Powers and repeated multiplication in Grade V

Children we have already studied about the concept of how to solve a rational number, Now we will talk about repeated multiplications of any number and math question related to it.
Let us say 2 * 2 * 2. Here we observe that number 2 is multiplied 3 times.
So this expression can be written as 2 > 3. We call it 2 raised to the power 3. This method of multiplication is called the concept of powers and repeated multiplication and comes under CBSE Board Syllabus.
Suppose we need to find the value of x>n, it means x is to be multiplied n number of times.
So if we write 2> 2 = 2 * 2 = 4
            similarly 3> 2 = 3 * 3 = 9
                          4 > 2  = 4 * 4 = 16
 and if we write 3 > 4 , we call it 3 raised to the power 4
                               = 3 * 3 * 3 * 3
                               = 81
We should also remember while solving powers that any number raised to the power zero is always 1.
so 4> 0 = 1
      5> 0 = 1
and 0 raise to any number is always zero. i.e. 0 > 3 = 0 *0 *0 = 0
Now solve 3 >0  + 2> 0
        As we know  that   any number raised to the power zero is always  1,
so  3 > 0 = 1 and 2 > 0 = 1
Putting these values in the given problem we get
             3 >0  + 2> 0  = 1 + 1 = 2 Ans.
 Similarly solve: 4> 0 * 2 > 0
             As we know  that any number raised to the power zero is always 1,
so  4 > 0 = 1 and 2 > 0 = 1

Putting these values in the given problem we get
             4 >0   *  2> 0  = 1 *  1 = 1 Ans.
This is all about the Powers and repeated multiplication and if anyone want to know about Sampling errors then they can refer to Internet and text books for understanding it more precisely.Read more maths topics of different grades such as Decimals and Place Values in the next session here. 

Direct, Indirect, Standard, and Non-standard Units

Hello friends,Previously we have discussed about antiderivative of fractions and in today's session we all are going to discuss about one of the most interesting topic of mathematics, standard and non-standard units of measurement and how we measure these units in direct/indirect manner in our everyday life which comes under central board of secondary education books.
First of all we will discuss what is standard units of measurements and how to solve math word problems related to it?
We deal with many measurement issues in our day-to-day life like somebody asks us about our weight and height then we answer directly that my weight is 30 kg and my height is around 4 feet . Why we give our answer in kilogram and feet because kilogram is standard unit of mass  and feet is the standard unit to measure height. So, we can say that standard units are those units which are generally used in our everyday life. Some of the important standard units of measurement are as follows
length = meter (m)
weight = kilogram(kg)
Volume = liter (ltr)
Time = second(sec)
Height = feet(ft)
Now further we discuss what is non standard unit of measurement?
Non standard units are those units which are not generally used in our daily life like
antique, ancient, archaic units like fathoms, acres, cubits, miles, stones, hundredweights, pounds, pecks, bushels, gills, pints, quarts, gallons .
Actually standard and non -standard units of measurement are related to each other like length conversion of units
1 myriameter = 10 kilometer
1 kilometer = 10 hectometer
1 hectometer = 10 decameter
1 decameter = 10 meter
1 meter = 10 decimeter
1 decimeter = 10 centimeter
1 centimeter = 10 millimeter
1 foot = 12 inch
1 inch = 1000 mils
and next chart describes conversion of units in weight
1 metric ton = 1000 kilogram
1 short ton = 2000 pounds
1 stone = 14 pounds
1 kilogram = 2.2 pounds
1 kilogram = 1000 grams
These are some conversion charts which tells us about connection between standard and non - standard units of measurement.
Now we are going to discuss our next topic direct/indirect measurement of units
When we do measurement of unit with help of measurement devices like thermometer for measuring temperature, scale to measuring length and weight machine to measure weight then this type of measurement is called as a direct measurement of unit like we measure marble with the help of our measurement machine and we get measurement result like weight of marble is 5kg , length is 20 meter and height is 2 feet.
When direct measurement is not possible then we use indirect measurement, where Indirect measurement is a technique that uses proportions between similar figures to find a measurement, like we have two similar figures of tree, one is big tree and other tree is small and we have to find out height of tree, then here we use proportional technique between both similar tree figure to measure the height of big tree.

3/h = 6/24 write a proportion
6h = 3*24 find cross products
6h = 72 solve equation
h = 12
So the tree is 12 ft tall.
This example shows how indirect measurement is done with the help of proportions. This is all about direct / indirect measurement of units.
So in this session we learn about standard, non-standard units of measurement and direct and indirect measurement of units. I hope you learn many things about measurement of units from this session and if anyone want to know about equally likely events then they can refer to Internet and text books for understanding it more precisely.Read more maths topics of different grades such as Problems on sum of angles for Grade V in the next session here.

Unit Conversion and Measurement in Grade V

Hi friends, Previously we have discussed about number sense worksheets and today's session is here for measurement and unit conversion in grade V from Maharashtra Board Syllabus. While studying measurement, we simply talk about some standard measuring units and will know how to solve math questions based on it. In earlier times people used to measure the length with palms, feet. but the problem faced were that the palms and the feet of the kids varied from that of adults.
Let us imagine a situation, a man asked his son to bring the rope of length of 10 palms from the market. when he returned back with the rope, father took the rope and measured it. father got annoyed, did you know why? Yes, the rope he received was only 6 palms long. No children, it was not the fault of the son, but simply the difference that existed as the measure of the palm of the son and his father was different.
To overcome such problems of measurements, the standard units of measurements were developed. To do any of the mathematical calculations on the objects, it must be remembered that the units are same. It means that addition, subtraction, multiplication, and division can be done on the lengths only if they are having same units.
If the units are not same we convert one unit to another. This process of converting one unit to another is called Unit conversion. Unit conversion is very important role in mathematics. The standard unit of measurement is as follows (want to Learn more about Unit Conversion,click here),
For length we use Meter
For weight we use Kilograms
For  capacity we use Liter
The hierarchy of units are as follows:
Milli
Centi
Deci
UNIT
Deca
Hecto
Kilo
The upper one i.e. milli is the smallest and the last appearing unit i.e. kilo is the largest one. When we have to convert smaller unit to the bigger unit, we do division and when we have to convert the bigger unit to smaller unit, we do multiplication. Let us understand it more clearly by an example:
To change 24 millimeter to centimeter we divide 24 by 10
   = 24/ 10 cm
= 2.4 cm
Similarly  to convert 125 millimeter to decimeter we divide 125 by 100
 = 125 / 100 decimeter
= 1.25 decimeter
In the same way to change centimeter to millimeter  we multiply by 10
 Convert 23 cm to mm
= 23 * 10 mm
= 230 mm
To convert kilometer to hectometer, we multiply by 10
 Convert 12 km to hectometer
 = 12 * 10
= 120 hectometer
Convert 12 km to decameter, we multiply by 100
= 12 * 100 decameter
= 1200 decameter
Convert 12 km to meter, we multiply by 1000
 = 12 * 1000 = 12000 meters
Now we take an example
Say  we have to add 5 Km and 25 meters/ As the units are not same, they cannot be added. So we either convert 5 km to meters  or 25 meters to km so that the units become same and the mathematical operation can take place.
So 25 m = 25 / 1000 km
   = 0.025 km
Now we write add 5 km and 0.025 km
= (5 + 0.025) km
= 5.025 km
In the same way by bringing the units same, we can do any mathematical operation on them.
So this is a brief article about unit conversion and measurement in grade V. If you have any problem in solving unit problems,Steps in problem solving and Problem solving strategies then you can take help of online calculators.

