LEARNING OBJECTIVES
This lesson will help you to lean
recording of data using tally marks.
collecting data and representing in terms of pictograph.
drawing inferences from the data at the appropriate level.
organising and displaying data in different way.
understanding and using the information quickly.
QUICK CONCEPT REVIEW
The information in a list can be in the form of names and numbers. Such information is called data. There are three steps of data handling -
STEPS OF DATA HANDLING
Collection of data
Data collection process includes:
Asking the right questions to the right people.
Collecting information from people.
Organising information in a table (using tally marks).
Example:
I want to know the favourite sport of class II. How can I do that?
To know the favourite sport of class II we need to:
select the right question: What is your favourite sport?
give options :
Hockey/Cricket/Tennis/Football
ask all the students of class II
organize information in a table
draw conclusions.
Recording and Representation of Data
Data are facts that are collected by counting things and events. The data can be represented through tally marks.
Tally Marks:
Tally marks are vertical lines. They can be counted in group of 5. One vertical line is drawn for each of the first four counts. The fifth is represented by a line across the previous four lines.
Representation of Tally Marks.
Amazing Facts
In Ancient Egypt and China, many times the whole story was narrated with the help of pictographs.
The modern artist Xu Binf developed a universal language consisting of pictograms used all over the world.
Tally marks are also called hash marks and tally sticks.
Example:
From above table it can be concluded:
Cricket is the most favourite sport.
Football is the least favourite sport.
15 students like hockey.
10 students like tennis.
Pictorial Representation of Data (Pictograph)
We can represent some numerical information (data) in the form of pictures, it is known as pictograph or pictorial representation.
Example: Raj recorded number of cloudy days for 4 weeks in a month.
QUICK CONCEPT REVIEW
Swati went to a gift shop. She liked a teddy bear how she can get the teddy bear from the gift shop.
Swati has to give money to the shopkeeper to
Get the teddy bear.
Currency
We need money to buy things. Money can be in form or a note or a coin.
In India, currency is used in the form of rupees and
Symbol of rupee is Rs. and paise is 'p'.
1 rupee = 100 Paise
Or 1 Rs. = 100 p.
Historical preview
The word rupee is derived from the Sanskrit word rupyakam, meaning a silver cooin.
Udaya is creator of the rupee symbol. The symbol (Rs.) is a combination of the Latin letter “R” and Devanagri letter “Rs.”
After Independence, the first coin was introduced in 1950.
Notes Coins
Expressing money
How to express or write money together when we take rupees and paise separately.
We write rupees as “”and paise as 'p'.
We use a point or dot (.) to separate rupees and paise.
For example.
Sonu purchased a toy car in 125 rupees and 75 paise.
How can we express this money?
We can express it as Rs.125.75.
We can write 10 rupees as 10.00 as it has no paise.
Exchanging Money
Let us understand this with the help of an example.
Suppose Rohit went to purchase a book of worth 100 rupees. He had money in Rs. 50 and Rs. 10 notes. How many notes of Rs. 50 and Rs. 10 he has to pay to purchase the book?
First, we have to know how to do the division of money.
Let us do the division of 100 rupees in different notes.
Rs. 50 note can further be divided into other notes. Rs. 50 is equivalent to five Rs. 10 notes. Also. Rs. 50 is equivalent to two Rs. 20 notes and one Rs. 10 note.
To purchase a book of worth Rs. 100, Rohit has to pay one Rs. 50 note and five Rs. 10 notes or two Rs. 50 notes. Can you tell in how many number of ways you can Purchase a lead pencil of worth Rs. 12? If you have each of the following type of coins with you.
There can be total 6 number of ways in which you can purchase a lead pencil of Rs. 12.
Addition and Subtraction of Money
Addition
Let us take an example.
Monty bought a packet of crayons Rs.25mdan ice-cream for Rs. 12. How much money did he spent?
Here, you can simply more...
LEARINING OBJECTIVES
This lesson will help you to:
define fractions, numerator and denominator
identify fractions using objects and shapes
differentiate between equal and unequal parts
Historical Preview
The word fraction actually comes from the Latin “fraction” which means to break.
It was the Arabs who added the line (drawn horizontally) which we now use to separate numerator and denominator.
Egyptians were one of the first groups to study fractions.
Real Life Examples
A year is divided in fraction of month is further divide into fraction of weeks. Half year is equal to 6-months.
In schools, the time is divided into equal fractions of periods for each subject.
