Vinay Pacha

Addition is defined as the process of combining two or more collections to form a third collection. The objects or collections which are being added are known as Addends and the result of the addition is known as Sum or Total. In this article, of ours we have compiled the Procedure on How to Add Whole Numbers with and without Regrouping, Representation of Addition, Properties of Addition of Whole Numbers, Solved Examples.

Do Read: Addition of Integers

Representation of Addition

The addition is written by using a mathematical operator plus “ + “, which is used to combine the objects and the equal symbol notated as “ = “ gives the total.

Example : 7 + 6 = 13

Seven plus six equals thirteen, where 7 and 6 are addends and 13 is the sum.

Properties of Addition of Whole Numbers

Property 1: Closure Property

Closure property states that any two whole numbers will add up to give another whole number. Suppose let us consider a and b are two whole numbers and they add up to obtain result c which is also a whole number that is a + b = c.

Example: 3 + 4 = 7, therefore 7 is also whole number

Property 2: Commutative Property

The commutative property states that the order of the addition does not change the value of the sum.
Let us consider a ,b are two whole numbers then a +b = b +a.

Example: let a = 5 , b= 7

5 + 7 = 7 + 5 = 12.

Property 3: Associative Property

The associative property states that when we add three or more whole numbers, the value of the sum does not change. We can group the numbers in any manner. The sum remains the same.

Let us consider a,b and c are three whole numbers , then a + (b +c) = (a + b) + c

Example: let a =3, b=4 and c = 6

3 + (4 + 6) = (3 + 4) +6 = 13

Property 4: Additive Property

Additive Property states that when zero is added to any whole number the whole number remains the same. Let us consider a as a whole number, then a + 0 = a = 0 + a.

Example : let a = 8

8 + 0 = 8 = 0 + 8

How to Add Whole Numbers? | Addition of Whole Numbers Step by Step

There are two different scenarios for adding whole numbers. They are along the lines

Case(i)

When the two numbers have the same number of digits

Step 1: Write the numbers vertically in columns.

Step 2: Starting from right to left, that is with one’s place add the digits in each place. If a sum in a place value is more than 9, carry to the next place value.

Step 3: From right to left, continue to add each place value, carrying if needed.

Case(ii)

When the numbers have different numbers of digits.

Step 1: write the numbers vertically in columns, it is easier to write the highest value on the top.

Step 2: Remember to write the lowest number in such a way that to line up the unit’s place of the highest number.

Adding Whole Numbers Examples with Solutions

Example 1:

Add 48 + 54 .

Solution:

Step 1: write the numbers in vertical columns and add the numbers in one’s place
i.e 8 + 4 = 12 , write 2 and carry 1 ten to the tens column

Step 2: Add the values in the tens place and also add the carry 1 ten
i.e 4 + 5 + 1 = 10

Therefore, the sum is 102.

Example 2:

Add 234 + 345.

Solution:

Step 1: write the numbers in vertical columns and add the numbers in one’s place
i.e 5 + 4 = 9 ( no carry)

Step 2: add the values in tens place
i.e 3 + 4 = 7 (no carry)

Step 3 : Add the values in hundreds place
i.e 2 + 3 = 5(no carry)
The sum is 579

Example 3:

Add 1046 + 2357

Solution:

Step 1: Add the values in ones place
i.e 6 + 7 = 13, write 3 and carry 1 ten to the tens place

Step 2: Add the values in the tens place and the carry forwarded

i.e 4 + 5 + 1 = 10, write 0 and carry 1 hundred to the hundreds place

Step 3: Add values in the hundreds place and also the carry forwarded
i.e 0 + 3 + 1 = 4(No carry)

Step 4: Add values in thousands place
i.e 1 + 2 = 3

Therefore, the sum is 3403

Example 4:
Justin’s family is going on a vacation. He packs 4 bags, his father packs 3 bags and his mother packs 2 bags. How many total bags are they taking on their vacation?

Solution:

Given
Number of bags packed by Justin = 4
Number of bags packed by Justin’s father = 3
Number of bags packed by Justin’s mother = 2
4 + 3 + 2 = 9 bags
Therefore, the total number of bags taking on their vacation = 9 bags

Example 5:

Add 35 + 234?

Solution:
Step 1: Write the highest number on the top and add values in one’s place
i.e 5 + 4 = 9(No carry)
Step 2: Add the values in the tens place
i.e 3 + 3 =6(No carry)
Step 3: Write the remaining 2 hundred value same
The sum is 269

Example 6:
In a bookstore, 356 A-type books and 78 B-type books are sold were sold per day. How many total number of books were sold per day?