Estimates of Measurements in Grade V

Hello Friends, in day-to-day life we deal with many measurement issues like somebody ask us about our weight and height and if you don’t  know about measurement of height and weight, then you don’t have answer. So it is required to know how we estimate measurement. So, in  today's session we all are going to discuss about one of the most interesting topic of grade V mathematics of tamilnadu education board, Estimates of measurements which is quite similar to the topic analytical geometry problems. 
First of all we discuss what is measurement.
Measurement is the process which is used to determine physical quantity in length, time, temperature etc. to standard unit of measurement like  length in meter, time in second or temperature in degree Celsius,You can also get math help online about  this topic.
Now further we discuss how we measure units of measurements.
Here we discuss measurement of five major units

• measurement of length : Basically measurement of length is done in meter and we have to know all basic conversions about length like  kilometer to meter, meter to centimeter etc. So I will show you a chart which shows how length conversion is done (want to Learn more about Measurements ,click here),

     1 myriameter = 10 kilometer
     1 kilometer = 10 hectometer
     1 hectometer = 10 decameter
     1 decameter = 10 meter
     1 meter = 10 decimeter
     1 decimeter = 10 centimeter
     1 centimeter = 10 millimeter
     1 foot = 12 inches
     1 inch = 1000 mils
If you know all these conversions about length then you can easily measure physical quantity in length term.

• measurement of weight : We generally measure weight in kilogram, but if we want to measure weight in grams and pounds , we have to  know all conversions about weight. I will show you a chart which shows all conversions about weight

     1 metric ton = 1000 kilograms
     1 short ton = 2000 pounds
     1 stone = 14 pounds
     1 kilogram = 2.20 pounds
     1 pound = 16 ounces
     1 kilogram = 1000 grams
With the help of this chart, we can easily measure weight.

• measurement of volume: We can generally measure volume in liter and we can also measure volume in other units of liter. We have to know all  conversions about volume and following chart makes it easier to do these these things.

1 liter = 1.057 quarts

1 milliliter = .001 liter

1 cup = 236.6 milliliter

1 ounces = 29.57 milliliter

With the help of this chart, we can easily measure volume.

• measurement of time : Basically we measure time in seconds, but if we want to measure time in millisecond or microsecond, then we have to know all things about time conversion and following chart shows all conversions about time

1 day  = 24 hours 

1 hour = 60 minutes

1 minute = 60 seconds

1 millisecond = .001second

1 microsecond = .000001 second

This chart teaches us how we measure time.

• measurement of temperature : Basically we measure temperature in Kelvin, but if we want to measure temperature in Celsius or other unit of  temperature, then we have to know all things about temperature conversion and following chart shows us how we do conversions of  temperature by using formulas

To convert celsius to kelvin : k= 273+c

To convert celsius to farenheit : 9/5C = F-32

To convert Farenheit to rankins : R = F+459.5

To convert Rankins to Kelvin : 9k = 5R

This chart teaches us how we convert temperature from Kelvin to degree Celsius and degree Celsius to Fahrenheit etc.

This is all about measurement of units and in this session we almost cover full concept of grade V mathematics topic Estimates of measurements. I hope you learn and use concept in your real life and If you want to know about Collect/organize/graph data then you can refer Internet.

Polygons in Grade V

Hello friends we are back again with another Geometry topic. Today we will have a look on Polygons, Triangles, and Quadrilaterals in grade V. We will learn what Polygons, Triangles and Quadrilaterals are their properties and types.
So let’s start with Quadrilaterals first. (also try quadratic formula calculator)
Quadrilateral is the combination of two words: quad means four and lateral means side. So Quadrilateral means four sides.
A Quadrilateral is the four straight sides, 2 dimensional closed shape.

Properties of Quadrilaterals:

• Has four sides or edges.
• Has four vertices.
• Interior angles has sum of 360 degrees.

Example:

         

The above shape is a quadrilateral and sum of angles are:
            118+94+80+68=360

Types of Quadrilaterals:
Rectangle has four sides and opposite sides are equal in length with every angle is right angle.


Parallelogram has parallel opposite side and are equal in length. Opposite angles are equal.

Rhombus: All sides are equal in length. Opposite sides and angles are equal. Diagonal of rhombus intersects each other at right angle.



Square: All sides are equal in length and all angles are equal 90 degree each. Opposite sides are parallel.



Trapezium has one pair of opposite side parallel and non parallel sides and base angles are equal.


Kite has two pair of side. Adjacent sides are equal in length. One pair of opposite angles is equal. Diagonal intersect at right angle.



Polygons: It is a Greek word where Poly means “many” and Gon means “angles”.  Polygons are 2 dimensional closed shapes with three or more sides. All sides are straight. Polygons names are based on sides and angles they have.

Now let us discuss about types of polygons.
Simple and Complex
Simple polygons has only one boundary and does not intersect itself whereas complex intersect itself.


Concave and Convex:
                                    Convex has no internal angle more than 180 degree and if there is any internal angles greater than 180 degree than its is called Concave.

