to help to isolate the variable that you are asked to solve or whose value you have to calculate.
Example: solve 4p = 9,
Using the multiplication principle we can easily the problem as:
Multiply both the sides of the equation by (1/4)
So doing this we get,
(1/4). 4x = ( ¼) . 9
By doing this we have isolated the  
      x = (9/4)
Also, be aware of problems where you might need to use both of these principles together.
Now have an example showing both the above described properties i.e. addition principle and the multiplication principle.
Example: solve the given equation and find the value of x?
3x - 4 = 13
Solution: first Use the Addition Principle to simplify the equation,
add 4 to each side.
 3x - 4 + 4 = 13 + 4  
 After simplifying, 3x = 17.
Now, use the multiplication principle and get the final answer or value of the variable,
Using the multiplication principle we get,
multiply each side by (1/3).  
  (1/3)3x = (1/3)17
  After simplification, the variable is isolated       
   x = (17/3).
Here are few more examples of equations so that you can easily grasp the concept of how to solve equations.
example: x + 2 = 4,
solution, apply addition principle, on doing so we get,
x+2 -2 = 4 - 2,
x = 2, thus variable x = 2.
 example: 2x + 4 = 8,
solution: 2x + 4 -4 = 8 -4,
2x = 4,
multiply by 1/2,
1/2 * 2x = 1/2 * 4,
x = 2,
thus we use both addition and multiplication principle and get the naswer of the variable as 2.
Example
Solve the equation for the variable x: x- 20 = 30
Solution:
x - 20 = 30
Add 20 on both sides of the equation
x – 20 + 20 = 30 + 20
x = 50
So, the answer is y = 50.
example:
Solve the equation for the variable x: (q/3) + 40 = 30
Solution:
(q / 3) + 40 = 30
Subtract 40 on both sides of the equation
(q / 3) + 40 - 40 = 30 - 40
(q / 3) = -10
Multiply 3 on both sides of the equation
(q / 3) * 3 = -10 * 3
q=-30
So, the answer is 30.
Now, move to the next important topic that we will learn today i.e. inequalities. The term inequality means the mathematical phrases are not joined with help of equal to symbol. To describe any inequality we always take the inequalities symbol. Generally we have four types of inequality symbol,
> : greater than,
<Less than,
<= less than equal to and the last is,
>= greater than equal to,
Whenever you get these types of symbols understand that the given expression shows the inequality and whenever you get the equal to symbol then understand that it is an equation.
Multiplied or divided by the same number on both side of the inequality but if we divide or multiply by a negative number, we must reverse the inequality sign. Let’s have few example of inequalities to get the concept of how to solve the inequalities problem.
Example:
Solve the inequality: 8y + 5 < 6y +7.
Solution:
We have, 8y + 5 < 6y +7
Subtract 6y on both sides of the equation
8y – 6y + 5 < 6y + 7 – 6y
2y + 5 < 7
Subtract 5 on both sides of the equation
2y+ 5 – 5 < 7 – 5
2y < 2
Divide by 2 on both sides of the equation
y< 1
So, all the numbers are lesser than 1.
Hence, the solution set is (-infinity, 1).
Example:
Solve the inequality: -2p – 8 < 6
Solution:
-2p-8<6
Add 8 on both sides of the equation
-2p - 8 + 8 <6 + 8
-2p < 14
Divide by-2 on both sides of the equation and the inequality sign is to be reversed.
p > -7
So, all the real numbers which are greater than -7. Hence, the solution set is (-7, infinity).
Solving linear inequalities is almost exactly like solving linear equations
Solve x + 3 < 0.
If they'd given me "x + 3 = 0", I'd have known how to solve: I would have subtracted 3 from both sides. I can do the same thing here:
X<-3
Then the solution is:
x < –3.
Inequalities problem may have infinite number of solutions. we get the solution of inequalities only when we have true statement. Solving an inequality is simple due to the movement of number and variable from one side to other. Whenever you solve linear inequalities we flip the the inequality sign and simply solve the problem and get  all possible solution of the problem.
This is all about the equations and inequalities. Friends! today we have finished all the algebra topics of grade V Tamilnadu education board that you study in this grade. In the next coming article we will focus on the remaining branches of Grade V mathematics that includes, geometry, number system, and many other branches. Students if you still have any problem In any of the topic that I taught then you can ask your problems and queries to me. Mathematics is that subject which needs lots of practice and if you do practice on daily basis then you can  solve all the different types of math problems and become master of the subject. Try to solve all the problems of mathematics daily and clear all your doubts with my help, or your teachers. To become master of subject you need to practice different topics daily. If you do so then no one can beat you in such a wonderful subject and you will get good grades.
In upcoming posts we will discuss about Math Blog on Grade V. Visit our website for information on integral calculator