QUICK CONCEPT REVIEW
Halves and Quarters
Half
Rahul and Akshay were hungry. They bought a muffin cake. They shared muffin cake by dividing it into two equal parts.
When a whole object is divided into equal parts, then each part is called a fraction.
In the above example. Part 1 and Part 2 are two fractions of muffin cake.
Part 1 is one half and Part 2 is another half.
Misconcept/Concept
Misconcept: A fraction such as \[\frac{3}{4}\]is a ‘quarter of three’
Concept: A fraction \[\frac{3}{4}\]means ‘three parts of quarter’?
Numerator and Denominator
A fraction is made up of two numbers which are divided by a line. The number that is written below the line is known as denominator.
Denominator shows how many equal parts something has been divided into.
The number that is written above the line is known as numerator.
Numerator shows how many parts of the whole is taken.
Quarters\[\left( \frac{1}{4} \right)\]and Three-Quarters\[\left( \frac{3}{4} \right)\] .
Let us take an example.
Sam, Jatin, Ravi and Jack bought a chocolate. They cut it into 4 equal parts.
Each part is called one - quarter \[\left( \frac{1}{4} \right)\] .
Suppose, Ravi ate his part of chocolate or we can say he ate \[\left( \frac{1}{4} \right)\] of the choclate.
How much share of chocolate was now left?
3 shares are left. We can say that. \[\frac{3}{4}\]or three-quarters of chocolate was left uneaten and one-quarter of chocolate was eaten by Ravi.
Let us take another example
A circle can be divided into two halves, and four quarter\[\left( \frac{1}{4} \right)\]parts as shown on the left side.
EQUAL AND UNEQUAL PARTS
Suppose circle is divided into 3 equal parts. Then, each part of the circle is its one-third part.
If we take any two shaded parts of these three parts together, we will have two-third of the total part.
It is written as \[\frac{2}{3}\]
The examples we have discussed so far are based on division into equal parts or fractions.
Now let us discuss about division into unequal more...
LEARNING OBJECTIVES
This lesson will help you to:—
identify patterns in shapes, numbers and letters, observe and extend given patterns.
create block patterns by stamping thumb prints, leaf prints, vegetable prints, etc.
create patterns from shapes, numbers and letters.
describe given patterns.
QUICK CONCEPT REVIEW
A pattern shows the same thing again and again. It is an arrangement of objects; numbers or letters with some fixed rule.
Look at the patterns made with circles and tiles.
In the first pattern you can see one shaded and one unshaded circle getting repeated.
In the second pattern a square is divided diagonally and shaded half.
KINDS OF PATTERNS
Patterns are of different kinds – repeating patterns and increasing or decreasing patterns.
1. Repeating Pattern
In repeating pattern same things appear again and again.
(a)
(b) A B A B A B A B
2. Increasing Pattern In increasing pattern things increase in size or number.
(a) X XX XXX XXXX
(b)
3. Decreasing Pattern In decreasing pattern things decrease in size or number.
(a)
(b) ABCD ABC AS A
NUMBER PATTERNS
Various patterns can be made by numbers.
We can guess the next number in a pattern.
Examples:
Increasing Pattern:
In increasing pattern numbers increase in a certain manner, for example.
In the above example numbers are increasing by two.
Historical Preview
Geometric patterns were the great source of decoration in Islamic art which include calligraphy and vegetal patterns.
Decreasing Pattern:
In decreasing pattern numbers decrease in a certain manner, for example.
In the above example numbers are decreasing by one.
Repeating Pattern:
In repeating pattern numbers are repeated in a certain manner, for example.
In the above example 1 and 2 are appearing one by one.
SHAPE PATTERNS
We can make a pattern with shapes.
In shape pattern shapes are repeated in a particular manner.
Examples:
Patterns given above are based on repetition of shapes.
Turning Shapes
A shape can be turned up, down, left, right again and again. We can see turning shape patterns in art and fabrics.
Examples:
TILES PATTERNS
The tiles which cover the floor of your house creates a pattern. The method of putting the tiles together without gaps is called tessellation.
Examples:
Amazing Facts
LEARNING OBJECTIVES
This lesson - will help you to:
understand the concept of time.
learn how to read time.
study about calendar and how to find a particular day and date in calendar.
Amazing Facts
All the blinking of eyes in one day equates to having your eyes closed for 30 minutes.
Different part of the world are located in different time zones which means that while you are having breakfast in the morning, someone in another part of the world is having dinner.
The year in which the month of February has 29 days is called a leap year and has 366 days which comes after every 4 years.
The clock is one of the oldest human invention.