Regular and Irregular:
                                    If a polygon has all sides and all angles equal than it is regular. otherwise irregular.


Types of polygons based on the sides:
Triangle has 3 sides and internal angle sum of 180.


Quadrilateral has 4 sides.


Pentagon has 5 sides.

Hexagon has 6 sides.



Triangle: As we have seen above a triangle is simple polygon with 3 sides and 3 angles.
The sum of internal angle is 180 degree.

Triangles are classified on the basis of their sides and angles.

Classification based on sides:
Scalene has no equal sides and no equal angles.


Equilateral has three equal sides and equal angles of 60 degree each.


Isosceles has 2 equal sides and two equal angles.


Classification based on angles:

Right Angle triangle has one angle of 90 degree and the side opposite to right angle is called hypotenuse. This is the longest side of the right angle triangle.



Acute angle triangle has all angles less than 90 degree. That is all angle are acute.



Obtuse angle triangle has a one angle greater than 90 degree. That is one angle is obtuse.

           
Now you all are familiar with the Polygons, Triangles, and Quadrilaterals and types of Polygons, Triangles, and Quadrilaterals. Just spend some time with concentration and you can easily identify and differentiate them.

In next post we will talk on Estimates of Measurements in Grade V. For more information on syllabus of economics for ICSE class 12, you can visit our website

Measurement in Grade V

Hello friends, how are you all today? Previously we have discussed about properties of rational numbers ,Are you ready for today’s session?
Our today’s topic is an interesting topic of mathematics. Measurement is the topic what we are going to read. In measurement we include Types of Measurements,help with math measurements, Measurement Problems in grade V of andhra pradesh board of secondary education. So students let's start now.
Measurement is the process of calculating or determining result of quantities. When I was a kid and my teacher asked me first what you know about measurement. I always found difficulty to answer back. Let me tell you a fact that you also deal with measurement daily but the thing is that you are not aware of it.
When you said to one of your friend that you are taller than him and he claims the same than you both stood stand by each other or use a tape to determine who is taller.
That means you are calculating your height or we can say it as you are measuring your height.
We use some units to compute them. Like in our example the unit of height is inches or feet. Likewise unit of mass for example our weight is measured in kilograms. And time, you all are familiar with the unit of time. What it is? It is seconds, minutes or hours.
Now after knowing measurement we will move on to the types of measurements their units and measurement problems. In measurement problems we learn how to convert one unit into other.(want to Learn more about Measurement ,click here),

Let us discuss about mass measurement. Mass is the amount of material in an object that are not effected by        the environment.
Based on the International System (SI) the unit of mass is Kilogram often denoted as kg.
We have seven base measurements and kg is one of them.

Different units of mass and their conversion:

10 milligrams	=	1 centigram
10 centigrams	=	1 decigram
10 decigrams	=	1 gram
10 grams	=	1 dekagram
10 dekagrams	=	1 hectograms
10 hectograms	=	1 kilogram
1,000 kilograms	=	1 metric ton

We generally say weight in place of mass. But weight and mass are two different quantities.
Mass is a measure that how much material some object can contain whereas  weight is the measure that how strongly gravity pulls some object.

Now we will go through time measurement:
To determine time we need some measurement unit. Based on the International System (SI) the unit of time is minutes. We also have second and hour etc to describe time.

Different units of time and their conversion:

1 minute = 60 seconds
1 hour = 60 minutes = 3600 seconds
1 day = 24 hours
1 week = 7 days
1 year = 365 days

Now I will tell you about volume measurement. Volume is the measure to compute the capacity of the object.
For example: How much a water bottle can contain is the capacity of that bottle.
Unit of volume is liter we often use lt instead of liter. Except liter we also have milliliter, centiliter etc units to measure volume.

Different units of volume and their conversion
1 milliliter = 0.001 liter
1 centiliter = 0.01 liter
1 deciliter = 0.1 liter
1 kiloliter = 1000 liters

We can also simplify this table as:
1000 milliliter = 1 liter
100 centiliter = 1 liter
10 deciliter = 1 liter

These all are some measurements, their types, and some measurement problems. Do refer some exercises on measurement and get perfect and if anyone want to know about Measures of central tendency/dispersion
then they can refer to internet and text books for understanding it more precisely. Read more maths topics of different grades such as Mean and median in Maths in the next session here.

Whole Numbers and Place Value in Grade V

Hello friends,Previously we have discussed about probability worksheets and  today we are going to discuss one of the important topics of math grade V of cbse syllabus which is whole numbers and place value. Whole numbers are the set of familiar numbers (0, 1, 2, 3, 4, and so on). When they are called counting numbers, zero is not included. The whole numbers are also called the positive integers (or the nonnegative integers, if zero is included) and they plays an important role to solve math problems.
The numbers 0, 1, 2, 3, ... etc.

There is no or decimal part and no negatives. We will begin our review of place values with a look at whole numbers. When writing large numbers it is a common practice to separate them into groups of three using commas as the separator. When separating into groups of three, start from the right and count toward the left.
Example: 3, 79 and 980 are all whole numbers.
Place value is the value of a digit as determined by its position in a number. The name of the place or location of a digit in a number. The ability to understand place values is an important mathematics skill measured in the Early Childhood Longitudinal Study. More specifically, students should be able to identify place values in integers to the hundreds place to achieve this skill. Simply the Place Value is the position of a digit in a number written in standard form determines the actual value the digit represents.This table shows the place value for various position (want to Learn more about Whole Numbers ,click here),

Place (underlined)	Name of Position
1 000	Ones (units) position
1 000	Tens
1 000	Hundreds
1 000	Thousands
1 000 000	Ten thousands
1 000 000	Hundred Thousands
1 000 000	Millions
1 000 000 000	Ten Millions
1 000 000 000	Hundred millions
1 000 000 000	Billions

We will take some examples for explanation.
Example:
The number 521092 has a 5 in the hundred thousands place, a 2 in the ten thousands place, 1 in the thousands place, 0 in the hundredths place, 9 in the tens place, and a 2 in ones place.
Example:
Four billion, sixty million, six hundred twenty thousand
4,060,620,000
And another example
9,568,125
Numbers, such as 9,568,125 have seven digits.  Each digit has a different place value.
The first digit is called the millions' place value. There are nine millions in the number 9,568,125
The second digit tells you how many sets of one hundred thousand are in the number.  The number 9,568,125 has five hundred thousand.
The third digit is the ten thousands' place. There are six ten thousands in addition to the nine millions and five hundred thousand.
The fourth digit is the one thousands' place which is eight in this example.
The fifth digit is the hundreds' place which is one in the number 9,568,125.
The next digit two is the tens' place.
The last or right digit is the ones' place which is five in this example.
Therefore, there are nine sets of 1,000,000, five sets of 100,000, six sets of 10,000, eight sets of 1000, one sets of 100, two sets of 10, and 5 ones in the number 9,568,125.

