Vinay Pacha

Are you confused about division? This article gives you information about division. It also explains the definition of division, the sign of the division, terms like Dividend, Divisor, Quotient, and Remainder, Facts about Division. You can also check the examples for a better understanding of the concept.

Also, refer:

• Facts about Multiplication
• Facts about Addition
• Facts about Subtraction

Division – Definition

It is one of the four basic arithmetic operations which gives the result of sharing. In this method, the group of things is distributed into equal parts. There are a lot of signs that people used to indicate division. The most common signs are ‘%’, and back slash’ /’. Some members also write one number up and another number down with a line between them.

In the division Equation, there are Four parts namely 1. Dividend 2. Divisor 3.Quotient,4.Remainder.The dividend is the number you are dividing up. The divisor is the number you are dividing up. The quotient is the answer. The remainder is the part of the dividend that is remained after division. The division is the inverse of Multiplication.

Example: 24%4=6.

24 is the Dividend.

4 is the Divisor.

6 is the Quotient.

Interesting Facts about Division | Division Facts Ideas to Learn

Here we will discuss the facts about division explained by considering few examples. They are along the lines

• When dividing the number by 1, the answer will always be the same number. It means if the divisor is 1, the quotient will always be equal to the dividend such as 50 ÷ 1= 50.
• Division by 0 is undefined. For example 25/0=undefined.
• The division of the same numerator(dividend) and Denominator (divisor) is always 1. For example: 4 ÷ 4 = 1.
• In a division sum, the remainder is always lesser than the divisor. For Example, 16%3 remainder is 1. 1 is smaller than 3.
• The dividend is always equal to the product of the divisor and the quotient with the addition of the remainder. Dividend=(Divisor × Quotient) + RemainderFor example 16%3 

   

  (3*5)+1=16

15+1=16

16=16

• The divisor and the quotient are always the factors of the dividend if there is no remainder. For Example 15%3=5

15*5=3

3*5=15

• The dividend is always a multiple of the divisor and the quotient if there is no remainder.  For Example 40%8=5 5*8=40, 8*5=40.

FAQs on Facts of Division

1. What is division?

In this method, the group of things is distributed into equal parts.

2. What is the sign of division?

The sign of division is %, backslash( /).

3. What will be the Quotient when the dividend and divisor are the same? 

The quotient of the same dividend and divisor is always 1.

4. What will be the Remainder when the dividend and divisor are the same?

The Remainder is zero when the dividend and divisor are the same.

5. In a division,  does the remainder is always lesser than the divisor?        

In a division,  the remainder is less than the divisor. If it is larger than the divisor, it means that the division is incomplete.

6. How to check the division if it is correct or not?

In division, the dividend is always equal to the product of the divisor, quotient with addition to the remainder.

Dividend=(Divisor × Quotient) + Remainder

Before learning the number five, every student or preschooler kid has to identify the numbers from 1 to 4 and know how to write the numbers 1 to 4 in words. In this article, we can gain the simple tricks to write the number five easily and learn how to write the number five in words. On this page, we can download the number five worksheet for free of cost. Take the downloaded number five worksheet printout which is useful for preschoolers and homeschoolers while learning the numbers in numeric numbers and words.

In this article, we learn how to write number five, trace and learn of number five, the advantages of learning number five, and numbers from 1 to 10 worksheets also available in this section.

How to Write Number 5? | Number Five Worksheet

Parents and teachers are suggested to help your child to learn the number five by writing it. So, download this number five worksheet to learn the numbers playfully because kids interested and love to play. At the starting stage children feel difficult to learn and remember the numbers. If you give the numerical numbers in picture form, children can learn easily and identify the numbers fastly. The below figure is how to write number five in numeric number and we have step also how to write number five in the first figure.

The above consists of five bells, five eggs, five Lollipops, and five oranges in that figure first two are filled, and the remaining two are blank only, so we can that two for your kid’s practice purpose. It is a decent thing if your child gets accustomed to practicing on the worksheet with a pencil. The above-mentioned three lines on the worksheet will help to enhance their handwriting skills. Parents and teachers guide the students to follow the instructions and rewrite the number five.

How to Number 5 in Words? | Trace and Learn to Write Number Five

Assist the students and kids to practice number five as many times as possible for a quick understanding of the topic. Many of the children don’t prefer to write while they’re playing. At that point, you need to show this handy Worksheet on number 5 and teach them the way to write the quantity joyfully. So that time kids will never feel they are learning something forcefully. So, parents and teachers try to engage your kid in learning numbers with the assistance of our free Number 5 Preschool worksheet.