Patterns and Relationships in Grade V

Hello friends! Today, you will learn about an interesting math topic which you will use throughout mathematics.  Grade V of Maharashtra state board, is the basic class in which students learn lots of topics that will be used throughout their math career. Grade V is considered as the primary grade and students learn the basic of multiple things and as they move to higher classes they implement the concepts on different types of problems.  In the anterior articles we have learnt different topics of the grade V that includes relationship between data, Prime and composite numbers, Variables, expressions, graphs, equations to solve problems and linear functions. In this section I make you aware with the other concepts of the algebra that includes: Solving one-step equations and Patterns and relationships. You can also take help of differential equations tutor.
First start with solving one step equations. In this you will learn how to solve equations. Afore, we move to this topic let’s have a brief idea of what equation is? Equation is the way to represent the mathematical numbers with different operators in a proper way and in this representation an equal to symbol is must which shows the equality between two mathematical statements. In the primary grade you must clear all your doubts so that in future you will not face any problem in the topics. Many students fear from this wonderful language as in early classes they don’t understand different topics properly and their concepts remain unclear. So kids try to overcome your doubts at the same time when they occur. Ok, now, come back to topic, in algebra you learn different types of equations, like linear equations, constant equations, equations with different variables, quadratic equations and many others.  You will all learn all these types of equation in the antecedent article.  Let’s start with the one step linear equation; a linear equation is an algebraic equation in which each term is either a constant or the product of constant and a single variable. Linear equation may possess one or more than one variable. The standard form of one step linear equation in one variable is given as: ax + b = c. the second type of linear equation is with two variables and its standard form is given as:  x + by = c.
In both the equations i.e. one step linear equation with one variable and one step linear equation with two variables ‘a’,’b’, and ’c’ are defined as the constant. Whenever we perform addition, subtraction, multiplication, or division of any number on both the side of the equation, the equality symbol (=) of the equation does not change. Now, move towards the example of the one step linear equation problems and see how to solve these types of problems with easy method.
Example:  x + 10 = 18,
Solution:  Solution of this problem is very simple let’s see the step used while solving the problems and so feel how simple it is.
X + 10 = 18,
Now, subtract 10 on both the sides of the equation, on doing this we get,
x + 10 -10 = 18 -10,
x = 8
So, the answer is x =8. In this you see how to solve the one step equations, solving one step equation is simply the moment of the numbers and we have to perform simple operations on them.
Next example:
a – 15 = 6,
Solution:  a – 15 = 6, in this simple example add 15 on both the side, you must be thinking that in above equation we subtract the number and in this we are adding the number why?  We perform the addition and subtraction operation on the basis of the problem, if in problems we have negative sign after the variable then we perform addition operation and we add that numeric value which is written after the symbol on both the sides. And if the add sign is present then perform minus operation.
This is we have subtraction sign so we add 15 on both the sides, on doing this we get,
    a – 15 + 15 = 6 +15,
a = 21,
Thus value of variable ‘a’ is equal to 21.
Now, a bit complex example of the same problem, perform one step solving operation on given equation:
4x = 28,
In this divide both the side with the coefficient of x, in this problem the coefficient of x is 4 so divide both sides with 4, this will give result as:
4x/4 = 28/4,
4 will get cancelled with4 on LHS and on RHS 28 is divided by 4,
x = 28/4,
x= 7
Thus variable x = 7 and this is the final answer.
Example: solve the one step linear equation for the variable a:
a/5 = -1,
In this equation, we multiply both the sides of the equation with 5 as:
(a/5) x 5 = -1 x 5,
In this, on LHS 5 will get cancel with 5 and on right hand side we will multiple 5 with -1.
a = -5, this is the final answer of the problem.
This is all about the how to solve one step equations. Using these methods you can easily solve these types of problems.
Now, we move to the next topic of today, in this part of the article we will discuss about Patterns and relationships. In mathematics we mainly deal with different types of number patterns. The patterns can be in the form of numbers or words.  Math is especially useful when it helps you predict, and number patterns are all about the prediction.  Let’s see few common examples of number patterns like number pattern, figure pattern, etc.  Let’s have few examples of the same. 2,4,6,8,10,12? In this series each number is increasing by sequence 2 so last numbers will be 12 + 2 = 14, and the other number of the sequence can easily be determined by adding the common difference.
Solve the following problem of mathematical pattern given below. Look the following number of sequence and calculate the value of unknowns?
Example: 15 22 29 36 43 X 57 64 71 78 85 Y
Solution: 15 22 29 36 43 X 57 64 71 78 85 Y
 In this sequence number is increasing by +7 or there is a difference of 7 in all the terms,
The previous number of X is 43 so X will be 43+7, X=50
The previous number of Y is 85 so Y will be 85+7, Y=92.
In this way we see how to determine the number pattern.
Example:  determine the number pattern and find the value of A and B?
85 79 73 67 61 55 49 43 A 31 25 B
Solution: 85 79 73 67 61 55 49 43 A 31 25 B
In this sequence numbers are decreasing by 6. To calculate the value of of A and B simply subtract 6 from the previous number of A and so on.
The previous number of A is 43 so A will be 43-6, A=37
The previous number of B is 25 so B will be 25-6,B=19
Now, we see the example of intermediate pattern, in this you learn how to understand that the given problem has intermediate pattern and how to solve them.
Example: The given information value of the table below explains numbers positioned into groups I, II, III, IV, V and VI. In which grouping would the following numbers belong?
a) 32
b) 33
c) 34