Example :In the numeral 7,015,384, what digit is in the...
  Ques                                                           Answer
a) Ones place ?                                                   4
b) ten thousands place ?                                     1
c) tens place ?                                                     8
d) millions place ?                                               7
e) hundreds place ?                                            3
f) hundred thousands place ?                             0
g) thousands place ?                                           5
So here we end with whole numbers and place value. I hope that this article will help you in solving problems related to whole numbers and place value and if anyone wants to know about Number systems in Grade V and Percentages in Grade VI then they can refer Internet.

How to tackle Decimals and Percentage problems?

Previously we have discussed about rational expressions applications word problems and Friends today i am going to teach you one important topic of grade V of karnataka board namely percents and Fractions.A linear array of digits that represents a real number, every decimal place indicating a multiple of a negative power of 10. A number written using the base 10.
For example, the decimal 0.1 = ¹/₁₀, 0.12 = ¹²/₁₀₀, 0.003 = ³/₁₀₀₀

A percent is a ratio whose second term is 100. Percent means parts per hundred. The word comes from the Latin phrase per centum, which means per hundred. In mathematics, we use the symbol % for percent.
Example  of percents
23/100 =23%, 3/100 = 3%
In math fractions, the denominator tells us how many parts the whole is divided into, and the numerator tells us how many of those parts we're dealing with.the number above the bar is called the numerator, and the number below the bar is called the denominator.
Example :  ¾          3 is numerator and 4 is denominator

Every fraction can be converted to a decimal by dividing. If you use the calculator to divide 3 by 4, you'll find that it is equal to 0.75.
Here is a table of commonly occuring values shown in Percent, Decimal and Fraction form:

                                 Percent                   Decimal                  Fraction
                                 1%                                  0.1                     1/100
                                 10%                                0.1                     1/10
                                75%                                 0.75                    3/4

Conversions from Percent to Decimal
Percent-to-decimal conversions are easy; you mostly just move the decimal point two places. The way I keep it straight is to remember that50%, or one-half,. In other words, you have to move the decimal point two places to the left when you convert from a percent (50%) to a decimal (0.50). divide by 100, and remove the "%" sign. (Know more about Percentage ,click here),
Some more examples are
27% = 0.27
104% = 1.04
0.5% = 0.005
To convert from decimal to present in divide by 100, and remove the "%" sign. The easiest way to divide by 100 is to move the decimal point 2 places to the left.
Example
0.123 = 0.123/100 = 12.3
To convert fromFraction to Decimal the easiest way to convert a fraction to a decimal  is to divide the top number by the bottom number (divide the numerator by the denominator in mathematical language)
Example: Convert ²/₅ to a decimal
Divide 2 by 5: 2 ÷ 5 = 0.4
Answer: ²/₅ = 0.4
To  convert a decimal to fraction  needs a little more work.
Example: To convert 0.75 to a fraction
First steps =0.75/1
       ^{=   0.75 × 100}/ _{1 × 100}     Then multiply top and bottom by 10 for every number after the decimal point (10 for 1 number, 100 for 2 numbers, etc)
  = ¾
To convert from fraction to percentage is to divide the top number by the bottom number than multiply the result by 100 and add the % sign,
Example: 38
First divide 3 by 8: 3 ÷ 8 = 0.375,
Then multiply by 100: 0.375 x 100 = 37.5
Add the "%" sign:     and the answer is  37.5%
To convert from percentage to fraction first convert to a decimal (divide by 100), then use the steps for converting decimal to fractions (like above).
Example 80% to convert in fraction
80/100 =0.80
^{0.8 × 10}/ _{1 × 10}   Then multiply top and bottom by 10 for every number after the decimal point (10 for 1 number, 100 for 2 numbers, etc)
And the answer is =8/10 = 4/5
So here we end with Decimals, percents and fractions. I hope that this article will help you in solving problems Decimals, percents and fractions and If anyone wants to know about Percentages in Grade VI and also about LCM, GCF, ratios and proportions then they can refer Internet.

How to Sketch Transformations?

Hello friends,Previously we have discussed about properties of rational numbers and now Sketching transformations which sometimes become a tough task and we need a continuous practice and hard work to understand this intersting and a bit complex topic. Here I am going to tell you the best way of understanding Sketching Transformations with geometry help. And this is for grade V of gujarat secondary education board. In basic transformation geometry there is two basic types that are rigid transformations and non-rigid transformations. And also there are three types of rigid transformations known as translations, reflections and rotations. In other words, a transformation is a copy of a geometric figure and copy holds certain properties. Let’s take a simple example when we copy/paste a picture on our computer. Then the original figure is called the pre-image and the new copied picture is called the image of the transformation. The rigid transformation is one in which the pre-image and the image both have same size and shape. In simple word transforms means to change. In geometry, a transformation changes the position of a shape on a coordinate plane. That means shape is moving from one place to another
 Translations: - The definition of a translation is every point of the pre-image is moved the same distance in the same direction to form the image. Let’s take an example of triangle each point of triangle is translated or moved 6 inches to the right and 4 inches up.In this case, the rule is 6 to the right and 4 up.  You can also translate a pre-image to the any combination of two of the four directions.
The transformation for this example would be T(x, y) = (x+6, y+4).
Reflections: - is a flip of an object over a line. The example of Reflection is given below. This will helps you to understand Reflection.(want to Learn more about Transformations,click here),
Reflection in the coordinate plane over x-axis: -    T(x, y) = (x, -y).
Reflection in the coordinate plane over y-axis: -    T(x, y) = (-x, y).
Reflection in the coordinate plane over line y = x: - T(x, y) = (y, x).
Rotation: - In rotation (turn) a letter can turn on a point away from its original position. When we watch the T move it turns in place so that it now looks like it is lying on its side and almost look like a clock hand turning around the face of a clock.
Scaling: - Scaling is a linear transformation and the scale factor is the same in all directions. It is also called dilation and the result of uniform scaling is similar to the original.
When one shape can become another using Turns, Flips and/or Slides called Congruent.
Resizing: - The other important Transformation is resizing. In resizing the shape becomes bigger or smaller.
Similar or Congruent: - In Similar or Congruent if one shape become another using transformation, the two shapes might be just similar.