QUICK CONCEPT REVIEW
A clock has numbers 1 to 12 on its face and 2 hands. The face of a clock is called dial.
As we have studied in earlier classes that the long hand in the clock is the minute hand and the short hand is called hour hand. The hour hand takes one hour to move from one number to the next.
The minute hand moves faster and takes one hour to move one round that is to start from 12 and to get back to 12.
We use am' for time from 12 midnight to just before noon. We use 'pm' for time from 12 noon to just before midnight.
READING TIME
How will you read a time? How will you know about your recess time? Come let us understand with some examples.
Look at the following clock.
Historical preview
During ancient times, when there was no clock or calendar, time was measured by the position of the sun, moon and other heavenly bodies.
The minute hand is at 12 and hour hand is at 8. Therefore time is 8:00. If it is morning, the time will be 8:00 am. If it is night the time will be 8:00 pm.
Now carefully observe following clock.
The numbers 05. 10, 15 shown on the clock face shows minutes. Count in fives to get these minutes.
Hour hand in given clock is between 1 and 2 and minute hand is at 6. Now multiply 6 by 5 to get the minutes. (\[\text{6 }\times \text{ 5 }=\text{ 3}0\]minutes).
Therefore time is 1 : 30. If it is morning the time will be 1:30 am and if it is noon then we will write 1: 30 pm.
There are 60 minutes in an hour and one minute is equal to 60 seconds
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds.
Real Life Examples
Clock helps us to set alarm to wake up in the morning.
A calendar helps us to know about the festivals and number of holidays in a more...
make difference between shorter and longer lengths.
compare objects by their weights
learn about simple balance.
compare containers by observing their capacity.
order containers as per their capacity.
Amazing Facts
A kilometers is less than a mile.
A small car weights about 1 tonn as 1 tonn = 1000 kilograms
QUICK CONCEPT REVIEWMESURENENT OF LENGTHHave you ever thought, how we can compare lengths of the two things? We can compare the lengths of two things by looking at them.Out of the two chocolates shown, which one is longer?It is easy to compare the length by keeping them side by side.How can we measure length?Let us discuss some methods to measure lengths.Real Life Examples
Measurement helps in taking proper medicine if you are ill, you need to take your medicine in the proper amount and quantity.
Cooking of all forms is based on proper measurements. All the ingredients should be added in appropriate quantity.
You purchase new clothes according to your size and length.
1. Non-standard UnitsWe can use hands pans, foot spans, cubits and paces to measure different lengths. For example, if you have to measure the length of your study table. How will you do it? You can use your hands pan to measure the length of table.Now measure the length of floor of your room using your pace.How much is it?2. Arbitrary UnitsWe can also use objects like match - sticks, pencils, nail-pins etc. to measure the lengths of big objects.For example, if you are asked to measure the length of your bat using a pencil. How will you do it?Here, the length of bat is equivalent to the length of 8 pencils.3. Standard UnitsWhen we use nonstandard units like hand spans foot spans the measurement are bound to be different. Because the lengths of different people are different. So we need to use standard units.We use standard units such as metre (m) and centimeter (cm) for accurate measurements of lengths. We can measure length more...
QUICK CONCEPT REVIEWDIVISIONDivision means equal sharing or making groups of equal things.Let us understand with the help of an example.Maria has 4 rabbits. She has 8 carrots that she wants to distribute equally among them. How many carrots will each rabbit get?This can be solved by using DivisionFirst Maria will give one carrot to each rabbitStep 1Then she finds that she still has some carrots. Now she gives one more carrot to each rabbit. Step 2There is no more carrot left now. Each rabbit gets 2 carrots. So, here Maria equally divides 8 carrots among 4 rabbits. Real Life Examples
When you are eating a pizza, you have to divide the pizza in equal parts so that everyone gets an equal share, you can use division.
If you have 10 chocolates and you want to share it with you want to share it with your 5 friend then you can use the method of division.
Properties of Division
It is the reverse of multiplication.
Division is repeated subtraction.
'-' is the symbol of division.
It does not always happen that a number divides completely. Sometimes some number is left that cannot be divided any further. Such a number is called remainder.
Dividing a number by 1
When we divide a number other than 0 by 1, we get the number itself.For example \[\text{8}\div \text{1}=\text{8}\] \[\text{1}0\text{ }\div \text{ 1 }=\text{ 1}0\]
Dividing O by a number
When we divide zero by a number we get '0' as answer.For example: \[0\div 6=0\] \[0\div 13=0\]
Dividing a number by itself
When we divide a number other than zero by the number itself we get 1 as answer.For example: \[10\div 10=1\] \[13\div 13=1\] \[0\div 0=0\]Historical Preview
An obelus \[(\div )\]is a symbol consisting of a short horizontal line with a dot above and below. The word ‘obelus’ comes from ancient Greek word for a sharpened stick or pointed pillar.