Solution:
Given
Number of A type books sold = 356
Number of B type books sold = 78
356 + 78 = 434 books
Therefore, the total number of books sold per day in a bookstore = 434 books

Example 7:

Peter bought 130 chocolates and his brother Stanley bought 80 chocolates. How many chocolates they have?

Solution:

Given
Number of chocolates peter have = 130
Number of chocolates Stanley have = 80
130 + 80 = 210 chocolates
Therefore, the total number of chocolates they both have is 210 chocolates.

In Statistics, the central tendency measures are namely Mean, Mode, and Median. We are using this central tendency to find the average value of the given set of numbers or data. Mean is used to find the average value of the given data. Mode is defined as repeated values of the given data.

The Median is defined as the middle value of the given data. In this article, we learn the definition of median, formulas, how to find the median, solved example problems on Median, advantages of the median, and disadvantages of the median, frequently asked questions on the median. Now, let us learn in detailed one of the measures called Median.

The median is different for different types of distribution. A median is a data or number that is separated by the higher half of a data sample, a probability distribution from the lower half. To find the median, first, the data should be arranged in order of greatest to the least value or least value to the greatest value.

Also Read:

• Mean
• Mode 
• Mean of the Tabulated Data

What is Median in Statistics?

In statistics, Median is the middle value of the given set of data, the data will be arranged in an order. The arranged data or observations can be either in descending order or ascending order.

Median is that the middle number during a sorted list of numbers. The median can be used to determine an approximate average, or mean, but is not be confused with the actual mean. If there is an odd number of data, the median value is the number that is in the middle, below, and above, or starting side and ending side have the same amount or the same size of data.

If there are even numbers of data or observations, then there is no single middle value, then the median is defined to be the middle two values are added and divided by 2. Consider an example of even numbers of data,

Example: Find the median of 2, 4, 6, 7

Solution: Given the data is 2, 4, 6, 7

Now we find the median of the data.

In even numbers of data, there is no middle value. So we can take the middle two values and then divided them by two.

Median = (4 + 6)/ 2 = 10 / 2 = 5.

Therefore, the median of given even data is 5.

Median Formula

To find the median of an odd number of data or observations and an even number of data or observations, we have different formulas. So it is necessary to recognize or identify first if we have the odd number of values or an even number of values in a given data set.

• If the total number of observations is even, then we have the formula to calculate the median. The formula is, Median = [{(n/2)}^th term + {(n/2)+1}^th term]/2 Where ‘n’ is the number of observations.

• If the total number of observations is odd, then we have the formula to calculate the Median. The formula is, Median = {(n+1)/2}^thterm where ‘n’ is the number of observations.

How to find Median in Math?

The median can easily found, in some cases and don’t even require calculations. The steps of finding median are as below,

1. Arrange the data in ascending order it means from the lowest to the highest value.
2. Identifying the number whether it is an even or an odd number of values in the dataset.
3. Based on the results of the previous step, further analysis may follow two distinct scenarios.
4. If the dataset or given data contains an odd number of values, the median is a central value that will split the dataset into halves.
5. If the dataset or given data contains an even number of values, then we can find the two central values that split the dataset into halves. Then, calculate the mean of the 2 central values. That mean value is the median of the dataset.

Advantages of Median

For calculating the median we have some advantages, few of advantages are given below:

1. Median can be calculated in all distributions.
2. Extreme values do not have any impact.
3. Median can be approximately determined with the help of a graph.
4. Median is simple to understand and easy to compute.
5. It can be calculated even if the values of all observations are not known or the data has an open-ended class interval.
6. It is most useful dealing with qualitative data.

Disadvantages of Median

Some of the disadvantages are also there for the median. The disadvantages of the median are:

1. It ignores extreme values.
2. It is not easy to arrange the data in order of magnitude when a large population is involved.
3. Median usually not representative of all values in the distribution.

Example Problems on Median

Example 1:

Find the median of 13, 15, 17, 25, 39?

Solution:

Given the data set is 13, 15, 17, 25, 39

Now we find the median of the value. Before finding the median, first, determine the given data set is an even number or an odd number.

The given data is an odd number. So the median is the middle set of value,

Therefore, the median of the given data set is 17.

Example 2:

Find the median of 2, 3, 5, 6, 7, 8, 12?

Solution:

Given the data set is 2, 3, 5, 6, 7, 8, 12

Now we find the median of the value. Before finding the median, first, determine the given data set is an even number or an odd number.

