Multiplication and Division in Grade V

Hello friends Today we are going to learn the topic of multiplication and division which is under the syllabus of V grade students in icse board.
Multiplication is a mathematical operation that indicates how many times a number is added to itself. 2 x 4 = 8 is an example of multiplication. The basic idea of multiplication is repeated addition and Multiplication can be done by multiplying positive and negative numbers.

For example: 5 × 3 = 5 + 5 + 5 = 15
Example of multiplication:
 2 × 2 = 4
3 × 4 = 12
12 × 3 = 36
21 × 2 = 42
6 × 7 = 42
32 × 3 = 96
111 × 4 = 444
454 × 2 = 908
11 × 2 = 22
0.9 × 3 = 2.7
0.8 × 8 = 6.4
1.2 × 2 = 2.4
1.0 × 5 = 5
0.0 × 2 = 0 and more details and examples can be found here. 
Let's now take some word problems related to multiplication which can be done using math word problem solver.
Example: The bus fare for a single person is 45 cents. What is the cost of 2 persons?
 Answer:  45 × 2 = 90 cents

Example: A shipment has 5 boxes. Each box weighs 125 kilograms. What is the weight of the shipment?
Answer:  5× 125 = 625
Example: An airplane can travel 635 kilometers in one hour. How far can it travel in 4 hours?
Answer:  635 × 4 = 2540 kilometer

Division is a mathematical operation that indicates how many equal quantities add up to a specific number.
8 ÷ 4 = 2 is an example of division.

Example of division
4 ÷ 2 = 2
6 ÷ 2 = 3
8 ÷ 2 = 4
9 ÷ 3 = 3
12 ÷ 4 = 3
33 ÷ 3 = 11
132 ÷ 2 = 66
200 ÷ 5 = 40
88 ÷ 4 = 22
72 ÷ 6 = 12
7777 ÷ 7 = 1111
30 ÷ 1 = 30
54 ÷ 3 = 18
Let's take some word problems related to division

Example: A class of 35 students was divided into 5 equal groups. How many students are in each group?
Answer: 35 ÷ 5 = 7

Example: Mary and Samantha have 84 pieces of candy altogether. If they split them in half, how many would each girl have?
Answer: 84 ÷ 2 = 42
Example: There are 16 cookies. If there are 4 kids and each kid gets an equal amount, how many cookies can each kid have?
Answer: 16 ÷ 4 = 4
Example: There are 32 kids on the field. If there are 4 different groups of kids, how many kids are in each group?
Answer: 32 ÷ 4 = 8

So here we end with multiplication and division problems. I hope that this article will help you in solving problems related to multiplication and division and more information about grade V mathematics and Addition and Subtraction in Grade VI can be found on the Internet.

Decimals Percents, and Fractions in Grade V

Hello friends, in this session we are going to learn some topics for grade V students. This article will include the small topics of grade V level like decimals, how to divide decimals,percents and fractions for grade V of west bengal board of primary education.
Now coming to point, the decimals are the type of notation to write numbers in the base ten. It is also referred to as the base ten or the denary number system. We can also say that a decimal number is a type of fraction that has denominator as power of ten, but they are always represented without a denominator term. For example we can take some of the decimal numbers as: 0.56, 0.3564, 10.456, 1.33333, and 243.85 etc.
A decimal always represents the part of a Whole Number and this fraction part of the number starts after the decimal separator or the points between digits so it is also a type of rational number. Sometimes the decimals have some of the repeating digits in the decimal number. For example, 1.788888, 0.1766666, 0.142142142, and 0.01234567 and many more. Now talking about the fraction of a number. The fraction of any number is also represents the part of a whole number but in some other manner. A fraction number shows that how many equal parts are there in any of the integer. In the term of notation of a fraction number, we write one number above another number having a line in between them. The above number is called as the numerator which shows how many parts of the number are there, below number is called as the denominator of the fraction it shows the total number of parts. The separator line shows the fraction of both numbers. For example we can give fraction numbers as ½, ¼, 5/6, 2/3, and 7/4 etc. Fraction is a type of rational number represented in some numerator to the denominator. ¼ shows that 1 part of a number is divided in to four equal parts. So, a decimal, a fraction and a rational number are related to each other and they all represent the same thing but in different manner of notation. For example decimal number 0.5 can be represented as 1/2 as fraction and for more information and example on decimal click here.