Translation of points: -
A point (p,q) can be moved to another position by applying a column matrix vector.
 The column matrix vector is just two numbers, one above the other surrounded by long brackets. The top number adds to the p-coordinate while the bottom number adds to the q-coordinate.
From the above I hope it would help you to understand Sketching transformations, geometry and if anyone want to know about Problem solving strategies and also on Estimating probability then they can refer to internet and text books for understanding it more precisely.

Math Blog on Grade V

Hello Friends,Previously we have discussed about list of rational numbers and today we are going to learn about the mathematics of the grade V of indian certificate of secondary education board. We will learn about some few discussion of syllabus of fifth standard mathematics. Grade V is the level of learning, after that the schooling ends, so these are the end years of the school for any child.
In grade fifth, we learns about the numbers as read the number having multiple digits like 100000 and locate, represent, identify and compare such numbers by the use of expanded or regular form of them. We should have the proper understanding of the place values for 0-4 places in number to the right and left places. We should be able to perform addition, subtraction, division and division the decimals. We should have the proper understanding of converting fractions to decimals related values. We can make the selections for the strategies for problem solving and we should also have mathematical thinking in problems solving. In term of measurements we should have understanding of length unit like inches, feet, yards, miles, millimeters, centimeters, meters, and kilometers and we also the proper use of these terms in problem solving. We should have ability to make rounds accurately in measurements. In term of geometry we learn about the plane figures, solid geometry, area, surface area, volume, perimeter, and circumferences etc. so for this we have the proper understanding of coordinate system on either map or grid.(To understnd geometry in more precise manner ,click here)
The grade V also includes the learning and modeling 2d and 3d objects. We learn about different types of polygons, symmetry of planes, and sides of them. It includes the use of venn-digrams to short the shapes having curved faces and their vertices. We can identify, sort, construct, measure, and also can apply a variety of shapes and figures in the geometrical and other problems. We should have the understanding of geometric properties and their relationship. As per shapes, we can classify them, their property and type like angle and type of the triangle (isosceles, obtuse etc.) also we have to know that the same thing can also be done with the help of protractor.
The learning and modeling 2d and 3d objects includes the description of characteristics of 2D shapes and 3D objects and relation between them. We should learn about the description of sides, vertices, faces, and edges of any of the shape in the 2D or 3D geometry. Several two- and three-dimensional games can also be used to understand the concepts regarding the dimension for the purpose of extend knowledge of students' about shapes and to give them hands-on experience working with shapes. Use of such game will help us to become familiar with the names and properties of two- and three-dimensional shapes and their views.
We have to learn about the money exchange problems, date models to read and write (model like Feb. 08, 1988, 06/01/2012 etc.).We should determine the value of equations when there is some missing terms in the operations, also ability to find the missing term in the equation having more than one operation.
In grade V we should also learn about some basic problems like Tools to solve problems, probability to design surveys, collection of data. We should discuss the real world need for some type of data and collection of that data. We should go through the logical reasoning and experiment regarding that collection of data.

How to solve mathematical Expressions:

While dealing with the mathematical numbers and various mathematical operations, we  come across various mathematical  expressions for example - algebraic expression which looks very complicated and are not so easy to be solved and came across cbse syllabus many times. To solve such expressions, we need to follow certain rules to get the correct solution.

Whenever we are given some mathematical equations to solve, These equations are to be solved in a particular order in order to get the proper solution to the expressions. This Order of Operations includes the following sequence:
1  parenthesis, (called Braces)
2. Of
3. Division
4. Multiplication
5. Addition
6. Subtraction.
 This sequence is remembered by the student as an acronym- BODMAS
First of all the braces are opened ,solved and then removed to make the equation in the simple form.(Learn more about mathematical expressions here),
 After every step, the equation / expression takes a simpler form,
Let us consider some  examples:
Solve the numerical expression 15 - [ 11 - 8 ÷ ( 17 + 3 * 2 - 19 )
 Here we solve the brackets in the order ( ), followed by , then [ ]
= 15 -  [ 11 -  8 ÷ (17 + 6 - 19) ]
 we have 17 + 6 - 19 = 4
 = 15 - [ 11 - 8 ÷ 4 ]
 = 15 - [ 11- 2 ]    As 8 ÷ 4 = 2
 = 15 - 9
= 6 Ans.
Solve the given numerical expression:
 11/2 of (2/3 - 3/5) + 1/2 ÷ 5/11-------(1)
 Here , following the heirachy of the above simplification procedure, first we solve:
     (2/3 - 3/5)
l.c.m. of 3 & 5 is 15, so by making the denominator =15 we get
 = ( 2 * 5 - 3 * 3 ) / 15
 = ( 10 -  9 )/15
= 1/15
  Putting this value in ( 1) we get
=  11/2 of  1/15  + 1/2 ÷ 5/11------ (2)
  In next step we solve "of "
  11/2 of  1/15
  = 11 /30
 Putting this value 11/30 in  (2) we get
 = 11/30    + 1/2 ÷ 5/11 --------- (3)
In next step we solve " ÷ "
 1/2 ÷ 5/11
= 1/2 * 11/5
= 11 / 10
Putting this value 11/ 10 in  (3) we get
 11 / 30  + 11 / 10
 Now taking L.C.M. of 10 and 30 = 30,
we get
= ( 11 + 11* 3 ) /30
= ( 11+ 33 ) / 30
= 44 / 30
Now converting into simplest form , we divide Numerator & denominator  2, w get
 = 22 / 15 Ans

 Solve the  Following:
21 -( 12 - 6 ÷ 3)------- (1 )
 In this given expression, we first consider the brackets,
 We solve the bracket
( 12 - 6 ÷ 3),
Now in Bracket , we first take division i. e.
6 ÷ 3 =2,
= (12 -2)
 = 10
Putting this value in eqn (1) we have
= 21- 2
= 19 Ans

In this way, by following proper procedure , order of operations, opening parenthesis systematically required  for solution, any given numerical expression can be solved and if you want to know about Math Blog on Probability and Statistics then refer Internet,Read more maths topics of different grades such as Mathematical Reasoning in the next session here.