We must be writing the number five in words with kids in between the above three spacing lines then we have good handwriting. Learning of five is very important and it has an important role in mathematics.

Interesting Facts to Learn about Number 5

The important facts about learning of number 5 are mentioned in the below section.

• 5 is an odd number.
• The set of natural numbers, 5 appears before four. The number after 5 is 6.
• Five is a prime number.
• It is also a Fibonacci number.
• Five is no ordinary number.
• The physical body also seems to follow that number five, we’ve five fingers on each hand and five toes on each foot.
• We even have the five senses: sight, smell, taste, touch, and hearing, and thus five sensory organs: eyes, nose, tongue, skin, and ears.

No longer ditch the math workbooks and printables, take the help of our Preschool Math Activities and teach your kid counting, math facts, number sense in an interactive way.

Read, More Worksheet Numbers:

Worksheet on Number One	Worksheet on Number Two	Worksheet on Number Three
Worksheet on Number Four	Worksheet on Number Six	Worksheet on Number Seven
Worksheet on Number Eight	Worksheet on Number Nine	Worksheet on Number Ten

Are you confused about the column method multiplication? you landed on the correct page where you will get full information about column method multiplication. This includes the definition of the column method multiplication, steps to follow the column method multiplication. You can also find examples of column method multiplication by completely going through this article.

Do Refer: Expansion Method of Multiplication

Column Method Multiplication | Long Multiplication

In column method multiplication, One number is written underneath another number and the numbers are multiplied together. It is also called long method multiplication.

For example 3  5

*2  5

——–——–——–

8    7   5

——–——–——–

Column Method Multiplication 3 Digit by 2 Digit

The steps to be followed for the column method multiplication of a three-digit number by a two-digit number is  as follows:

1. Multiply the one’s digit of the number by one’s digit of the multiplier.
2. Multiply the tens digit of the number by one’s digit of the number.
3. Multiply the Hundred’s digit of the number by one’s digit of the multiplier.
4. Multiply the one’s digit of the number by the tens digit of the multiplier.
5. Multiply the tens digit of the number by the tens digit of the number.
6. Multiply the Hundred’s digit of the number by the tens digit of the multiplier.
7. Add the products.

The same procedure has to be followed for the multiplication of the two-digit number by the two-digit number.

Examples of Column Method Multiplication

Example 1:

Multiply 53, 23 by column method multiplication.

Solution:

1. Multiply the multiplicand by one’s digit of the multiplier.

5 3

*3ones

——–——–—

1  5  9

——–——–—

2. Multiply the multiplicand by tens digit of the multiplier.

5   3

*2tens

——–——–——–

1   0   6

——–——–——–

3. Add the products.

159 ones+106 tens

=159*1+106*10

=159+1060

=1,219.

The product of 53,23 is 1,219.

It means   5   3

*   2  3

——–——–——–——–

1      5      9               —->   53*3=159

1         0       6     0               —->  53*20=1060

1

——–——–——–——–——–

1         2       1       9                   ——>53*23=1219

——–——–——–——–——–

Example 2:

Find Multiplication of 455,32 by column method multiplication?

Solution:

1. Multiply the multiplicand by one’s digit of the multiplier.

4  5   5

* 2 ones

——–——–——–——–

9     1     0

——–——–——–——–

2. Multiply the multiplicand by tens digit of the multiplier.

4    5    5

*3tens

——–——–——–——–

1 3 6  5

——–——–——–——–

3. Add the products.

910 ones+1365tens

=910*1+1365*10

=910+13650

=14560.

Multiplication of 455,32 is 14560.

It means

4    5     5

*3     2

——–——–——–

9     1     0             —->455*2=910

1    3   6    5     0            —–>455*30=13650

1

——–——–——–——–

1    4      5     6    0               —–>455*32=14560

——–——–——–——–——–

Example 3:

Find the multiplication of 1234,34 by column method Multiplication.

Solution:

1. Multiply the multiplicand by one’s digit of the multiplier.

1    2    3   4

*4ones

——–——–——–——–

4   9      3     6

——–——–——–——–

2. Multiply the multiplicand by tens digit of the multiplier.

1   2   3    4

*3 tens

——–——–——–——–

3  7   0    2

——–——–——–——–

3. Add the products.

1234*4ones+1234*3tens

=1234*4+1234*30

=4936+37020

=41,956.

Similarly, we can do multiplication of the four-digit number, multiplication of the five-digit number by two-digit numbers.

Column Method Multiplication of 4 Digit by 2 Digit Examples

Example 1:

Find the multiplication of 34251,62 by column method multiplication?