The concept of percentage also comes from fraction and decimal numbers. The term percent stands per 100 and represented by the sign “%”. It shows that there is not some part of 100 items or of whole items. For example a basket of fruits having 5 fruits, 3 are apples and 2 are oranges then the percentage of the oranges can be given as 2/5 = 40/100 = 40%, and percentage of apples are 3/5 = 60/100 = 60%. So the percentage is used for the comparison of different numbers, for example we consider the exam result in the form of percentage, profit and losses are considered in the percentage. So we can say that the decimals, percents and fractions are the different ways for showing same value in the number system.
 
The figure shows half of a cake (1/2) as fraction, as decimal 0.5, and as percentage it is 50%.

This is all about the Decimals Percents, and Fractions and if you want to know about Decimals and Place Values and want to Solve Rational Numbers Problem then they can refer to internet and text books for understanding it more precisely.

 

Addition and Subtraction in Grade V

Hello friends! We are back again with an interesting topic of mathematics. Today’s topic is most basic topic of mathematics. Today we will learn addition and subtraction and numbers for a grade V student from Karnataka state board. We will start with numbers.
Numbers start from 0, 1, 2, 3, 4, 5 and so on and are called whole numbers. Numbers that start from 1, 2, 3, 4, and so on are called real numbers. Numbers are the base of mathematics. There are several operations that are performed on numbers. For example: Multiplication, division, Addition and Subtraction.
But here we specifically talk on Addition and Subtraction.

Addition is the operation to total something. By means of total we mean to club two or more numbers. The “+” symbol is used to denote the operation of addition.

Example:
Suppose we have two numbers “P” and “Q” and “R” is the total after the addition operation.
                        P + Q = R
And in words “ P plus Q equals to R ”.

Now let’s take number’s example.

Single digit addition:
                                    2 + 2 = 4
                                    4 + 5 = 5 + 4 = 9
                                    7 + 3 = 3 + 7 = 10
Do you notice something in above examples? No! See if we change the order of number then the result will remain the same. It will not change.

Two digits addition
                                    11 + 3 = 14
                                    26 + 24 = 50
                                    65 + 25 = 90
Similarly we can add “n” digit numbers.
By following the process below
Step 1: arrange the digits of the number in column form.
Step 2: Now add it as the single digit number starting from right to left. If carry is generated then count it on the column left to it and put the result in the last row.
Example:
                        Add 123+345+789
               1 2 3
            +3 4 5
            +7 8 9
        ------------
           1 2 5 7


Subtraction is the operation to taking out something. The minus (–) symbol is used to denote the operation of subtraction.
Example:
Suppose we have two numbers “P” and “Q” and “R” is the result after the subtraction operation. So the subtraction operation is defined as:

                        P- Q = R
And in words “ P minus Q equals to R ”.

Now we take the numbers example.

Single digit subtraction:
                                    4 - 1 = 3 but 1 – 4 = -3
                                    5 - 3 = 2 but 3 – 5 = -2
                                    4 - 3 = 1 but 3 – 4 = -1
Do you notice something in above examples? No! Subtraction operation is not same as addition. If we change the order of number then the result will be changed too. This shows that the order of numbers is important.

Two digits subtraction:
                                    19 - 13 = 6
                                    26 - 24= 2
                                    60 - 20 = 40

Similarly we can subtract “n” digit numbers.

By following the process below:
Step 1: arrange the digits of the number in column form.
Step 2: Now subtract it as the single digit number starting from right to left. If the above number is smaller than the number down then borrow from the number in left column.

Example:
            Subtract 987-342
              9 8 7
            - 3 4 2
          --------
              6 4 5


Aren’t they very easy? It will take no time to get master. Just spend some little time and you will be perfect in it.
In upcoming posts we will discuss about Decimals Percents, and Fractions in Grade V. Visit our website for information on Correlation Coefficient

Operations on Fractions in Grade V

Hello Friends, in today's session we all are going to discuss about one of the most interesting and a bit complex topic of mathematics,Order of Operations  on fractions and mixed numbers, which are usually studied in grade V of board of secondary education andhra pradesh. Here I am going to tell you the best way of understanding these topics.
Now we will first start with fraction:
math fractions is represented as a part of whole number. Fractions have numerator and denominator. Some examples of fractions are ¼, ¾. Fraction are of three types proper fraction, improper fraction, and mixed fractions. Let’s see some operations on fractions:

1.    Addition of fractions:

While adding two fractions we must take care that the denominators of the fractions to be added must be same. If the denominators are different then find the LCM of the denominators and put each one in its equivalent form. Then simply add the numerators.