The given data is an odd number. So the median is the middle set of value,

Therefore, the median of the given data set is 17.

Example 3:

Determine the median of 6, 8, 3, 7, 5?

Solution: 

Given the data set is 6, 8, 3, 7, 5

Now identify the given data as odd data or even data.

The number of observations is odd, so the given data has 5 observations.

The number of observations is n, n = 5

Now arrange the given numbers in ascending order we get,

3, 5, 6, 7, 8

we know the formula, for calculating the median of odd observations is,

Median = {(n+1)/2}^th term

Median = {(5+1)/2}^th term

Median = (6/2) term

So, the 3rd term is 6.

Therefore, the median for the given dataset is 6.

Example 4:

John’s family went through seven different places tour. The price of entry tickets for zoo park differs from place to place. Calculate the median of the ticket cost.

10.79, 12.61, 20.09, 15.84, 19.96, 25.11, 16.75

Solution:

Given the data set is 10.79, 12.61, 20.09, 15.84, 19.96, 25.11, 16.75

Now arrange the given data in ascending order. we get

10.79, 12.61, 15.84, 16.75, 19. 96, 20.09, 25.11

The given data set is the odd number of observations. so the median is the middle of the data.

Therefore, the median of the given data set is 16.75

Example 5:

Determine the median of given even observations of data 2, 4, 6, 8, 11, 14?

Solution: 

Given the even observation data set is 2, 4, 6, 8, 11, 14

Now arrange the given data in ascending order, but the given data is already in ascending order.

The  number of observations, n = 6

We know the formula to calculate the median of even observations is

Median = [(n/2)^th term + {(n/2)+1}^th term]/2

Median = [(6/2)^th term + {(6/2)+1}^th term]/2

Median = (3^rd term + 4^th term)/2

Hence the 3^rd term is 6 and the 4^th term is 8

The median is  = (6+8)/2

= 14/2 = 7

Therefore, the median of the given even data set is 7.

Simple Method for finding Mean without using Median

Given data is 2, 4, 6, 8, 11, 14

Now we find the median of the given data.

Before finding the median, you can arrange the given data in ascending order. But the given data is already in ascending order.

In median, we have an even number of observations, then find the mean of the middle two values.

We know the find the mean or take middle two values and sum is divided by two we get the median value.

Median = (6+ 8 )/ 2

Median = 14 / 2 = 7

Therefore, the given data set median is 7.

Frequently Asked Questions on Median

1. Is it better to use median or average?

Median is determined by ranking the data from largest to smallest and identifying the middle so that there is an equal number of data values larger and smaller than it is. Under these median gives a better representation of central tendency than average.

2. Define the Median?

In statistics, Median is the middle value of the given set of data, the data will be arranged in an order. The arranged data or observations can be either in descending order or ascending order.

3. List the advantages of Median?

1. Median can be calculated in all distributions.

2.Extreme values do not have any impact.

3. Median can be approximately determined with the help of a graph.

4. Median is easy to understand and easy to compute.

4. What is the rule of Median?

Arrange your numbers in numerical order. Count how many numbers you have. If you have an odd number, divide by 2 and the remaining middle data is to get the position of the median number. If you have an even number, take the middle numbers or data sum and divide by 2. The dividend result is the value of the even number median.

5. What are the properties of Median?

The properties of the median are,

1. Median can be applicable for the ordinal level.
2. It may not be an actual observation within the data set.
3. It is not suffering from extreme values because the median may be a positional measure.
4. Median exists in both quantitative data and qualitative data

6. Where the Median is used?

1. The exact midpoint of the data or value distribution is needed.

2. There extreme values or data in the distribution

Are you interested to know the facts about subtraction? This page helps you to get full knowledge on Subtraction. Here you will find entire information such as Definition, Facts of Subtraction. Get to know the cool facts about subtraction as a part of your learning try to apply them to your real-time math problems so that you can obtain the solutions quickly. You can understand the basic subtraction facts clearly with our clear-cut explanations provided.

Do refer: Facts about Addition

Subtraction – Definition

Finding the difference between two numbers is called Subtraction.’-‘ sign is used to represent subtraction.  Subtraction is the opposite of Addition. Every addition problem can be rewritten as Subtraction. For Example 75-30=45, 60-30=30 etc.