Solution:

1.Multiply the multiplicand by one’s digit of the multiplier.

3   4  2   5  1

*2

——–——–——–——–

6  8 5     0    2

——–——–——–——–

2.Multiply the multiplicand by tens digit of the multiplier.

3   4  2  5  1

*6 tens

——–——–——–——–

2 , 0 5,  5  0 6

——–——–——–——–——–

3. Add the products.

3425*2 ones+3425*6 tens

=3425*2+3425*60

=68502+ 2055060

= 2,123,562.

Are you confused about the Expansion method of multiplication? This page gives you clear information about the expansion method of multiplication. This will include the Definition of the Expansion method, Steps to follow for the expansion method of multiplication. You can also find examples on the Expansion Method of Multiplication of a 2 digit number by 1 digit number, Expansion method of multiplication of a three-digit number by 1 digit number, Expansion method of multiplication of a three-digit number by 2 digit number.

In the Expansion Method of Multiplication, you will give each digit a value based on its place value within the number. For Example Expanded form of 654=600+50+4.

Do Check:

• Multiplication by Ten, Hundred and Thousand
• Word Problems On Multiplication

Expanded Method Multiplication Steps | How to Multiply using Expansion?

The steps to be followed for the Expansion Method of Multiplication are as follows

1. Write the problem in expanded form.
2. Multiply the digits in the one’s column by the bottom digit and write your answer.
3. Multiply the bottom digit by tens column on top and write the answer.
4. Add the Products.

Here we will solve some examples of multiplication of 2 digit numbers and 3 digit numbers by 1 digit numbers.

Example 1:

Multiply 62, 5?

Solution:

1. Write the expanded form of a number and then multiply by 5.

(60+2)*5

2. Multiply 5 with 2 and 5 with 60 and then add the products.

60*5+2*5

=300+10

=310.

Multiplication of 62,5 is 310.

Example 2:

Multiply 125, 5?

Solution:

1. Write the expanded form of 125 and then multiply with 5

(100+20+5)*5

2. Multiply 5 with 100,20,5 and then add the products.

=100*5+20*5+5*5

=500+100+25

=625

Multiplication of 125,5 is 625.

Multiplying a combination of numbers by 1 digit number will result in several products being added together.

2 digit by 1 digit =2 products added together.

3 digit by 1 digit =3 products added together.

4 digit by 1 digit = 4 products added together.

Example 3:

Find the multiplication of  1254, 6?

Solution:

1.The expanded form of 1254 is 1000+200+50+4.

2.We can write this as follows:

1000 200 50 4

*6

——–——–——–——–

——–——–——–——–

3. Multiply 6 with 4,50,200,1000′ and then add the products.

1000*6+200*6+50*6+4*6

=6000+1200+300+24

=7524

Multiplication of 1254,6 is 7524.

Multiplication of Three-Digit Number by a Two-Digit Number

Follow the steps for multiplication of a three-digit number by a two-digit number.

• Write the three-digit number and two-digit number in expanded form.
• Multiply the one’s digit on the bottom by one’s column.
• Multiply the one’s digit on the bottom by tens column.
• Multiply the one’s digit on the bottom by hundreds column.
• Multiply the tens digit on the bottom by one’s column.
• Multiply the tens digit on the bottom by the tens column.
• Multiply the tens digit on the bottom by the hundred’s column.
• Add the products.

Examples of Multiplication of Three-Digit Number by Two-Digit Number

Example 1:

Find the Multiplication of 363 by 26

Solution:

1.Expansion form of 363 is 300+60+3

2.Expansion form of 26 is 20+6.

We can write this as follows:

300  60  3

*20     6

——–——–——–——–

——–——–——–——–

3. Multiply the one’s digit on the bottom by the one’s digit on top. i.e.6*3=18.

4. Multiply the one’s digit on the bottom by the tens digit on top. i.e.6*60=360.

5. Multiply the one’s digit on the bottom by the Hundred’s digit on top. i.e.6*300=1800.

6. Multiply the tens digit on the bottom by the ones digit on top. i.e.20*3=60.

7.Multiply the tens digit on the bottom by the tens digit on top. i.e.20*60=1200.

8. Multiply the tens digit on the bottom by the hundred’s digit on top. i.e. 20*300=6000.

9. Add the products. i.e.12+360+1800+60+1200+6000=9438.

Multiplication of 363,26 is 9,438.

Multiplying a combination of numbers by a 1 digit number will result in several products being added together
3 digit by 1 digit= 3 products added
3 digit by 2 digit= 6 products added
3 digit by 3 digit= 9 products added.

