Math Blog on Probability and Statistics

Hello students, As a Tutor, I am going to discuss about Probability and Statistics. In mathematics, an average of a statistical data is value representation of entire data. Statistics deals with the collection, presentation, analysis and interpretation of numerical data. In other sense, statistics means data, the word data means information or set of given set in numerical figures in which we study mean, median and mode that are calculated on the set of data.
Some limitation of statistics
1.      Statistics deals with group and does not deal with individuals.
2.      Statistical laws are not precise. They are accurate on average only.
Now, we will discuss about Probability. Probability shows the uncertainty of occurrence of an event. Probability is used in many fields like :- commerce, science, whether forecasting etc.
Rule for probability: in mathematically, we have
Probability of an event A i.e. P(A) =a/b
Where a =number of favorable to the occurrence of A
b = total number of possible sample and
a-b = number of unfavorable to the occurrence of A.
We also notice that
P(A) =P( inverse of A) =(a/b)+(a-b)/a = 1 i.e. P(A) +P(not A) =1
Now, we take some examples for solving problem on probability.
Example 1:- a die is thrown once. Describe the sample space (s).1, 2, 3, 4, 5, 6
1.      What is the probability that the number ‘1’ turns up?
2.      What is the probability an odd number turns up?

Solution (1) :- the sample space : 1,2,3,4,5, 6
Since there are 6 equal parts likely number of probability of getting 1 is:
P(1) = number of events/total number of samples =1/6
Solution (2) :- let A=(an odd number) =1,3,5 so x(A) = 3
Probability of getting odd numbers= x(A)/x(s) =3/6 =1/6
                                                                                                 

In next post we will talk on grade V. For more information on biology syllabus for class 10 ICSE, you can visit our website

grade V

In this section we all are going to discuss about geometry help and lines of symmetry which are usually studied in grade V. Here I am going to tell you the best way of understanding these topics.Now let us start with basics about geometry:
Geometry is on the whole about the points, lines, angles, areas, volumes etc. And to learn it we should keep some points in our mind. A point is represented as a dot in a plane, a line is described as the collection of points, a line does not have any end point, a line segment is a part of line that has two end points, a ray is defined as a line which starts from a point and extends in a direction forever, when two rays start from same point then they form an angle between them, plane can be defined as a flat surface that extends forever. Triangle, circle, quadrilateral, polygons etc. are the examples of geometrical shapes.
Now let us talk in detail about Lines of symmetry. When an image or a figure is folded from the middle and if the half part is completely symmetric to the other half part or in other words one half part is mirror image of the other part then that figure or image is said to be symmetric. And when you unfold that figure or image you will see a line of crease, that line is known as line of symmetry. Let’s see lines of symmetry of some shapes.
Lines of symmetry of triangles:
In a triangle we can have 3, 1 or 0 number of lines of symmetry.
                          
Equilateral triangle ( having all sides and angles equal )
It has 3 lines of symmetry.
                     
Isosceles triangle ( having two sides and angles equal )
It has 1 line of symmetry
                
Scalene triangle ( having no sides and angles equal )
It has no lines of symmetry

Lines of symmetry of quadrilaterals:
There are many types of quadrilaterals

                 
Square ( having all sides and angles equal and also all angles are 90 degrees )
It has 4 lines of symmetry.
         
             
Rectangle ( having opposite sides equal and all angles are 90 degrees )
It has 2 lines of symmetry.

            
Irregular Quadrilateral
It has no lines of symmetry

                  
Kite
It has 1 line of symmetry.

                     
Rhombus ( having all sides equal in length )
It has 2 lines of symmetry.

Lines of symmetry of regular polygons:
In a regular polygon we have all sides and angles equal to each other.

                                       
Regular Pentagon ( having 5 sides )
It has 5 lines of symmetry

                 
Regular Hexagon ( having 6 sides )
It has 6 lines of symmetry

               
Regular Heptagon ( having 7 sides )
It has 7 lines of symmetry

                  
Regular Octagon ( having 8 sides )
It has 8 lines of symmetry

Lines of symmetry of circles:
A circle has infinite number of lines of symmetry and the lines of symmetry must be go through the radius of circle.