                     p/q + r/q = (p + r)/q

2.    Subtraction of fractions:

While subtracting two fractions we must take care that the denominators of the fractions to be subtracted must be same. If the denominators are not same, find the LCM of the denominators and put each one in its equivalent form. Then simply subtract the numerators.

                     p/q - r/q = (p - r)/q

3.    Multiplication of fractions:

While multiplying two fractions simply multiply the numerators together and then multiply the denominators together and simplify them.

                     p/q x r/s = (p x r)/(q x s)

4.    Division of fractions:

While dividing the fractions, simply take the reciprocal of the second fraction and multiply both the fractions together.

           p/q ÷ r/s = p/q x s/r = (p x s)/(q x r)

Now let’s move to the second topic i.e. Mixed numbers:
A mixed number is represented as the integer number followed by the proper function. Let’s see some operations on mixed numbers and to know more about mixed fractions click here:

1.    Addition of mixed numbers:

          Steps for addition

1. Convert mixed number to improper fraction.
2. Now take the LCM by multiplying the numerator and denominator of fractions by a factor to obtain the lowest possible common denominator for the two fractions.
3. Perform the addition of the numerators
4. Reduce the answer if possible.
5. If the answer is an improper fraction convert it to a mixed number.

2.    Subtraction of mixed numbers:

          Steps for subtraction

1. Convert mixed number to improper fraction.
2. Take the LCM by multiplying the numerator and denominator of fractions by a factor to obtain the lowest possible common denominator for the two fractions.
3. Perform the subtraction of the numerators
4. Reduce the answer if possible.
5. If the answer is an improper fraction convert it to a mixed number.

1. Multiplication of mixed numbers:

          Steps for multiplying

1. Convert mixed number to improper fraction.
2. Multiply the numerators and multiply the denominators of the fractions.
3. Reduce the answer if possible.
4. If the answer is an improper fraction convert it to a mixed number.

4. Division of mixed numbers:

         Steps for division

1. Convert mixed number to improper fraction.
2. Take the reciprocal of the second fraction.
3. Multiply the numerators and multiply the denominators of the fractions.
4. Reduce the answer if possible.
5. If the answer is an improper fraction convert it to a mixed number.

This is all about the operations of fractions and mixed numbers in grade V
and if you want to get details on Multistep Problems in Grade VI then you can refer to the internet and text books.

Fractions in Grade V

Hello friends, in this chapter of mathematics we are going to learn about the fractions of the numbers taken from school education Karnataka board. We will learn that how to simplify fractions and also learn about all of the types of fractions.
In term of definition, the Math fractions are the part of any number. Fractions are the number in the form of some numerator to some denominator. Both numerator and denominator are integers in nature. They are like a rational number in mathematics and are in the form of a / b. The numerator part shows the parts and the denominator shows the whole part that can make the whole number by combining them. For example, 3/2 has numerator as 3, shows that the fraction 3/2 has three equal parts and denominator as 2 means two same quantities will form the whole number. Fraction numbers can also be represented in the form of decimal number and by the use of negative exponents. So decimal numbers are also a type of fraction which are found by the decomposition or simplification of the fractional numbers. The decimal fractions always are as that they have the denominator in the power of ten. For example, 0.2 represents the fraction 2/10 or that also equals 1/5, and 0.75 represents the fraction ¾ and each are the simplified number found from the fractional numbers.
Now talking about simplification of the fraction number. Let me first introduce you with the types of fractions. So there are three different types of fractions. They can be listed as:
1.       Proper fractions: Proper fractions are the fractions whose numerator term is less than that of denominator number, for example: ¼ is a proper fraction because numerator value is smaller than that of denominator value.
2.       Improper fractions: These are the fractions which has numerator value larger than that of denominator value of the number. For example: 5/2 is a improper fraction because numerator value is greater than that of denominator value.
3.       Mixed fraction: Mixed fraction is the third type of fraction, which is mixed because it is represented in the form of some simplified form of the improper fraction. Some of the improper fractions can be simplified in the form of proper fraction with a whole number. These proper fractions with integers are termed as the mixed fractions. For example 22/3 can be written as  in figure:

Now talking about the simplification of the fractions, so the simplification of the fraction involves the reduction of the fractional number in to simple form. For example say any fraction 3/9 can be reduced to 1/3. To do this, we have to find the greatest common factor (GCF) from both the numerator and denominator and then we divide both by the GCF until there are no any more common factors in both numbers. The improper fractions get simplified by different ways. We have to change these numbers in the mixed fraction for simplification. For example: 25/7 can be written as:  .

In next post we will talk on Operations on Fractions in Grade V. For more information on Chain Rule, you can visit our website

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