This article helps you know the information regarding the definitions of addition and subtraction. This web page also helps you to understand the word problems on Addition and subtraction. By going through this article completely you can see the solved word problems on addition and subtraction.

Do refer: Word Problems on 4-Digit Numbers

Addition

Take two or more numbers and add them together is called Addition.’+’ sign is used to represent the addition. The numbers that are taken for adding are called addends. The result of the Addition is called Sum.

For Example 7+3=10, 4+5=9.

Here in 1st Example, 7, 3 are called addends.

10 is called sum.

In the second example,4,5 are addends.

9 is called Sum.

Subtraction

Subtraction means finding the difference between two numbers. The ‘-‘ sign is used to represent the subtraction. The parts of subtraction are Minuend, Subtrahend, Difference. The minuend is the number from which the other number is subtracted. The number subtracted from the minuend is called Subtrahend. The result of subtraction is called Difference. For example, 6-2=4.

Here 6 is called Minuend.

2 is called Subtrahend.

4 is called Difference.

Mixed Addition and Subtraction Word Problems

There are no rules to solve the problem easily, but a systematic approach can help us to solve the problem.

Word problems based on addition are two types.

1. When objects of two or more collections are placed together.

2. Increase in number takes place.

Example 1:

Raju has 10 blue color pens and 18 red color pens. How many pens does Raju have?

Solution:

number of blue Color pens=10

number of red color pens=18

Total number of pens=10+18=28.

Example 2:

Sita has 10 chocolates. Her mother gave her 5 chocolates. How many chocolates does Sita have?

Solution:

number of chocolate Sita have=10

Mother given chocolates=5

The total number of chocolates Sita have=10+5=15.

Word Problems based on Subtraction are several types

1. Partitioning: given away, taken away, remove.
2. Reducing: Find out how many have been given away, how much remains.
3. The inverse of addition: How much more to be added.
4. Comparison: More than/less than.

Example 3:

In a godown, there are 1500 rice bags. 600 rice bags are given away for distribution. How many rice bags are there in the godown?

Number of rice bags=1500

Number of rice bags given away=600

Total no of rice bags=1500-600=900.

There are 900 rice bags in the goadown.

Example 4:

Rajesh spent 3000 rs on groceries in April month. He spent an extra 1500 more in may month. How much money does he spend in the two months?

Solution:

Rajesh spent money in April=3000rs.

Rajesh spent money in may=3000+1500=4500rs.

Rajesh spends money in both the months=3000+4500=7500rs.

Example 5:

Solve 1235+(8564-3452).

Solution:

The first preference is given to the numbers in the brackets. So subtract 3452 from 8564.

8      5        6         4

-3       4         5         2

——–——–——–——–——–

5          1           1        2

——–——–——–——–——–

Now add the number 5112 to 1235.

5     1      1     2

+1      2       3     5

——–——–——–——–——–

6        3       4      7

——–——–——–——–——–

Example 6:

Subtract 1236 from the sum of 5678+3456.

Solution:

First, add 5678,3456.

1       1     1

5     6      7      8

3      4      5      6

——–——–——–——–

9        1       3       4

——–——–——–——–

Now subtract 1236 from 9134.

8   10    12

9     1       3       4

-1      2       3      6

——–——–——–——–——–

7       8        9      8

——–——–——–——–——–

Start subtracting from one’s place. We can not subtract 6 from 4 so borrow it from tens digit and the tens digit is decreased by 1. Now 14-6=8.Write 8 under units place. We can not subtract 3 from 2 so borrow it from hundreds digit and hundreds digit is decreased by 1.Now 12-3=9. Write 9 under tens place. After borrowing from thousand’s place subtract 2 from 10 and write the digit 8 under hundreds place. Subtract 1 from 8 and write the result under thousands place.

Example 7:

Find the number, which is

(i) 3254 greater than 5328.

(ii) 2341 smaller than 7354.

Solution:

(i) The number is 3254 more than 5328.

5   3    2     8

3    2    5      4

Find the number, which is
(i) 1240 greater than 3267.
(ii) 1353 smaller than 5292.

Solution:

(i) The number is 1240 more than 3267

3    2     6     7

1     2      4      0

Find the number, which is
(i) 1240 greater than 3267.
(ii) 1353 smaller than 5292.

Solution:

(i) The number is 1240 more than 3267

1

3     2      6     7

1      2      4     0

——–——–——–——–

4        5        0     7

——–——–——–——–

Therefore, the number=3267+1240=4507.

(ii) 1353 smaller than 5292.