I	1	7	13	19	25
II	2	8	14	20	26
III	3	9	15	21	27
IV	4	10	16	22	28
V	5	11	17	23	29
VI	6	12	18	24	30

Solution: In this pattern the remains when the number is divided by 6 determine the collection.

1. 26 + 6 = 32 remainder 3 (Group II)
   b) 27 + 6 = 33 remainder 3 (Group III)
   c) 28+ 6 = 34 remainder 5 (Group IV)

In this way you can easily solve the intermediate pattern.
Now, here is an example of advance pattern. A number of students were at a networking meeting. Every student exchanges his record with each additional student who were there.
If there were 11students, how many students’ records were exchanged?
Solution: 10+9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 55 exchanges
55 × 2 = 110 records
If there were 11students, 110 records were exchanged.
In this way you can easily understand the different mathematical patterns present in different forms. Apart from this you will also deal with even number pattern, odd number, prime number, skip number patterns, before and after patterns and many more. Pattern is the simple topic which only needs concentration to solve the problem once you understand the type of the pattern you can easily calculate the value of unknowns or nth terms. If you do practice of different types of number patterns then you can easily differentiate the type of patterns simply by analyzing the problem.
In next post we will talk on Equations in Grade V. For more information on standard deviation calculator, you can visit our website

Linear Functions in Grade V

Hi my dear friends! Once again I am here as math problem solver to solve you queries. In this article we will focus on the algebra topic of grade V. In the previous articles you learn relationship between data, Prime and composite numbers and variables, expression and graphs. Now, we move to the next topic of the same Grade in Algebra section that is how to use equations to solve several mathematical problems and graphing linear functions.  Before we move to, how to use equation to solve problems first focus on equations and its different types.  Equation is simply a combination of one or more terms that are joined by different operators and one most important operator that defines equation is called as equal to (=) symbol.  Equation may contain numerical, alphanumerical, expression, etc.  Equation is the simple form of representing mathematical statement and they are joined by an equal to sign.

Now, after brief introduction of equations let’s switch to the different forms of equations:-

1. The very first equation is that which have solution. In these types of equations we can find the value of different  variables, which are present in equations  like  x, y, z. let’s have its example, 

5a + b = 12, ….(1)

7a – 2b = 21…..(2)

As in these equations we are having two variables so, two equations are required in order to calculate the value of the variables. To solve such type of equations we can easily use the elimination or substitution method. 

Like in the above equation we can use elimination method, but for this we have to make the either value of ‘a’ or ‘b’ same in both the equations. in order to take the value of any of the variable same in both the equations simply multiply the equation one with 2 so that we can get the value of b same in both the equations. 

=>(5a + b) x 2 = 12 x 2, ………(3)

 =>7a – 2b = 21  …………(4),

10a + 2b = 24, 

7a – 2b = 21, 

Now, both the terms of’ b’ are same and having opposite side so we can simply add both the equations. On doing so, we get,  

13a = 45, 

So, a = 45/13, 

If we put the value of a in any of the above equation, we get the solution of the problem or we can say we get value of both the unknowns, which are commonly called as variables.  Put value of a in equation one and we get value of b as:

5 x (45/13) – b = 12, 

-b = (12 x 13) / (5 x 45), 

-b = 156 / 225, 

b = -156 /225. 

As I mentioned here that equation with solution, need some method to get the solution of several problems. we can use the following methods in order to get the solution of equations:-

a) Elimination method.  In this we find the solution of the equation in such a way that we try to eliminate any of the variable and by finding the value of one we replace its value and find the value of the other variables. 

b) Substitution methods: replace the value of the variable with some numeric value.  

c) Graphing method in this we represent the equation on graph and get the solution on graph. 

d) Trial and error method: in this method we find the solution of problems by fixing things, or by obtaining knowledge

e) Taylor method: A Taylor series method is of general applicability and it is the standard to which we can compare the accuracy of the various numerical methods for solving an I.V.P. 

f) Numerical method:  in this we do study of algorithms that use numerical approximation for the solution of the problems of mathematical analysis.

g) Solving equations using inverse functions: in this we use to solve an equation in order to find what values fulfill the condition stated in the form of an equation.