Interesting Facts about Subtraction

1. Subtraction with small numbers can be done horizontally. For example 25-5=20, 85-10=75,40-10=30 etc.

2. Subtraction is done vertically with large numbers. Numbers are written under place value. For example

Th     h    t    u

4     6      7    9

-3     4      5     6

——–——–——–

1      2        2     3

——–——–——–

To get the predecessor of the number ‘1’ is subtracted. For Example

3 6 8

–   1

——–——–

3 6  7

——–——–

4. Zero subtracted from any number does not change the value. For example

3 6 8

–  0

——–——–

3 6 8

——–——–

5. Minuend is the number from which the other number is to be subtracted. The number that is subtracted is called the subtrahend and the result is called the difference. Minuend, Subtahend, the difference are parts of the Subtraction problem.

Example           6   4    3

-3    2    1
——–——–——–

3     2     2

——–——–——–

Here 643 is called minuend,321 is called subtrahend.322 is called the difference.

6. To find the missing subtrahend, the difference is subtracted from the minuend.

Minuend – difference = subtrahend.

Example:

8   4

–  —    —
——–——–

4      2

——–——–

Here 8,4 is called Minuend.

4,2 is called the difference.

working:

8   4

-4   2

——–——–

4   2

——–——–

7. For finding the missing minuend, the difference is added to the subtrahend.

Difference + subtrahend = minuend

Example:

…  …

-2  1

——–——–

6    3

——–——–

Working:

6      3

+ 2    1

——–——–

8      4

——–——–

8 4 is the missing minuend.

6   3 is the difference.

2 1 is the subtrahend.

8. Subtracting 1 from a number means counting down the number.

For example 5-1=4, 8-1=7, 4-1=3 etc.

9. Any number subtracted from itself is always Zero. This is called Self Subtraction.

For example 4-4=0, 7-7=0 etc.

How to Subtract a Large Number from a Small Number?

To subtract a large number from a small number follow the borrow method.

Example :

For example, consider the numbers 8463 and 5665 for subtraction.

Solution:

1. Arrange the numbers according to the place values. Start subtracting from units place. Since we can not subtract 5 from 3 borrows ten from tens digit. Now 13-5=8. Write 8 under units place.

5      13

8    4     6      3

-5     6     6      5

——–——–——–

8

——–——–——–

2. We can not subtract 6 from 5 so borrow and then subtract 6.Now 15-6=9.Write 9 under tens place.

3        15     13

8     4      6      3

-5     6      6      5

——–——–——–

9      8

——–——–——–

3. We can not subtract 6 from 3 so borrow and then subtract. Now 13-6=7.Place digit 7 under hundreds digit.

7    13      15  13

8      4     6     3

-5     6    6      5

——–——–——–

7         9    8

——–——–——–

4. Subtract 5 from 7.Write 2 under thousands digit. Now the difference is 2798.

7       13      15    13

8        4        6       3

-5         6        6       5

——–——–——–——–

2        7          9         8

——–——–——–——–

FAQ’s on Subtraction Facts

1. What is Subtraction?

To find the difference between two numbers is called subtraction.

2. What is Minuend?

The minuend is the number from which the other number is to be subtracted.

3. What is Subtrahend?

Subtrahend is the number that is subtracted.

4. How to find the missing minuend?

For finding the missing minuend, the subtrahend is added to the difference.

5. How to find missing Subtrahend?

For finding the missing subtrahend, the difference is subtracted from the minuend.

6. What are the parts of the Subtraction Problem?

The parts of the subtraction problem are Subtrahend, minuend, and the difference.

7. What is the Difference?

The result of the subtraction is called the difference.

If you are searching for four-digit number word problems, you have landed on the correct web page that gives the information regarding how to solve word problems on four-digit numbers. You can also see the solved examples of word problems on four-digit numbers. Try to practice using these 4 Digit Problems and test your knowledge and improvised on the area accordingly.

Read More:

• Addition of 4-Digit Numbers
• Addition of 5-Digit Numbers

Word Problems on Four-Digit Numbers

Here we will solve some of the word problems on 4-digit numbers. Apply the same method for solving the word problems on 4-digit numbers.

Example 1:

In a school, there are 4530 boys and 6890 girls. How many students are there in the school?

Solution:

Number of boys in the school=4530

Number of girls in the school=6890

Therefore, the total number of students in the school=4530+6890=11,420.

Example 2:

In a garden, there are 5200 red roses, 2040 white roses, and 1000 orange roses. How many roses are there in the garden?

Solution:

Number of red roses=5200

Number of White roses=2040

Number of orange roses=1000

Total number of roses in the garden=5200 + 2040+1000=8,240.