QUICK CONCEPT REVIEWMULTIPLICATIONWhat is a Group?Let us understand with the help of examples.There are 5 pencils in this box. We can say this is group of 5 pencils.Now consider two boxes of pencils.These are 2 groups of 5 pencils each. Equal groups Look at these three groups of birds.There is an equal number of birds in each group i.e., 3.To find the total number of birds, the same number is added again and again. This repeated addition is called multiplication. Amazing FactsAny two number multiplied in any order or sequence gives the same answer.For Example: \[10\times 2=20\]and \[2\times 10=20\]PROPERTIES OF MULTIPLICATION
'x' is the symbol of multiplication.
When we multiply the number, the answer is called the product.
\[4\times 2=8\]In this example, the number 8 is the product.
When a number is multiplied by 0 or 0 is multiplied by a number, then the product is always '0'.
\[0\times 1='0'1\times 0='0'\]Real Life ExamplesIf you want to buy 10 dozens of banana then you can calculate the number of banana as well as its price by the method of multiplication.For Example.1 dozen = 12 bananas10 dozen = \[12\times 10=120\]bananasIf cost of 1 dozen banana is Rs. 10Then const of 10 banana can be calculated as:\[10\times Rs.10=Rs.100\]Let us discuss some examples: 1. Look at the 3 lots of 5 pencils Each lot has 5 pencils, Therefore, 5 + 5 + 5 = 15. or '3 x 5 = 15 or "3 multiplied by 5 is 15'. or '3 times 5 is 15.' 2. How many legs will 5 horses have?Each horse has 4 legs. So, 5 horses will have \[\text{4}+\text{4}+\text{4}+\text{4}+\text{4}=\text{ 2}0\text{ Legs}.\]In this 4 is repeatedly added more...
understand the concept of addition and subtraction.
add and subtract 2-digit numbers.
add and subtract with or without regrouping.
QUICK CONCEPT REVIEW ADDITIONSSuppose you have 3 apples and your friend gives you 4 more apples. How many apples will you have?Here, you need to learn addition.3 + 4 = 7So, you will have 7 apples with you.Let us learn some methods to do addition.Also, you should know that '+' sign is used as a symbol of addition.PROPERTIES OF ADDITION
Adding 0 to a number gives number itself.
For example 3 + 0 = 3
Addition is an associative property.
3 + (2 + 5) = (3 + 2) + 5 = 10
Order of addition does not matter, e.g.
12 + 13 = 13 + 12METHODS OF ADDITION(a) Putting together 4 + 3 = 7Here, we combine the two collections and find the total. Let us take another example 3 + 2 + 1 = 6 (b) Addition without regroupingExamples:1. Add 2 + 6 + 7Here, first you have to add 2 and 6. Then finally add 7 to the sum.2. Add 23 + 12\begin{align} & Arrange\,the\,\,\,\,\,\,23\xrightarrow{{}}\,tens+\,\,\,ones \\ & number\,in\,\,\,\,\,\,\,\,\,\,\,12\xrightarrow{{}}\underline{\,ten\,\,\,\,\,\,+\,\,\,ones} \\ & column\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,ten\,\,\,\,\,\,\,\,\,\,\,\,ones \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,Add\,\,\,\,\,\,\,\,\,\,\,\,Add \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,tens\,\,\,\,\,\,\,\,\,\,\,\,\,ones \\\end{align} You can write 16 and 27 in columns.(c) Addition with regroupingExample:Add 16 + 27
\begin{align} & \,\,\,\,16\xrightarrow{{}}\,\,\,tens\,\,\,+\,\,\,ones \\ & +\,27\xrightarrow{{}}\underline{\,ten\,\,\,\,\,\,+\,\,\,ones} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,ten\,\,\,\,\,\,\,\,\,\,\,\,ones \\\end{align}
13 can be written as 1 ten and 3 ones.So, 3 tens + (1 ten + 3 ones) = (3 tens + 1 ten) + 3 ones. = 4 tens + 3 ones =43Hence, the sum 16 + 27 = 43(d) Addition with carry over methodExample:Add 39+46
Real Life ExamplesThe large numbers are used to keep records of:
Population of a country.