Generally we use the above two methods to solve the problem. In Grade V you learn only these two methods of solving the equation. The other methods are used to solve complex equations and you learn these methods in senior grades.

Now, move to the next type of equation i.e. equation without solution these type of equation have no solution that means we cannot determine the value of the variables. 

Let’s see an example of this, that what we mean by no solution problems, 

0 = -2, 0 = 12, 7=8

Examples: 5x + 4 -7x = 6x +7 – 8x – 5

Step:1. 4 + 5x – 7x = 6x – 8x + 7 – 5

Step:2. 4 – 2x = -2x + 2

Step:3. 2x – 2x = 2 – 4

Step: 4. 0 = -2. 

The other type of equation includes: 

Linear equation, Radical equations, constant equations, quadratic equation, equations with different variables and exponential equations. Let’s have a gist of all the different types of equations, start with the very first type of equations, 

a) Linear Equation: this is the most common type of equation which plays a vital role in mathematics. A linear equation is similar to an algebraic equation. The linear equations standard form is given as: 

y = mx +c, 

In this equation, m is the slope of the line and b is defined as the y intercept. Example of linear equation are: x= 3y + 15, 

X + y = 20, and other such type of examples. 

b) Radical equations: This type of equations defines the fractional exponent over variables. Fractional exponent is one of the ways to represent the radical terms or roots.   

Example: y + root 14 = 67, 

Root x + 5 = -9, 

c) Constant equation:  In the constant type of equation variable value cannot be changed. For example: x + 5 = 0,  2a + 6 = 7 . 

d) Quadratic equation: An equation which possess one or more terms but the higher degree of the equation is two. The degree is neither less than two not greater than that. The standard form of the quadratic equation is given as: 

ax² + bx + c =0. Let’s see few example of the quadratic equations,

1) 4a² + 6b - 89 = 0.
2) 4z² + 44z + 14 =0.
3) 5b² – 5b = 16.

e) equation with different types of different type of variables,

 1) Equation with one type of variables: The equations which possess only one variable is known as one type variable equation. Such as:

1.) 11x + 9 = 14

2.) 5p - 4 = 0

3) 6a = 6

2) equation with two different types of variables: in this equation we have two variable like x and y., a and b, etc. example of two types of variable: 

7a + 76b = 12

2.) 8p – 8q = 74

3) 34a + 36b - 72 = 0.

3) Equation with three kinds of variables: The equation which has only three types of variable is known as equation with three types of variables. Like a, b and c are present in the same equation or other such type of variables may also be present.

Examples: a.) 52x + 52y - 22z = 72

a.) 13a - 62b + 23c = 34

c) 1p + 22q -72r + 12 = 0.

f) Exponential equations: This type of equation is somewhat similar to exponents and they contain the powers in the equations. here are few examples of such type of equations that includes: 

a^b Here "a" is base and "b" is exponent.

Here, "a" multiplies "b" times.

2.) 4² Here 4 is base and 2 is exponent.

Here, 4 multiply 2 times.

(4)(4) = 16.

g) Differential equations: you learn this type of equation in higher classes. 

After this, now move to the other topic of today that we will study. After the equations to solve problems let's switch gear towards the Linear functions. What do you mean by the term linear equation? A polynomial function of single degree is called as the linear functions.  In this, we related dependent variables with another independent variable in a simple manner. If we have any mathematical equation in which there is no independent variable that is raised to a power which is greater than one, then we will get a straight line if we trace a graph of the simple linear function with one independent variable like y = mx + c. and you all know that this is the standard form of linear equation so it must give a straight line graph. 

Let’s move on the different form of the linear functions. To define linear function f with the first degree equation: f = ( X, Y)/ Y = mx + b where m and b are constants, x and y is called a linear functions. The function derives a straight line while graphing.

Mainly, three type of linear functions are defined and they are  given as:

1. Slope-Intercept Form 

 y = mx +b.

2. Point Slope Form 

m = (y - y1) / ( x – x1).

3. General Form is given as:

 Ax + By + C = 0.

Do practice of the entire concept daily and become the master of the subject.

In upcoming posts we will discuss about Patterns and Relationships in Grade V. Visit our website for information on 12th biology syllabus Maharashtra board

Prime Numbers in Grade V

Hello friends, today in math help session, we will learn about the few interesting topics of Grade V. algebra 1 (also you can play number sets algebra 1 worksheets) is taught to students of grade V and in this we learn several interesting topics. As you all know the building block of anything must be strong. If we have strong base then you can set up the strong building. The same case impels with mathematics if your basic concepts are good then no one can defeat you in the this subject. Math is all game of concepts and once you come up with all the concepts you become the master of the subject. In this article we will talk about the few interesting topics of mathematics that you study in Grade V. Let’s start with the very first topic that is, relationship between data. In this students learn how to determine the relation between the different information given in any problem.