4      12        8     12

5    2      9    2

-1     3      5     3

——–——–——–——–

3      9       3     9

——–——–——–——–

Therefore, the number=5292-1353=3939.

Example 8:

In a village, there is a 26000 population. Men are  15968. Find the women population in the village?

Solution:

Total population of the village=26000.

Men’s population=15968

Women population=26000-15968=10032.

This article gives you the information regarding multiplication definition, how to solve the word problems on multiplication of 2 digit numbers. You can also check the solved examples for a better understanding of the concept.

In multiplication, groups of equal sizes are combined and the result is obtained. Multiplication can be called repeated addition. Multiplication is represented by the Cross symbol, or asterisk ‘*’, or dot’.’.Multiplication has three parts1. Multiplicand 2. Multiplier 3. product  The multiplicand is the number being multiplied by another number. The multiplier is the number that you are multiplying by. When two numbers have multiplied the result we get is called product.

Consider some examples of multiplication of 2 digit numbers. Follow the same procedure for multiplication of 2 digit number by 2 digit number.

Read More: Facts about Multiplication

Word Problems based on Multiplication by 2 Digit Number

Example 1: 

Ram has a pen. The cost of a pen is 50rs. Find the cost of 20 pens?

Solution:

Cost of  a pen=50

cost of 20 pens=50*20=1000.

Therefore, the cost of 20 pens=1000.

Example 2:

A Notebook contains 90 pages. Find out the total no of pages in 50 notebooks?

Solution:

No of the pages in the notebook=90

No of pages in 50 notebooks=50*90=4500.

Therefore, no of pages in 50 notebooks=4500.

Example 3:

Rakesh has a packet that has 25 sweets. Rakesh has 15 such packets. How many sweets does Rakesh contain?

Solution:

No. of sweets in a packet=25

No.of sweets in 15 packets=15*25=375.

so Rakesh has 375 sweets in 15 packets.

Example 4:

Siri saves 90rs every day. How much she saves for 90 days?

Solution:

Siri saves everyday=90

Siri saves for 90 days=90*90=8100.

so Siri saves 8100 in 90 days.

Example 5:

In a school, 30students can accommodate each class. How many students are required to accommodate in 10 such classes?

Solution:

No of students in each class=30

No of the students in 10 such classes=10*30=300

so no of the students in 10 such classes=300.

Example 6:

A Shopkeeper sells 80 chocolates every day. How many chocolates does he sell in April month?

Solution:

The shopkeeper sells chocolates every day=80

The shopkeeper sells chocolates in April month=80*30=2400.

so shopkeeper sells 2400 chocolates in April month.

Example 7:

In a class, there are 90 students. How much money can be collected if each student donates 80 rs for the Drought relief fund?

Solution:

No of students in the class=90

Money collected by 90 students=90*80=7200.

Therefore total money collected by the class=7200.

Example 8:

The water tank capacity is 50 liters. What is the total capacity of water in 50 such tanks?

Solution:

The capacity of the water tank = 50 liters

The total capacity of water in 50 such tanks=50*50=2500.

The total capacity of water in 50 tanks=2500lit.

Example 9:

If there are 50 oranges in one basket, then how many oranges are there in 20 baskets?

Solution:

No of oranges in the basket=50

no of oranges in 20 baskets=50*20=1000.

So total no of oranges in 20 baskets=1000.

Example 10: 

There are 50 rows in a cinema hall and there are 23 seats in each row. How many persons can be seated in the hall?

Solution:

No of rows in a cinema hall=50

No of seats in each row=23

No of persons can accomodate=50*23=1,150.

The total no of persons can accommodate in the hall=1,150.

Example 11:

How many runs will Yuvraj score by hitting 20 centuries?

Solution:

No of runs for a centuary=100.

No of runs scored for 20 centuries=20*100=2000.

Therefore, the total no of runs scored by Yuvraj by hitting 20 centuries=2000.

Wondering how to add two integers, don’t worry you landed upon a perfect page. This page will explain how to add two integers, what are rules to be followed, What are key points you should remember.  Solved examples provided on the Addition of Integers make it easy for you to understand the concept.

Also, Check:

• Addition of Integers on a Number Line
• Representation of Integers on a Number Line

Addition of Integers

Adding whole numbers is pretty easy because there are really only two possibilities. You will be either adding two positive numbers or subtracting two positive numbers. But adding two integers is more complicated because with negative numbers in the mix, there are a lot more possibilities.

Now that we know we have few possibilities. Let’s see what they are.

1. The addition between two positive numbers.
2. The addition between two negative numbers.
3. The addition between a positive and a negative number.