Employees in companies.
Patients in hospitals.
QUICK CONCEPT REVIEW:
The number which is largest in a given series of numbers is known as the largest or greatest numbers.
For example: 12, 32, 49, 60In this example, 60 is the greatest number.
The number which is smallest in a given series of numbers is known as the smallest number.
For example: 5, 35, 40, 75In this example 5 is the smallest number.COMPARING NUMBERSWe use following signs to compare numbers.'>' means greater than'<' means smaller than'=' means equal toLet us take an example. Which number is greater between 20 and 9?Amazing Facts
The number after an even number is an odd number.
From number 0-1000, the letter ‘a’ appears only in the number name of 1000 (one thousand)
\begin{align} & \begin{matrix} T & O \\ 2 & 0 \\\end{matrix} \\ & 2\,digits \\\end{align} \begin{align} & \begin{matrix} T & O \\ {} & 9 \\\end{matrix} \\ & 1\,\,\,digits \\\end{align}
20 has one more digit then 9. so, it is greater than 9.\[\text{2}0\text{ }>\text{ 9}\]Let us take another example.Which is greater 25 or 35?Both 25 and 35 have 2 digits. In this case, greater number at tens place will be checked since 3 > 2.Therefore, since 35 > 25.ORDER OF NUMBERS Let us take an exampleIn the given image I, these children are ready to start a race. They are standing in order from smallest to greatest. When we write numbers from smallest to greatest, they are in increasing or ascending order.As shown in image II, the children are now standing in order from greatest to smallest. When we write numbers from greatest to smallest, they are in decreasing or descending order. Now try to arrange 36, 20, more...
Amazing Facts
From above table it can be concluded:
Example: Raj recorded number of cloudy days for 4 weeks in a month.
Expressing money
Rs. 50 note can further be divided into other notes. Rs. 50 is equivalent to five Rs. 10 notes. Also. Rs. 50 is equivalent to two Rs. 20 notes and one Rs. 10 note.
To purchase a book of worth Rs. 100, Rohit has to pay one Rs. 50 note and five Rs. 10 notes or two Rs. 50 notes. Can you tell in how many number of ways you can Purchase a lead pencil of worth Rs. 12? If you have each of the following type of coins with you.
There can be total 6 number of ways in which you can purchase a lead pencil of Rs. 12.
Addition and Subtraction of Money
Addition
Let us take an example.
Monty bought a packet of crayons Rs.25mdan ice-cream for Rs. 12. How much money did he spent?
Here, you can simply more... 
When a whole object is divided into equal parts, then each part is called a fraction.
In the above example. Part 1 and Part 2 are two fractions of muffin cake.
Part 1 is one half and Part 2 is another half.
Misconcept/Concept
Quarters\[\left( \frac{1}{4} \right)\]and Three-Quarters\[\left( \frac{3}{4} \right)\] .
Let us take an example.
Sam, Jatin, Ravi and Jack bought a chocolate. They cut it into 4 equal parts.
Each part is called one - quarter \[\left( \frac{1}{4} \right)\] .
Suppose, Ravi ate his part of chocolate or we can say he ate \[\left( \frac{1}{4} \right)\] of the choclate.
How much share of chocolate was now left?
3 shares are left. We can say that. \[\frac{3}{4}\]or three-quarters of chocolate was left uneaten and one-quarter of chocolate was eaten by Ravi.
Let us take another example
A circle can be divided into two halves, and four quarter\[\left( \frac{1}{4} \right)\]parts as shown on the left side.
EQUAL AND UNEQUAL PARTS
Suppose circle is divided into 3 equal parts. Then, each part of the circle is its one-third part.
If we take any two shaded parts of these three parts together, we will have two-third of the total part.
It is written as \[\frac{2}{3}\]
The examples we have discussed so far are based on division into equal parts or fractions.
Now let us discuss about division into unequal more... 
In the first pattern you can see one shaded and one unshaded circle getting repeated.
In the second pattern a square is divided diagonally and shaded half.
KINDS OF PATTERNS
(b) A B A B A B A B
2. Increasing Pattern In increasing pattern things increase in size or number.
(a) X XX XXX XXXX
(b) 
3. Decreasing Pattern In decreasing pattern things decrease in size or number.
(a) 
(b) ABCD ABC AS A
NUMBER PATTERNS
In the above example numbers are increasing by two.
Historical Preview
Geometric patterns were the great source of decoration in Islamic art which include calligraphy and vegetal patterns.
Decreasing Pattern:
In decreasing pattern numbers decrease in a certain manner, for example.