Learn Number System

Today we are going to learn about Number systems which is a part of cbse syllabus,
and learning Number systems can be useful for your Homework help.
Number system is said to be as the set of numbers on which one or more operations are performed like addition or multiplication.
Number system consists of real numbers, natural numbers,rational number and complex numbers to name  a few.
Number system is a way of counting  things. it is a way of identifying the quantity of something.
The most commonaly used system of numerals is the hindu- Arabic numerals.
Number system consists of natural numbers:
Natural numbers consists of set of all whole numbers greater than zero.

We are now going to discuss about the types of numbers
1.     Natural numbers
2.     Whole numbers
3.     Integers

Natural numbers: Numbers are classified according to type. The first type of number is the "natural" numbers:
Eg 1,2,3,4,5  (Learn more about natural numbers here),
The next type is the "whole" numbers, which are the natural numbers together with zero
For example we can say that 0,1,2,3,4,5
Prime numbers:
Prime numbers are the numbers which are only divisible by one or itself
Like 2,3,4,5,
Odd numbers : odd numbers are the numbers which are not the multiples of two like 3,5,7 etc they always end with the numbers like 1,3,5,7,9,11
Now we explain other types of numbers like
Even numbers: these numbers always end with numbers,0,2,4,6 or 8
Now we learn about the other number like
Rational numbers: a ational number is a number which can be expresses as a ratio of two integers.non –integer rational numbers are usually written in the form of a/b an b is not equal to zero.
Irrational numbers: these are the numbers which are not rational
We can take the examples like 3.14
Real numbers: these are those numbers which are made up of both rational and irrational numbers.
Imaginary numbers: The imaginary numbers are the numbers are the numbers based on the imaginary number i
Now we have a brief idea about the numbers and the types of numbers
Number system is also the most important part of grade V mathematics .
Number system and the type of numbers are set of operations related to addition and multiplication
Numeral system is also known as the numeral system.
We can further explain the grade V mathematics related to Number system and the types of numbers as follows.
The  most commonly used system of numerals is known as Arabic numeral or hindu-arabic numeral.
A number system is the set of symbols used to express quantities as the basis for counting, determining order, comparing amounts, performing calculations, and representing value. It is the set of characters and mathematical rules that are used to represent a number.

Thus we can now sum up and say that the number system,The types of numbers are the basis of maths and is important for understanding and solving various topics related to mathematics.
So now we have the full knowledge of the number system, types of number system and the above information will  help the students of grade V
in understanding the basic number system and If anyone wants to know about Steps in problem solving then they can refer Internet and text books.

Probability in Grade V

In V Grade of cbse board, we are going to get Introduction to Probability,
Basically probability means the possibilities of the occurance of a particular event and its possible outcomes.
Let us first see what an experiment is ?(want to know more about experiment then refer to online math tutor available on Internet)
An experiment which can produce some well defined outcomes is called an experiment.
All the Outcomes of an experiment are called events
Suppose we are making predictions for if it will rain or not: then there are two possible  outcomes,
1. It may rain
2. It may not rain
In probability we talk about any event that occurs in the universe and on that particular event. The process of making predictions takes place and the possible outcomes are taken into considerations.
Let us consider an event of a child going to school on Monday, the possible outcomes are
1. He may come to school.
2. He may not come to school.
This is called probability.
We use probability in our daily life. We usually find the events occuring in our life, sometimes we speak some sentences like:
Most probably my grandmother will come tomorrow.
I doubt that if  you will pass this time.
There are high chances that we will reach in the finals of the tournaments. All these words explain about the possibilities of the any event to occur.
Suppose we take any event of throwing a coin. The possible outcomes are Head (H) and Tail (T)
After throwing the coin either Head or Tail will be appearing.
So probability of getting a head P(H) = 1 out of 2.
                                                   p(H) = 1/2

 probability of getting a tail P(T) = 1 out of 2. 

                                                   P(T) = 1/2
The chances are  that  either the Head or Tail will appear as one of the outcome.
If two coins are thrown at random, then the possibilities of the outcomes are HH, HT, TH, TT
If we throw a dice we observe that one of the possible outcomes are 1, 2, 3, 4, 5, 6. It means that when the dice is thrown, one of these outcomes will appear. So  these are called the  probability of  occurrence of any event.
The possibility of getting a number 1 = 1 out of 6 => p(1) = 1/6
The possibility of getting a number 2 = 1 out of 6 => p(2) = 1/6
The possibility of getting a number 3 = 1 out of 6 => p(3) = 1/6
The possibility of getting a number 4 = 1 out of 6 => p(4) = 1/6
The possibility of getting a number 5 = 1 out of 6 => p(5) = 1/6
The possibility of getting a number 6 = 1 out of 6 => p(6) = 1/6(To know more about probability click here)

We study probability in  all aspects of life.
If we put 10 marbles in a box, out of which 5 are red in color, 3 are blue in color and 2 are green. If we have to take out one marble out of the box, what is the probability of 1getting a red marble = P (red) = 5/10
    2) getting a blue marble = P(Blue) = 3/10
    3) getting a green marble = P (green ) = 2/10

So this is the way we study Steps in problem solving for probability . I hope that what I have told is sufficient for you and to know about 4th Grade Probability and Statistics you can refer to Internet.

Math Blog on Grade V

Multiplication is said to be as the basic operation related to the elementary mathematics in any education board.

In simple words we can say that the multiplication is the mathematical operation of scaling one by another by multiplying positive and negative numbers or positive - positive and negative - negative numbers.

The other functions of the elementary mathematics are addition, subtraction, and division.

To understand the multiplication let just take an example and If you want you can take On line tutors help also,

Suppose 3 is multiplied by 4 it can be written as 3 X 4 or 4 + 4+ 4 which is also equal to 12.