Key Points to Remember while Adding Integers

Remember the below-mentioned key points whenever your performing addition on integers.

• Adding a negative is the same as subtracting a positive number, Which means if we are adding a negative number and subtracting the same positive number. The result obtained will be zero.
• Subtracting a negative is the same as adding a positive, Which means if we are subtracting a negative number and adding the same positive number. The result obtained will be zero.

Rules to Add Integers

Now we know possibilities and key points. Let’s see the rules which we need to follow to perform the addition of integers.

Rule 1: If the sign of both the integers is the same then we need to perform addition, and take the same sign for the obtained result.

Rule 2: If the sign of both the integers is different then you have to subtract those integers and take the sign of the largest integer for the obtained result.

Rules to Add Integers Examples

Example 1: Addition of two positive integers

Add 12 + 88

Solution:

We are adding two positive integers, So according to our rule, we have to add both the integers and take the same sign for the result.

So, 12 + 88 = 100

Answer: 100.

Example 2: Addition of two negative integers.

Add (-78) + (-62).

Solution:

We are adding two negative integers, So according to our rule, we have to add both the integers and take the same sign for the result.

So, (-78) + (-62) = (-140)

Answer: 100.

Example 3: Addition of two integers which are having a different sign.

Add (-105) + (25).

Solution:

We have two integers with different signs, So according to the rule we need to subtract both the integers and take the sign of the largest number for the result.

So, (-150) + 25 = (-80).

(-80)

FAQs on Rules of Addition of Integers

1. Can we add two integers which are having different sing?

Yes, we can add two integers having different sing.

2. What is 0 mean in integers?

Zero, is known as a neutral integer because it is neither positive nor negative.

3.What can be an integer?

An integer can always be a positive or negative whole number and a zero.

4. Can a fraction number be an integer?

No, a fraction number can’t be an integer.

This page will help you understand how the addition of integers is performed using a number line. What are the rules and steps that are to be followed while performing the addition of integers on the number line along with few examples. Solved Examples on Addition of Integers on a Number Line will make it easy for you to understand the problem-solving approach used and then apply it to similar problems you face later on.

Do Read: Representation of Integers on a Number Line

How to Add Integers on a Number Line? | Steps for Adding Integers Using a Number Line

For adding any two integers on a number we have to follow a step-by-step process as following.

1. Initially, we need to draw the number and mark integers accordingly.
2. As we have two numbers, first we have to represent the first number on the number line.
3. Then we have to move as many units as the second number given, move towards the right if the second number is positive, and move towards the left the second number is negative.
4.  After making the required moves with both numbers we will reach our answer.

Rules for Adding Integers on a Number Line

Below are two important that you should always remember when performing addition on a number line.

•  Whenever we are adding a positive integer we move to the right side of the number line because we are increasing in value.
• Whenever we are adding a negative integer we move to the left side of the number line because we are decreasing in value.

Let’s jump into our examples with all possible combinations for better understanding.

Addition of Integers on a Number Line Examples

Example 1:

-3 + 4

Solution:

So we have to start at a negative 3, then we have to add a positive 4.

That means we are increasing in the value, So we are going to move to the right.

As shown in the below image. We stared at -3 and then we are adding a 4 by moving four times towards the right.

So we ended up on positive 1.

-3 + 4 =1

Example 2:

(3) + (-5)

Solution:

In this example, we have a positive 3 and a negative 5. Here we have to start at a positive 3 and then we have to add a negative 5, So here we are decreasing in value. This means we will move to the left side on the number line.

As shown in the below image. We have to start at a positive 3, then move 5 times towards the left side because we are adding a negative 5.

By doing so we ended upon -2.

Example 3:

(-1) + (-8)

Solution:

Here we have a negative 1 and a negative 8. We have two negative numbers, which means we are adding one negative number with another negative number. So we decreasing the value, Which means we will be moving towards the left on the number line.

As shown in the below image. We have to start at a negative 1, then move 8 times towards the left side because we are adding a negative 8.

By doing so we ended up on a negative 9.

Answer: (-1) + (-8) = -9.

Example 4:

6 + 3

Solution:

Here we have a positive 6 and a positive 3. We have two positive numbers. which means we increasing the value, So we will be moving towards the right on the number line.

As shown in the below image. We have to start at a positive 6, then move 3 times towards the right side because we are adding a positive 3.

By doing so we ended up on a positive 9.

6 + 3 =9.

FAQs on Addition of Integers on a Number Line

1. What is the formula for adding integers?

Whenever we are performing addition if two integers are having the same sign add them. if two integers are having different signs subtract them.