What do you understand by Prime Numbers and Composite numbers? Start with prime numbers; it is defined as a number that can be evenly divided only by one and number itself. The other condition for this is that the number must be whole number and greater than one. In other words we can also define the prime number as a whole number that has only two factors in which one is number itself and other is one. On the other side a composite number is that which has other factors also in addition to one and itself. The two numbers zero and one are neither considered as prime number nor as composite number. Zero and one are out of the family of prime and composite numbers. All Even numbers are divisible by two and so set of all the even numbers greater than two. Composite numbers are that numbers which end with five and zero are divisible by five. The prime numbers between 2 and 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.
A positive integer is a composite number if it has a positive divisor other than one or itself. It can also be explained as any positive integer than one that is not on group of prime numbers. In mathematical language n>0 is an integer and there are integers 1< a, b<n in such a way that n = a X b, then ‘n’ is composite number. So, according to definition of prime numbers and composite number, every integer greater than one is either a prime number or a composite number.


For instance the number 14 is a composite number. How? Are you thinking this then relax I will explain how 14 is be a composite number, 14 is having one and itself as its factor. Apart from this, it has other factors also, 14 can also be written as: 7 X 2. The number 14 is now having four factord including 1, 2, 7 and 14 so we can easily say that 14 is a composite number. Now who will tell me what is 2? Ya friends, 2 is a prime number because it has only two factors one and itself. So, 2 is a prime number.

Now, take few more examples of composite and prime numbers so that you can easily understand the concept of the problem. Now, what is 5 a prime number or a composite number? 5 is a prime number because it has two factors only that includes: one and number itself. And in composite more than these factors should be present. Now one more example of this, is 25 a prime number or composite number? As 25 can be factored as 25 = 5 X 5. The 25 is having more than two factors so it is considered as composite number not a prime number. The number 25 is having 1, 25 and 5 as its factor, which is satisfying the condition of composite number.

Now, move to next topic that is “variable”, it is a “symbol” or “name” that stands for a value. For example: a + b, here ‘a’ and ‘b’ both are variables. In other terms we can define the same variable as a value that may change within the scope of a given problem or set of operations. In opposite of this a constant is used, which defines a constant value. A constant is a value that remains unchanged, in unknown and undetermined terms. Both these concepts are fundamental to many areas of mathematics and its different applications. Students let’s clear the example with help of previous studies that you had done. In the primary classes when teacher asks you to solve different questions of finding the unknown, what you use to do? You try to find the unknown value by applying different operations that are defined in the problem. Like, _+ 4 = 8,
In this problem you use to calculate the value of blank space by changing the position of constants like,
_ = 8 – 4,
_ = 4,
Thus in blank place we have to put 4, in order to get the answer,
4 + 4 = 8.
In the same way we use to solve the problems involving variables. In grade V the blank space is replaced with help of variables. The variables can easily be used in place of numeric value. In the same problem variable can be put as: x + 4 = 8,
In this blank is taken by variable x, and we can solve this same as of above problem.
Take constants on one side and variables on the other side. Generally, we use to place variables on left side and constants on right side. Whenever we change the position of constants and variables we used to change the sign of the constant and variables. Like if on side side any number is positive than on left side it is negative. In above example:
X + 4 = 8, take 4 on the left side and when we take 4 on other side we have to change the symbol of the 4 here it is positive on the other side it is negative.
X = 8 -4,
X = 4. Thus answer is 4. Or value of variable is 4. Now, let’s see few more examples of the same problem, like
2x + 4 = 14 – 4x,
In this problem we have one variable x, but it is defined on both the sides, so take the x values one side and constants on the other side of the equal sign. On doing so we get,
2x + 4x = 14- 4,
6x = 10,
X = 10/6,
X = 5/3
In this the value of variable x is equal to 5/3. One more example of the same type problem.
X + 2x + 3x – 4 + 8 – 5 = 0 in this, problem all the terms are given on the same side, no need to take tension follow the same strategy that I have explained in this article, i.e. of taking constants on one side and variables on the other side of the equal sign.
X + 2x + 3x = 5 +4 – 8,
6x = 9 -8,
6x = 1
And, x = 1/6. In this way you can simply calculate the value of the variable or variables by simply moving the numbers and constants from one side to other and performing operations on them.
Now, move to the other important topic of grade V i.e graphs. Graphs are the simple way of representation of data with the help of graph you and easily place the data on the graph and the other person can easily understand the problem. In the graph we have two axes one is defined as x- axis and other is defined as y- axis. The horizontal line is the x- axis and the vertical line is defined as y- axis. Whenever we have to plot the values we place the values on both the axes according to the requirement. Usually we divide the graph in 4 quadrants, the two are of x and two y. first is + x quadrant, next is + y quadrant, third is –x and the last is – y. With the help of graph you can easily understand the problem.
In grade V students learn the graphs of data management and probability, geometry and spatial geometry, number sense and numeration, pattering and algebra.
Kids it is quite difficult to draw the graph here, but I have given you an overview which will help you while solving this type of problems. In short I can only say that graph representation is the best way to solve any problem as in this we can easily determine the data that what is given to us and what we have to calculate.
This is all about all the three topics from my side, if you face any problem and you can ask your problems and I am here to answer all your queries and to help you in learning mathematics.