Multiplication can also be written using the multiplication sign (X) between the two terms ,like 3 X 4 Multiplication. The result is expressed with an equal sign =

 For example,

2 x 3=6

3 x 4= 12

(in words we can say that ,"two times three equals six")

2 x 3 x 5= 30

2 x 2 x2 x2 x2 =32

Multiplication is also denoted with either a middle dot (.)

Examples of multiplication 5.2

The numbers to be multiplied are generally called the factors" or "multiplicands".  

The result of a multiplication is called a product and is a multiple of each factor  For example, 15 is the product of 3 and 5, and is both a multiple of 3 and a multiple of 5.(More multiplication examples)

What is division?

Division is an arithmetic operation and is denoted by the symbol ÷ ,

Let us take an example of division suppose if c times b is equal to a ,t can be written as

c X b = a

and here b is not equal to zero

then

a/b = c

suppose 6 ÷2 =3

here a is the dividend and b is the divisor and c is the quotient

further we can say to understand division that if its written a/b or a÷ b

then it can be read as a is divided by b, or  “a by b” or a over b

What is inverse relationship?

Inverse relationship can be explained in simple words as the mathematical relationship in which one variable increases and the other variable decreases.

To understand the concept of inverse relationship we can take any day to day example

Education and unemployment are inversely related..if the rate of education increases the rate of unemployment.

The inverse relationship can more easily be understood with the help of an example on multiplication and division

Suppose we have 3 X 7 = 21, which means multiplication of 3 and 7 produces a result of 21.

Now if we talk about division

21÷ 7 = 3, i.e division of 21 by 7 gives a solution of 3

And division of 21 by 3 gives a solution of 7

Thus Inverse relationship is also known by the other name as the negative relationship.

We now have an understanding of the Multiplication, Division, Inverse relationship for the students of Grade V.

So to sum up the three topics for grade V we can say that the Multiplication,Division and Inverse relationships are related to each other.
Multiplication and division situations consists an important part of the Grade V mathematics in other words it is the basis of maths.

LCM,GCF ,ratios for the students of Grade V

Today we are going to learn about LCM,GCF ,ratios for the students of Grade V of tamilnadu  education board.
For the Grade V we can define LCM (least common multiple), GCF ( greatest common factor) ,ratios
The description of the above mentioned topics is as follows and you can get more help regarding this on free math tutoring available on the Internet.
What is LCM?
LCM  or  the least common multiple is said to be as the common and the least set of numbers.
In order to find out the LCM we first of all write out the multiples of the numbers and after that we find out the common multiples of the given numbers.
Then to finally find out  the LCM we choose the least out of them and it is called as the LCM

LCM is said to be as the number  theory. to further understand the LCM  we can understand it with the help of an example. Suppose we have to find the LCM of 4 and 6?
Multiples of 4 are:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76 etc.

and the multiples of 6 are:

6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 

Common multiples of 4 and 6 are simply the numbers that are in both lists:

12, 24, 36, 48, 60, 72,

So the least common multiple  or the LCM of 4 and 6 is the smallest one of those: 12
It is also known by the other name as the "lowest common denominator" or LCM which is taken out before we add the two fractions.For more LCM examples click here.
 What is GCF and how to find the greatest common factor?
GCF is also known as the greatest common factor.or greatest common divisor or,highest common multiple.
The GCF is the largest or the greatest of the common factor of any two  or more given numbers.

Let us take an example to understand the GCF:
Example of GCF: suppose we have to find out the GCF of 15 and 30
The factors of 30 are 1,2,3,5,6,10,15 and 30
The factors of 15 are 1,3,5,15
The common factors are 1,3,5,15
The greatest common factor or the GCF is thus 15

Ratios:
Ratios is said to be as the  relationship between two numbers of same kind.we can express it in the form of a:b.The numbers A and B are sometimes in ratios also called  as the terms.
Let us try and understand the ratios with the help of an example

suppose we  have 10 pairs of socks for every pair of shoes then the ratio of shoes: socks would be 1:10 and the ratio of socks : shoes would be 10:1
ratios can be written in various forms
we can express ratios like a:b, a/b, or a to b
let us try and understand ratios  with the help of an example

• let us suppose there are 16 ducks and 9 geese in a park..
• we can express them in the form of the ratios as follows
• ratio of ducks: geese 16:9 or 16/9, 16 to 9

from this we now have a knowledge about the LCM,GCF and ratios and To get information about Multiplication facts and tables and Grade V  Problem solving strategies you can refer to Internet.

Number Line in Grade V

Hello friends, we hope you have understood our previous articles. Today I am going to discuss number line and representation on a number line in mathematics which is included in every education board for grade V. So friends let’s start with number line. In previous article we have discussed the lines. Now we will discuss the number line.
In mathematics, a number line is an image of a straight line which has several points which are real numbers(Real Numbers Definition). These points are called integer. Thus, real numbers are represented in each direction.
A line number has positive number and negative number that is held at correct points online, in zero condition it’s in center point of the number line where right side is positive number and left side is negative number.
Number line is a method that specifies the particular sequence of integer. In this sequence assigning number to lines is to assign every line a unique number, which is starting with 1 and also incremented by 1 for each successive line .The number line is usually represented  by horizontal line as well as vertical line as shown in this figure.

Here are some steps to draw a number line
1.       first you draw a straight line because it is represented by horizontal line
2.       draw the arrow both of end number
3.        you point the origin on the number line
4.        positive number should be on the right side at the number line
5.       Negative number should be left side at the number line
6.       Mark all integer number over the number line
7.       Plot the given number over the number line.
Let’s see the number line based problem and for more practice you can refer to Number Line Worksheets.
Example:
 Points on a number line: there are two people X, Y. X walks towards 2 points and Y walk backwards 3 points.

The solution of this problem is given below
In this, first X is start from 0. In this problem X moves towards 2 point.
So X person is right side on the number line position of 2.
Second person   starting from 0. In this problem Y moves backwards to 3 point.
So Y person is left side on the number line position of -3.

So friends let’s see the other part of this topic which is Decimal on number line:
In mathematics decimal number is represented by placing a point on number line. In other word you can say that a fraction which has denominator with power of ten is denoted by decimal point. The number system is also developed with ten as base. The decimal point for number increases in powers of ten from right to left and decrease from left to right in same powers.
Basically number line is used for locating a decimal number at corresponding place. By this figure you can understand.