In the above example numbers are decreasing by one.
Repeating Pattern:
In repeating pattern numbers are repeated in a certain manner, for example.
In the above example 1 and 2 are appearing one by one.
SHAPE PATTERNS
Patterns given above are based on repetition of shapes.
Turning Shapes
A shape can be turned up, down, left, right again and again. We can see turning shape patterns in art and fabrics.
Examples:
TILES PATTERNS
The tiles which cover the floor of your house creates a pattern. The method of putting the tiles together without gaps is called tessellation.
Examples:
Amazing Facts
READING TIME
How will you read a time? How will you know about your recess time? Come let us understand with some examples.
Look at the following clock.
Historical preview
/7_Mesurement_(Length_weight_and_Volume)_files/image001.gif)
It is easy to compare the length by keeping them side by side.
How can we measure length?
Let us discuss some methods to measure lengths.
Real Life Examples
/7_Mesurement_(Length_weight_and_Volume)_files/image002.gif)
For example, if you have to measure the length of your study table. How will you do it?
You can use your hands pan to measure the length of table.
/7_Mesurement_(Length_weight_and_Volume)_files/image003.gif)
Now measure the length of floor of your room using your pace.
How much is it?
2. Arbitrary Units
We can also use objects like match - sticks, pencils, nail-pins etc. to measure the lengths of big objects.
For example, if you are asked to measure the length of your bat using a pencil. How will you do it?
/7_Mesurement_(Length_weight_and_Volume)_files/image004.gif)
Here, the length of bat is equivalent to the length of 8 pencils.
3. Standard Units
When we use nonstandard units like hand spans foot spans the measurement are bound to be different. Because the lengths of different people are different. So we need to use standard units.
We use standard units such as metre (m) and centimeter (cm) for accurate measurements of lengths. We can measure length more... 
Then she finds that she still has some carrots. Now she gives one more carrot to each rabbit.
Step 2
There is no more carrot left now. Each rabbit gets 2 carrots.
So, here Maria equally divides 8 carrots among 4 rabbits.
Real Life Examples
Look at these three groups of birds.
There is an equal number of birds in each group i.e., 3.
To find the total number of birds, the same number is added again and again. This repeated addition is called multiplication.
Amazing Facts
Any two number multiplied in any order or sequence gives the same answer.
For Example: \[10\times 2=20\]and
\[2\times 10=20\]
PROPERTIES OF MULTIPLICATION
Each lot has 5 pencils,
Therefore, 5 + 5 + 5 = 15.
or '3 x 5 = 15
or "3 multiplied by 5 is 15'.
or '3 times 5 is 15.'
2. How many legs will 5 horses have?
Each horse has 4 legs. So, 5 horses will have
\[\text{4}+\text{4}+\text{4}+\text{4}+\text{4}=\text{ 2}0\text{ Legs}.\]
In this 4 is repeatedly added more... 
4 + 3 = 7
Here, we combine the two collections and find the total.
Let us take another example
3 + 2 + 1 = 6
(b) Addition without regrouping
Examples:
1. Add 2 + 6 + 7
Here, first you have to add 2 and 6. Then finally add 7 to the sum.
2. Add 23 + 12
\begin{align} & Arrange\,the\,\,\,\,\,\,23\xrightarrow{{}}\,tens+\,\,\,ones \\ & number\,in\,\,\,\,\,\,\,\,\,\,\,12\xrightarrow{{}}\underline{\,ten\,\,\,\,\,\,+\,\,\,ones} \\ & column\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,ten\,\,\,\,\,\,\,\,\,\,\,\,ones \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,Add\,\,\,\,\,\,\,\,\,\,\,\,Add \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,tens\,\,\,\,\,\,\,\,\,\,\,\,\,ones \\\end{align}
You can write 16 and 27 in columns.
(c) Addition with regrouping
Example:
Add 16 + 27
\begin{align} & \,\,\,\,16\xrightarrow{{}}\,\,\,tens\,\,\,+\,\,\,ones \\ & +\,27\xrightarrow{{}}\underline{\,ten\,\,\,\,\,\,+\,\,\,ones} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,ten\,\,\,\,\,\,\,\,\,\,\,\,ones \\\end{align}
13 can be written as 1 ten and 3 ones.
So, 3 tens + (1 ten + 3 ones)
= (3 tens + 1 ten) + 3 ones.
= 4 tens + 3 ones
=43
Hence, the sum 16 + 27 = 43
(d) Addition with carry over method
Example:
Add 39+46