In upcoming posts we will discuss about Linear Functions in Grade V. Visit our website for information on 12th biology Maharashtra board syllabus

Syllabus of Grade Vth

Present syllabus of math of any class includes at least a fraction of every mathematical branch. Higher classes includes detailed study of every branch but that time nothing looks pretty newer to students because in their earlier classes they are already introduced with almost every math branch. Today in this article we are going to elaborate the content of Vth grade mathematics. Important thing of this grade is that in this earlier stage of study the students get to learn the basics of three major branches of mathematics that are Algebra, Geometry and Statistics. Not only these but also some other topics like mathematical reasoning are embedded in grade V math content to increase student's analytical quality for solving various kind of math queries.

Major topics of grade V math are as Place value and number sense, Fractions and mixed numbers, Geometry, Add and subtract fractions, Data, charts and graphs, Patterns, and Algebra Word Problems"> Algebra Word Problems (also read on rational expression word problems). All these are categorized in six units of syllabus. These units are as Algebra, Geometry, measurement, number and operations, probability and statistics, and Mathematical reasoning.

Let us start with first unit of grade V maths, Algebra. Introduction of Algebra is also done in previous grade but Algebra is one of the vast branch of math that's why to make you more informative about it and its problems  solution a procedure, this grade is also embellished with some important points of algebra. 7 newer terms are here this time to deal with like Relationship between data, Prime and composite numbers, Variables, expressions, graphs and equations to solve problems, Linear functions, Solving one-step equations, Patterns and relationships, and Equations and inequalities. Important terms like variables, integer co-efficient, and constants that are required to form any Algebraic equation are defined in grade 4 and here students have to use these to form an algebraic expression. This is not going to be hard for students because only linear functions are to be formed in this grade. Apart from this, a different topic that is Inequalities is also included in this unit. When we individually learn inequality concept then it seems simple but when eventually it is included with linear equations that time it causes a bit difficulty because explanation of the equation now can't be done in similar way.

Now let us move to next unit of grade V syllabus that is Geometry. In comparison of other units of this branch, Geometry content is on the heavier side with lots of sketching techniques of linear mathematical shapes. To know what exactly you guys has to face in this unit, let us go through its content which includes Simple geometric constructions, Parallelism, perpendicularity, congruence, Points on a coordinate grid, Perimeter using grids, Sketching transformations, Sketching transformations of congruent figures, Problems on sum of angles, Modeling 2-d and 3-d objects, Polygons, triangles, quadrilaterals, Lines of symmetry, and Geometric concepts. Most of the topics of its content are related to Sketching and to perform it, students have to be pretty accurate with their measurement and perimeters. Query related to Angles requires the knowledge of basic geometry construction rules because without them angle determination is not easier for students. Once you get completed with the linear shape construction, the other task is to deal with lines symmetry and this is nicely defined in last chapter of Second unit of grade V syllabus.

After completion of two units of this grade math, students are very well aware of Algebra and geometry, but the third branch of mathematics that is included here requires some additional analytical skills and to develop those skills students has to go through 3rd and 4th unit that are Number and operations and Measurement.

Let us take each of them one by one and see what actually you need to learn in that. First start with measurement, as the name suggest it includes various techniques to measure quantities in different standard units and for this task an individual chapter as Unit Conversion is included in this grade. We know that there are several physical units and so the number of standard units automatically raises. Chapters included in this unit are Unit conversions, Measurement – problems, Temperature, elapsed time – problems, Direct/indirect, standard/non-standard units, and Estimates of measurements.

Once you get completed with Measurement the next step is deal with Number and its operations. This unit is stated in the middle of the grade V math syllabus and this is the most vast part of it because it includes total description of number presentation and all the possible operation that can be performed on those numbers. The order of topics is arranged in pretty refined manner that helps you to understand the whole scenario of Number system. Major content list of this unit includes Whole numbers- place value, Decimals - place value, Representation on a number line, Equivalent/improper fractions; mixed numbers, Compare and simplify fractions, Decimals, percents and fractions, Addition and subtraction, Common and prime factors (also try factoring calculator), exponents, Operations on fractions and mixed numbers, Estimate solutions, Multiplication problems, Division problems, Powers, repeated multiplication, LCM, GCF, ratios, Order of operations, Number systems, and Multiplication/division - inverse relationship. One thing for sure is that after completion of this unit you will definitely feel pretty confident in favor of your mathematics and analytical skills because every possible arithmetic operation implementation is defined in this unit.