              

In upcoming posts we will discuss about Probability and Statistics. Visit our website for information on syllabus of economics for ICSE class 12

Number systems in Grade V

Welcome children! In earlier classes we have studied about Number systems. In Math Grade V of Karnataka state board sslc syllabus we will study more about them.
We know that all counting numbers are called natural numbers. But any time we need to measure some units like weight, length or capacity of any container, we usually start from 0.
This series of numbers starting from 0, 1, 2, 3... up to infinite is called a series of whole numbers.
So we can say that whole numbers are measuring numbers and natural numbers are counting numbers. Number system in math has a very important role to play in our life.
In fact our life revolves around the numbers

If we need to count the number of students in a class, or number of books in your bag we always start the counting by 1 not by zero (0).
 Now let us look at some common properties of numbers.
1. Zero (0) is called Additive Identity, which means if we add or subtract zero to any number, the result remains unchanged.
      E.g. 45 + 0 = 45 and 37 - 0 = 37
2. One (1) is called multiplicative identity, which means if we multiply or divide any number by 1, the result remains unchanged.
 E.g.: 65 * 1 = 65 and 24 / 1 =24
 3 . Both addition and multiplication satisfies closure property, which means if any two natural numbers or whole numbers are added or multiplied, the sum and the
        Product is also a natural number. E.g. 2  + 5 = 7. Here 2 and 5 are added to give 7.
        We can observe that 2 and 5 are natural numbers and the sum is also a natural number.
        Similarly  2  *  5 = 10. Here 2 and 5 are multiplied to give 7.
        We observe can that 2 and 5 are natural numbers and the product 10 is also a natural number

In next post we will talk on grade V. For more information on algebra 2, you can visit our website

Problems on sum of angles for Grade V

Hello kids, in this math solver blog, we will discuss about Problems on sum of angles for Math Grade V. Before, we move to the topic, it is necessary to know about the angles. An angle is created when two lines or two rays meet at a point. The rays are called the sides of the angle. Now I am going to tell you about the different types of Problems on sum of angles. The different angles are Central Angle, Complementary Angles, Congruent Angles, Corresponding Angles, Interior Angles and Exterior Angles. Let us talk about about these angles one by one. (also read on consecutive exterior angles)
Central Angle: - Central angle of a circle is formed by two lines (radius) and circle consists of arcs and central angles. The value of central angle is measured with the help of the arc length and the radius.
Complementary Angles: - If the sum of the two angles is 90⁰ they are called Complementary Angles and if the sum of two angles is 180⁰ than they are called supplementary angles. Consider an angle of 26⁰. Supplementary angle of 26⁰ is 154⁰ as 26⁰ + 154⁰ = 180⁰.
Congruent Angles: - if two angles have the equal measure then these two angles is said congruent. Angles play an extensive role in geometry. Most of geometric figures are classified based on their angles.



Corresponding Angles:-When two parallel lines cut by a straight line at different points then Corresponding Angles are formed.
Interior Angles: - Angle measures at the interior part of an enclosed shape are called as interior angle. That shapes play a vital part in geometry. Simply interior angles are the plane figure that is formed at the vertex, where two rays meet. Every shape in geometry possesses interior and exterior angles.
Exterior Angles:- Exterior Angles  is the angle between a side of a polygon and an adjacent side or any angle formed by line cutting across two other lines and located on the outside the lines. These are the angles some basic angles which are generally used for solving the angles problems.
Now I am going to tell you about Polygon and formulas for Sum of Angles. Usually polygon is a 2-D closed figure that consists of three or more than three line segments. The lines that shape a polygon are called its sides. The point where two successive sides of a polygon meet is called the vertex. The total space inside the boundary is called as the area of a polygon and the area is measured in terms of square unit.  Polygon area is usually calculated using the side length of a polygon. There are many types of polygons: Complex Polygon, Concave Polygon, Congruent Polygons, Convex Polygon, Irregular Polygon and Perimeter of a Polygon.

In upcoming posts we will discuss about Number systems in Grade V. Visit our website for information on CBSE 10th science syllabus

Order of Operations in Grade V

Hi Children! While doing mathematical operations and to get the correct answer for operations on rational numbers we need to learn proper order of the operators. In order to learn order of operations in math, we need to remember BODMAS taken from CBSE, where
B stands for Bracket
O stands for Of operator
D stands for Division
M stands for Multiplication
A stands for Addition
S stands for subtraction.
This means that first all the operations in the brackets are to be performed followed by operator "of", and then we check if there exist division operation, we perform division. Then we check the expression for multiplication, if there is a multiplication operator, and then we multiply. Then we check for addition in the expression and add the terms followed by subtraction to be done at the last.
Let us understand it more clearly through an example:
 Solve 20 - 2 * 10/2 + (6 - 2)
To solve the above expression we first look at the braces and solve as follows:
 (6 - 2) = 4, so the given expression becomes as:
   = 20 - 2 * 10/2 + 4
 Now we take into consideration the operation of division and perform 10 / 2
 We get 10 / 2 = 5; now put this value in the above expression we get:
   20 - 2 * 5 + 4
 Now next comes the turn of multiplication operator, we get:
  2 * 5 = 10,
 Similarly now we replace this value in the above expression, we get:
 = 20 - 10 + 4
 Now we add 4 to -10 and get 10 + 4 = -6
 = 20 -6
 = 14 Ans.
In this way various mathematical expressions can be solved by ordering operations. 