2. Can we perform subtraction on integers using the number line?

Yes, we can perform subtraction of integers using a number line.

3. What is an integer?

Any whole number is called an integer. Integers can be positive numbers or negative numbers.

4. How do integers work?

Integers are whole numbers with positive and negative values. We can perform mathematical operations like addition, subtraction, multiplication, and division on integers.

In this article, we will learn one of the data represented in statistics that is a line graph. Statistics deals with the study of collecting data, analyzing the data, interpreting, organizing, and presenting the data. In statistics to represent the information or data, we use bar graphs, piecharts, tables, graphs, picturing, and so on.

Let us learn line graph definition, types of the line graph, examples, how to construct a line graph, and so on. A line graph is a graph used to represent the data in the form of a straight line or curve line of any two quantities of indirect or direct variation.

A line graph is a unique graph that is commonly used in statistics. It represents the change during a quantity with relevance to another quantity.

Also, Read Similar Articles:

• Construction of Pie Chart
• Construction of Bar Graphs

Line Graph – Definition

A line graph may be a kind of chart accustomed show the information that changes over time. We plotline graphs by using several points connected by straight lines. A line graph also called a line chart or line plot. The line comprises two-axis one is the x-axis and another one is the y-axis.

• The x-axis is known as the Horizontal axis.
• The y-axis is known as the Vertical axis.

A line graph or line chart is a chart that shows a line joining several points or a line that shows the relation between the points. The line graph represents quantitative data between two changing variables with a line or curve line that joins a series of successive data points.

Types of Line Graph

Line graphs are 3 different types namely,

1. Simple Line graph.
2. Multiple Line graph.
3. Compound Line graph.

Simple Line Graph: In a simple line graph only one single line is plotted on the graph, it represents the variations of two quantities.

Multiple Line Graph: In multiple line graph consists of more than one single line is plotted on the same set of axes, it represents the same data variations at two different cases.

A multiple line graph is also known as a double line graph. It can effectively compare similar items over an equivalent period of your time.

Compound Line Graph: In this, the information can be subdivided into two or more types of data. This type of line graph is termed a compound line graph. Lines are drawn to indicate the part of a complete. The top line shows the overall and therefore the line below shows part of the whole. The distance between every two lines shows the scale of every part.

Based on the nature of lines with respect to coordinate axes, three different types of line graphs are there,

Vertical Line Graph: In this line graph, representing the line variation is parallel to the y-axis and perpendicular to the x-axis. It means x-axis data is constant and y-axis data is varying (not constant).

Horizontal Line Graph: In this graph, representing the line variation is parallel to the x-axis and perpendicular to the y-axis. This line graph represents x-axis data is changed and the y-axis data is not changing (constant).

Straight Line Graph: In this line graph, the line variation of any two quantities is represented by a straight line. The straight-line graph also known as linear graphs indicates the line variation with curved lines called a curvilinear graph.

A linear function has the form,

y = mx + c, where m and c are constants.

Parts of Line Graph

Several items are associated with the parts of a line graph. A few of the important terms that are associated with line graph are mentioned below,

Title: Every line has a title. The title explains what graph is to be plotted and it gives a brief idea of the quantities being represented.

Labels: The line graph has a label on both the side and the bottom that indicates the type of data is represented in the graph. The x-axis describes the data points on the line and the y-axis describes the numeric value for each point on the line.

Bars: Bars are used to measure the data number.

Data values: Data values are the particular numbers for every piece of information.

Scale: The scale is the numbers that explain the units utilized on the line graph.

Origin: The purpose of intersection on both axes has named the origin. It will be represented by the letter ‘O’. At this point, both the values are variable quantities are zero.

Coordinate Axes: The vertical line and horizontal line that are intersecting each other and mutually perpendicular to each other. These axes are generally labeled as xx and yy. The two quantities are proportional to each other and represent a certain value on the coordinate axes.

How to Construct a Line Graph? | Steps to Make a Line Graph

The following are the steps to construct a line graph using a given data. If we have data tables, then we draw line graphs using tables. Line graphs offer a wonderful visual format of the result data collected over time. To plot the line graph to follow the below steps,

Step 1: Choose a suitable scale using data from the data tables.

Step 2: Draw or construct the horizontal axes and vertical axes which are important in the line graph, and label the scale of vertical axes and horizontal axes.

Step 3: Based on the corresponding values place the points on the graph.

Step 4:  Join the points plotted on the graph with the line segment using the freehand method.

Multiple Line Graph or Double Line Graph

A double line graph may be a line graph with quite one or two lines. A graph that compares two different data over a period of time. A double line graph shows how to change the period of time. The double line graph shows two line graphs within one chart. Double line graphs are used to compare trends and patterns between two different information.