Its time to make you known for the fourth branch of mathematics whose introduction is only included in this grade but as students like you, move into their upper classes that time problems of this branch will cause a definite hard work because of their uncertainty. Here only the basic terms, which are used to form statistics problems are placed in front of you and most important amongst them is Probability. Probability is defined for any event that is about to occur. Point is that, the solution of the probability query is a guess but for this also some standard applications are used, which are included in upper grade syllabus. Here students has to deal with topics like Possible outcomes, making predictions, Mean, median, mode, range, Collect/organize/graph data, and Comparison of data sets. These topics are only included to make students learn about the terms by which in actual probability queries are being resolved.

Apart from all these standard math branches, one more part of mathematics have its importance that is mathematical reasoning. When students pass out from their higher classes and go through some competition exams for further studies that time the role of mathematical reasoning is very important because a huge number of queries are related to reasoning in exams. But mathematical reasoning is only included in earlier grades so its merely required to learn it in proper way here. In grade V math syllabus few topics are included to help you in reasoning questions. These topics are as Mathematics in daily life, Steps in problem solving, Problem solving strategies, Tools to solve problems, Tools to record observations, Informal and mathematical language, Make generalizations, and Justify solutions.

While learning any of the math topic students need to understand one thing that only by learning the concepts the queries are not going to resolved easily. It will only happen when they practice and imply those learnt principles on various kind of mathematical queries.

To make it more easier for you there are various Online math tutoring websites that are providing Online math learning with several moderate options to make user more friendly with the tutor while having math lessons. The reason of success of these online services is their 24 x 7 hours provided assistance, so whenever you feel problem while doing your math homework and want somebody to help you instantly then just access the web and ease your math problems with the quality math solver guidance. Online math tutors who provide this marvelous service also avail options like live online chat, scheduled online math test, video conference, virtual learning and worksheets solving sessions. The access of this websites contents also looks easy because of very well categorization of every class content with respect to various mathematical branches.

In this article we have explored the whole grade V math syllabus with their require fundamental description, now its all up to you that how you deal with all these topics. But if any time students feel problem then a virtual online math tutor is always there for help him out. Students favor online math tutoring in present time because it is the way of giving lessons that suits there schedule also, for example student can set the daily schedule according to his appropriateness for having math lessons or also can randomly do that. Authority of having review of per-learned lesson is also in student's hand that helps him to recap anything he wants. Many things and ways are there to support students in their studies but they all need one thing from students side and that is his determination.

In upcoming posts we will discuss about Prime Numbers in Grade V. Visit our website for information on 12th physics syllabus Maharashtra board

Solve fifth grade algebra using PEMDAS

Friends, today I am going to discuss about algebra solver, fifth standard mathematics topics like variables, equations etc. Students may understand how to perform basic math functions like subtraction, addition, division, decimals etc. But another possibility is that students might not know how to put all the functions together to solve a complex equation. If students start doing tasks in random manner or in improper manner then students can end up with completely incorrect results or answers. Whenever students opt to sole equations, they just remember the mnemonic device that is “ M-DAS,” which refers to Maths, Division, Addition and Subtraction. (you can also play solving equations with variables on both sides worksheet to improve your skills)

Fifth grade mathematics topics like equations, expressions etc. consists of the following parts : addition, subtraction, multiplication and division, and along with decimals and fractions. Starting from the basic what we need to do is to understand the problem and what steps required to solve a given problem. Few of the ways are:

First way is: Convert all of your decimals to fractions or convert all of your fractions to decimals, if the equation comes to solve contains a mix of both. If students want to convert fractions to decimals, what he/she needs to do is simply divide the numerator by the denominator. While converting decimals to fractions what requires is, ignore any zeros on the far right for example ignore zero in the given value 6.40. Now make a fraction with all of the numbers in the decimal over a number corresponding to the last decimal. Now the final step is to represent fraction in terms of tenths if the last value or number of the fraction is in the tenth place, this will vary according to place of the last number. For example
6.50 can be represented as 65/10 in the fraction form.

Second method: The second way is to evaluate or solve all the multiplication and division tasks. What we need to do is to mention product or quotient in place of the multiplication or division part of the equation.

Lets take an example to elaborate the above statement in the mathematical manner. In the equation
4 x 10 + 4.4 / 0.4 - 3.6 - 5,
First multiply 4 x 10 which give us 40. Then divide 4.4 by 0.4, getting 11.
After you replace "4 x 10" with "40" and "4.4 / 0.4" with "11,"
Your equation should read: 50 + 11 - 3.6 - 4.