Below you can see decimal point on a number line and for further details about number line refer this:


Now let us discuss about how a decimal number is written on a number line and how fractions and decimals are converted into each other.
When a denominator of fraction is 10 or power of 10 then number is converted into decimal. Let’s see example:
2/10, 14/100,136/1000 are also written as
2/10 = 0.2
14/100= 0.14
136/1000=0.136

So friends that was the brief definition of the number line for grade V.Here you have seen that how to draw a number line.  It has another properties which is discuss in next session and in that we will have discussions related to Math Blog on Grade VI also.

Factors and Exponents in Grade V

Hello friends today in this session of mathematics we are going to learn about some of the topics related to factors and exponents. This article will include the some of the topics of V grade of maharashtra state education board like common factors, prime factors, and exponents.
Now talking about the common factors for the grade V, we should have a understanding of the factors that what they are, So, the factors are the numbers that on multiplying positive and negative numbers produces another number. Each number has at least two factors. For example 12 = 2*6 so factors of 12 are 2 and 6. Now common factors are the numbers which are  common in two or more numbers. In math question we use the greatest common factor (GCF). The GCF is the number which is shared in both of the numbers. The greatest common factor is the number which is largest in the common factors. For example the GCF of the 24, 36, and 48 is 12 and GCF of 15, 30, and 105 is 15.
Factors of 24      =             1, 2, 3, 4, 6, 8, and 12
Factors of 36      =             1, 2, 3, 4, 6, 12, and 18
Factors of 48      =             1, 2, 3, 4, 6, 12, and 24 and for more gcf examples refer this link
Now talking about prime factors. The prime factors are the type of factors that are also prime in nature. These also on multiplication produce the original number. For the example the prime factor of 12:
12           =             2 * 6
                =             2 * 2 * 3
                =             2² * 3
So, prime factors of 12 are 2 and 3. The number 12 can also be written as 2 * 6 but 6 is not a prime number so it is not a prime factor for the number 12. Another example would be 15 which have the prime factor as 3 and 5 because both of the numbers are prime in nature. To find the prime factor we perform the prime factorization of the number. Prime factorization of a number is done for the purpose to find the prime number. For example performing the factorization on some of the numbers to find prime factors as:
12           =             2 × 2 × 3                (prime factors 2, 3)
15           =             3 * 5                       (prime factors 3, 5)
24           =             2 * 2 * 2 * 3         (prime factors 2, 3)
147         =            3 * 7 * 7                (prime factors 3, 7)
The prime factors of an integer are numbers which divides that integer with no remainder and didn’t leave any remainder.  The term exponent can be understood here by some of the definition that the exponents are the type of shorthand’s that comes for the replacement of the repetition of several numbers in the factorizations.
Just for example we consider some of the numbers:
24           =             2 * 2 * 2 * 3
This can be written in the form of exponent as 2³ * 3. Here 3 in the power of two is the exponent. The exponent shows that how many times the number is multiplied with a itself. The number that is being multiplied, as 2 in this example, is called as “base”. We also call it “rising to the power” where exponent is the power. In the example 48 = 2⁴ * 3, 2 is base and 4 is exponent on the 2. It is pronounced as “2 to the power 4” or “two to the four.

This is all about the Factors and Exponents and if anybody wants to know about Factorizing a Trinomial by splitting the middle terms and also  Mathematical Reasoning then they can refer to Internet and text books for understanding it more precisely.





 

Compare and Simplify Fractions in Grade V

Hi friends, in today's session we all are going to discuss about one of the most interesting topic of mathematics that is Fractions, Types of Fractions, Compare and how to simplify fractions which comes under west bengal board of secondary education syllabus. Basically when we divide an object into a number of equal parts then each part is known as fraction. A fraction consists of an integer(what are the rules for adding and subtracting integers) numerator and a denominator. The denominator must be non-zero. The numerator shows a number of equal parts and the denominator shows how many of those parts make up  whole . For example 5/7 is a fraction in which the numerator 5 tells us the fraction indicates 5 equal parts and the denominator 7 tells us that 7 parts equal a whole. There are three ways of writing a fraction that are a common fraction, a decimal and a percentage. Now we are taking an example which shows these three ways. One fourth of an object can be written as,To know more about fractions click here
a common fraction=1/4
a decimal =0.25
a percentage 25%.
Always remember one thing, denominator can never be 0.
Now I am going to discuss about the types of fraction. There are three types of fractions that are proper fractions, improper fractions and mixed fractions. These are explained below,
in proper fraction numerators are less than the denominators. For example in fraction 3/4, the numerator is less as compared to the denominator. This is called proper fraction.
In improper fraction the numerator is either equal to or greater than the denominator. For example 7/5, 13/5, 5/3 etc. are not proper fractions. These are improper fractions. The fraction 5/5 is also an improper fraction. 13/10, 13/4 are the examples of improper fractions. The numerator is greater than the denominator. These types of fractions are called improper fraction.
Every natural number is an improper fraction because they can be written as a fraction in which 1 is its denominator. For example, 3 = 3/1, 35 = 35/1, 63 = 63/1, etc.
Mixed fraction is a combination of a whole number and a proper fraction is called a mixed fraction. 11 1/3,101 7/10 and 76 7/11 are the some examples of mixed fraction. In other words mixed fraction contains two parts that is a natural number and a proper fraction e.g. 34  4/5, 53  3/4, 12  1/5 etc. Now the properties of mixed fraction,
Property 1: When we convert it into an improper fraction then we multiply the natural number by the denominator and add to its numerator. The new numerator over the denominator is the required mixed fraction.
Property 2:  When we divide the numerator by the denominator we get the quotient and remainder then the quotient is the natural number part and the remainder is the proper fraction part of the mixed fraction.
Now we were doing the comparison and simplification of fractions. When we want to know that which fractions is large or small then we need to compare those fractions and for the purpose of comparison we just simplify those fractions. To understand this, I am taking an example that is we will compare 2/5 and 3/8 for which fraction is bigger. We need to convert each fraction to decimal that is 2/5=0.4 and 3/8=0.37. So, the bigger fraction is 2/5.
This article gives the brief information about fractions and their types. If you want to know more about Order of Operations in Grade V and also Estimation of Solutions in Grade VI you can visit many website. These websites also provide solvers where you can solve your problems.