The following are the steps to plot a double line graph or multiple lines graph,

Step 1: First choose the appropriate scale using the data from the data tables.

Step 2: Draw or construct the horizontal axes and vertical axes and label the scale of vertical axes and horizontal axes.

Step 3: Based on the given data, plot the points on the graph for both lines.

Step 4: Join the points plotted on the graph with the line segment separately of both lines using the freehand method.

Step 5: Finally draw two line graphs within one chart.

Line Graph Examples with Explanation

Example 1:

The temperature of a city from 5 am to 8 pm on a day was recorded in the form of a line graph as shown below. Observe the graph and answer the following questions.

(i) At what time the temperature was 40⁰ F?

(ii) What was the maximum recorded temperature?

Solution:

Given the temperature of a city from 5 am to 8 pm in the form of the line graph.

Based on given temperature data we can calculate the given questions,

(i) Given the temperature data in the form of the line graph.

Now we can find the temperature of 40 degrees F timings.

Based on the given line graph, the temperature of 40⁰ F timing is,

The temperature was 40⁰ F at 5 am and from 5 pm to 8 pm.

(ii) Given the data is in the form of the line graph.

Now we find the maximum temperature on the given line graph.

Based on the given data the maximum recorded temperature is,

Therefore, the maximum recorded temperature was 60⁰ F.

Frequently Asked Question’s on Line Graph

1. What are the five types of Graphs?

The five different graphs are Line graphs, Bar graphs, Histograms, Pie charts, Pictorial graphs, and frequency polygons. Graphs are the best way to visualize data and display the data in statistics.

2. How do you explain the line graph?

Line graphs are drawn the independent data on the horizontal axes or x-axis and the dependent data on vertical axes or y-axis. Line graphs are accustomed to tracking changes over a brief period of your time and long periods of your time.

3. What is the use of a Line graph?

The important use of a line graph is to track the changes over a short period of time and a long period of time. It is also wont to compare the changes over an equivalent period of your time for various groups. Line graphs always better to use the line than the bar graphs, whenever small changes exist. They use the road graph plotting the points over the horizontal and therefore the vertical axis. It usually represents the period of time of the information.
4. How do you draw a line graph?

The following are the steps to draw a line graph,

1. Choose a suitable scale using data from the data tables.
2. Draw or construct the horizontal axes and vertical axes which are important in the line graph, and label the scale of vertical axes and horizontal axes.
3. Based on the corresponding values place the points on the graph.
4. Join the points plotted on the graph with the line segment using the freehand method.

5. What is the advantage of a Line Graph?

A Line Graph is a way to summarize how two different types of information are related and how they vary depending on one another.

In this article, you will learn how to write the number two. Here we have a worksheet for free of cost to learn number two writing. Worksheet on number two will help the children to recognize the number name and remember it easily. It helps preschool students to learn the number names in words. You can download this number two worksheet free of cost to help your kids. Teachers can also take the printout of this worksheet to learn the numbers efficiently.

On this page, you can get the free printable worksheets that are useful to learn numeric numbers in words and how to write the numbers from 1 to 10.

How to Write Number Two? | Hand Writing of Number 2

At the starting stage children feel difficult to learn and remember the numbers. So if you give them the numerical numbers in picture form, children can learn easily and identify the numbers fastly. Number 2 means double or we have 2 things or objects. Generally, numbers are used to count objects or things. Suppose an example, When we have 2 biscuits means, the quantity of biscuits is two. So, it is very important for every kid to learn the numeric numbers as soon as possible in an easy method.

The below figure shows the number two representation in object forms as well as how to write number two,

Writing Two in Numbers | Trace and Learn How to Write Two in Word?

Writing the word multiple times is known as Tracing. After practicing tracing, children can write the number two in a numeric way and number two in words on their own. Below tracing figures are on number two both in numeric and word form, so that your children will get habituated easily. Also, this worksheet on the number two helps kids to have more practice. For beginners, who is yet to practice with a pencil this worksheet will be more useful and can be the best way. In tracing we give dotted lines which helps the children to memorize as well as improve their handwriting.

Parents, teachers, students can download this Worksheet on Numbers Two for free of cost. In this worksheet, we can see two shoes, two chappels, two hand gloves, and so on the number two represented on dotted lines. Preschool students are advised to write the number two on the dotted lines so that they can learn the process of writing and can recognize the number easily.

No longer ditch the math workbooks and printables, take the help of our Preschool Math Activities and teach your kid counting, math facts, number sense in an interactive way.

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