Third way: Question is how to perform all the addition tasks. The most suitable manner is to replace the addition task with the acquired sum. Let’s take the same above example, the above formed equation can be further simplified as we all know that 50 + 11 = 61, so replace 50 + 11 with 61. Now the equation becomes 61 – 3.6 - 4

Fourth way: now the final task is to perform all subtractions. If the equation consists of more than one subtraction task, move from left to right. In the above example, first solve and perform subtraction task that is 51 – 3.6 which give us 47.4. Then subtract 4 from 47.4 , getting the final number that is 42.4.
Following the same example, first perform the subtraction task: 61 - 3.6, which equals 57.4. Then subtract 5 from 57.4, getting the final number, 52.4.

Variables are generally used to explain the general situations or real time situations and they can also be used to solve problems that in anyway would be very difficult or even impossible to solve. Whenever we are going to solve algebraic expressions or any kind of word problems, we will see the use of these applications.

Till now we have done expressions, playing with fractions, doing basic mathematical operations like addition, subtraction, multiplication and division. Now moving towards I am going to discuss about fifth grade Linear equations. In fifth grade linear functions or equations, variables are raised to power one and the equation does not contain any variable in denominator, no variables to any power other than one and no variable with under root sign.

In linear equation what we are doing is to solve the equation or getting a value of variable let’s take “x”. Solve for x means to isolate x on one side of the equation and move everything else on the other side.
X = number
Here number is the desired value which satisfies the original equation. That is when the number is substituted for the value x, the equation is true.
Let’s take an example to understand it better: in the given equation 2x + 5 = 1 we need to calculate the value for x then what we need to do is: we just need to place all the constants on one side and variables on the other side:
2x = 1 -5
2x = -4
x = -2.
Here x = -2 is the solution as we can check it in following way : 2(-2) + 5 = 1 is a true statement. For any other number, the equation or statement would be failed or results in false. For confirmation, if we mention the value of x = 3, the equation would be 2(4) + 5 = 1, which is false.
Another important thing to understand is that not every equation will have a solution. For example
x + 2 = x + 4 has no solution. It can be explained as that there is no number that can be added to two and be the same quantity as when it is added to 4. If student opt to solve for x, he/she would end up with the false statement 2 = 4.

Now I am going to discuss about how to solve an equation. In order to solve equations and to verify solutions whatever you get, first priority is that you must know the order of operations. The following order is required: Named as PEMDAS or we can say that BODMAS(B = Bracket, O = Off)

P—parentheses is the first to solve
E—exponents (and roots) are the second to perform
M—multiplication is the third
D—division third (multiplication and division should be done together, working from left to right)
A—addition is the fourth operations to be done.
S—subtraction is the fourth (addition and subtraction should be done together, working from left to right)

Another important thing is to understand the basic operations required to solve an equation. When performing with fractions you should always think of numerators and denominators as being in parentheses.
Eighth grade equations can be solved in many ways, but the general method to solve a fifth grade equation will be :
First: Both the sides of equation need to be simplified
Second: Collect all terms with variables in them on one side of the equation and all non-variable terms on the other (this is done by adding/subtracting terms).
Third: Factor out the variable.
Fourth: Finally what is required is division. Divide both the sides of the equation by the variable's coefficient.

Let’s take an example to understand it better: 2(a – 3) + 7 = 5a – 8
2a – 6 + 7 = 5a – 8
2a + 1 = 5a – 8
1 = 3a – 8
3a = 9
a = 9/3
a = 3.

Another method to solve an equation for the unknown is that we need to use inverse operations which help us to isolate the variable. These inverse operations undo all the operations that have been done to the variable. This shows that inverse operations are basically used to move quantities across the equal signs.

Let’s take an example to understand it better: In the given equation: 4x = 8
Here x is multiplied by the 4, so to move 4 across the equal sign, what we need to do is to un-multiply the 4. Therefore what is required is to divide both the sides of the equation by 4 or we can say that we can multiply each side of the equation by 1/4. In the above equation 4 + x = 8, if we want to move 4 across the equal sign or opposite side then what we need to do is to un-add 4. It can be simply stated as subtract 4 from both the sides of the equation.
In simple mathematical manner we can say that whatever we added  must be subtracted and whatever we subtract must be added. Similarly whatever we multiplied be divided and what is divided must be multiplied.

Now moving forward we all are going to learn, How can we simplify Fractions and using the Associative Property to solve Linear Equations problems. What we need to perform, find the LCD (Lowest common division) of all fractions and multiply both the sides of the equation by this number. Then, distribute this quantity on each side of the equation. In next chapter we are going to elaborate it.

In upcoming posts we will discuss about Syllabus of Grade Vth. Visit our website for information on West Bengal council of higher secondary education syllabus