 

In next post we will talk on Problems on sum of angles for Grade V. For more information on linear equations, you can visit our website

Decimals and Place Values

Hello children, let us discuss about decimals in mathematics from CBSE sample papers.

Decimals numbers are commonly used in all walks of our life such as business, medicine, measurement, mass, unit, and currency. (also read on properties of decimal numbers)
Decimals are part of a type of numbers in mathematics called as mixed numbers. A mixed number is combination of whole number and decimal part values.
Place value: The value of a digit is determined by its position in a number which is called place value. Place value is used to indicate the position of number system.
The place values are called as following
1-one
  10 – Ten
  100 – hundred
 1000- Thousands
10000- Ten thousands
100000- hundred Thousands
1000000-million
10000000-ten million
100000000-hundred million
1000000000-billion



Place value of decimal point:
                                                     The following table is representing the place value of decimal point values.

10 = 101 Tens

1 Ones

. Decimal point

1/10 = 10-1 Tenths

1/100 = 10-2 Hundredths

1/1,000=10-3 Thousandths

1/10,000=10-4 Ten thousandths

 Here 10¹ represent the tens place value of whole number system.
10⁰ represent the ones place value of whole number system.
’.’ represents the decimal point number.
10^-1 represents the tenths place value of decimal number system
10^-2 represents hundredths place value of decimal number system
10^-3 represents thousandths place value of decimal number system
10^-4 represents ten thousandths place value of decimal number system.



Let’s see the example: find out decimal point value of this given number 12.768

Sol:  here we have given number 12.768

We start from 1 number
Here 1 represents the type of whole number its place value is tens then original number is 1*10=10
Now start with number 2
Here 2 represent the type of whole number its place value is ones then original number is 2*1=2
Decimal point is separates the whole number.
Third number 7 is represent the type of decimal number and its place value is tenths then original value of 7 is   7*0.1=0.7
Fourth number i6 is represent the type of decimal number and its place value hundredth then the original value of 6 is 6*0.01=0.06
Fifth number 8 is represent the type of decimal number and its place value thousandths then the original value of 8 is 8*0.001=0.008


Let’s see the above example in expanded form:
Sol: given number is 12.768
12.768=    12+ 7/10+6/100+8/1000
So, 12.768 has one tens, two unit, seven tenths, six hundredth, eight thousandths


Let’s see the other example:
Ex: find the place value of this numbers: 456, 0.456,54
Sol:  let‘s see first number: 456
4 numbers is hundred place
         5 number is tens place
      6 ones place

Now we see Second number: 0.456
4 number tenths place
5 number hundred’s place
6 number thousand’s place

See the third number: 54
5 number tens place
4 ones place

In upcoming posts we will discuss about Order of Operations in Grade V. Visit our website for information on algebra help

LCM, GCF, ratios and proportions

Previously we have discussed about rational expressions applications and now we are going to study about LCM and GCF  which stand for least common multiple and greatest common factor respectively. In icse text books of Grade V, we are going to study about LCM and GCF.

If we have two numbers and need to find LCM of the given numbers, then we first write the factors of the two numbers and then find the product of all the factors. We should remember that the factor occurring in both the list should be written only once. Let us use an example to make it clearer:

Find the LCM of 10 and 15.

First write the numbers as the product of prime factors separately.

 10 = 1 * 2 * 5

15 = 1 * 3 * 5

5 and 1 appear in both set of prime factors, so they will be written only once while finding LCM.

 So LCM of 10 and 15 = 1 * 5 * 2 * 3

                                  = 30

 Now to find GCF, first find the prime factorization of the numbers whose GCF is to be calculated.

Then take the factors which exist in both the lists and find their product.

Thus we will get GCF. (Know more about proportions in broad manner here,)

E.g. Find the GCF of 10 and 15.

First write the numbers as the product of prime factors separately.

 10 = 1 * 2 * 5

15 = 1 * 3 * 5

 5 and 1 appear in both set of prime factors.

 So GCF of 10 and 15 = 1 * 5

The ratio of two quantities with same unit or same kind is the fraction of one quantity over another, we can also express in lowest term. The two terms are in proportion if we see that the lowest form of the two ratios gives the same result.

e.g. 5 :50 and 1: 10 are the two ratios, to check these ratios are in proportion, we convert 5 : 50 to lowest term by dividing both numerator and denominator by 5 and get 1: 10 . So we observe the two given ratios are in proportion.

In the next blog we will discuss the topic of Order of Operations in Grade V and if anyone want to know about predictions then they can refer to Internet and text books for understanding it more precisely.

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