Example 3:

In a village, there are 6050 males and 5678 females. What is the population in that village?

Solution:

Number of males in the village=6050

Number of females in the village=5678

The total population in that village=11,728.

Example 4:

In a library, there are 5420 computer books,3560 chemistry books, and 4289 English literature books. How many books are there in the library?

Solution:

Number of computers books=5420

Number of chemistry books=3560

Number of English books=4289

Therefore, the Total no of books in the library=5420+3560+4289=13,269.

Example 5:

In a School, there are 6000 children. If 3250 are boys, How many are girls?

Solution:

Total no of children in the school=6000

Total no of boys=3250

Therefore, the total no of girls=6000-3250=2750.

Example 6:

There are 8560 rice bags in the godown.5200 are taken out for distribution. How many bags are left in the godown?

Solution:

Total no of rice bags in the godown=8560

No of rice bags taken out for distribution=5200

Therefore, The total No of rice bags that are left=8560-5200=3,360.

Example 7:

There are 5000 rice bags and 6040 wheat bags in the godown.2000 rice bags are taken out for distribution. How many bags are there in the godown?

Solution:

No of rice bags in the godown=5000

No of rice bags taken out for distribution=2000

Total no of rice bags in the godown=5000-2000=3000

no of Wheat bags in the godown=6040

Total no of bags in the godown=3000+6040=9040.

Example 8:

There are two friends. one friend has 1050 rice bags and the other friend has 3050 wheat bags. Two friends contain how many bags?

Solution: 

No of rice bags=1050

No of wheat bags=3050

Two friends contain bags=1050+3050=4,100.

Example 9:

If two four-digit numbers are added the sum is 4000. One number is 1000. Find out the other number?

Solution:

The sum of the two numbers = 4000.

one number=1000.

The Other number=4000-1000=3000.

Example 10:

In a village, there is a 5000 population.2030 are doing jobs and gone out of the village. How much population does the village have?

Solution: 

no of population=5000

no of people going out of the village=2030

Total no of the population in the village=5000-2030=2970.

Example 11:

In an election, the number of votes polled is 8000.200 people are not voted due to various reasons. How many people are there in the village?

Solution:

The number of votes polled=8000.

People who are not voted=200

Total no of people in the village=8000+200=8200.

If you are confused about how to add five-digit numbers? This article gives you clarity on the addition of five-digit numbers. Here you can find the definition of a five-digit number, the addition of the five-digit number with and without carryforwards. You can have a better understanding by going through the article completely. You can also check the examples on the addition of five-digit numbers with answers in the further modules.

Do Refer: Addition of Four-Digit Numbers

Five-Digit Numbers – Definition

Five-Digit numbers contain only five digits. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are the digits. Every digit in the number has a place value. The place value of the number starts from right to left are units, tens, hundreds, thousands, ten-thousands, lakhs, etc. The face value of single-digit numbers is the same.

How to Add Five-Digit Numbers? | Addition of Five-Digit Numbers

The addition of a five-Digit Number is the same as the addition of a two-digit,three-digit,four-digit number.

• Arrange the numbers in the place values and then start adding from units place.
• Write the sum under unit value.
• If the sum is >9, write the last digit under ones and carry forward another digit under tens. Add the tens digit along with carryforward.
• If the sum is greater than 9 write the last digit under tens and carry forward another digit to hundreds. Add the hundreds digit along with carryforwards.
• If the sum is greater than 9,  place the last digit under hundreds and carry forward another digit to thousands.
• Add the thousands digit along with the carry forward. If the sum is greater than 9,  write the last digit under thousands and carry forward another. Add the ten thousand’s digit along with the carry forward. Place the digits under ten thousand.

Consider some of the examples for a better understanding of the Concept Addition of Five Digit Numbers.

Five Digit Numbers Addition Examples

Example 1:

Add the five-digit numbers 54328,45571. Find the sum?

Solution:

Tth      Th       H          T        O

5         4        3          2        8

+ 4        5         5         7         1

——–——–——–——–——–——–

9          9           8           9          9

——–——–——–——–——–——–

Example 2:

Add the five-digit numbers 35847,14562. Find the sum?

Solution:

1. Arrange the numbers and start adding the digits from ones.

3    5    8    4    7

+     1    4    5   6    2

——–——–——–——–

9

——–——–——–——–

2. Add the digits in the tens place. Since the sum is greater than 9, place the last digit 0 under tens place and carry forward 1to hundreds digit.

1

3     5       8       4       7

+1      4       5      6       2

——–——–——–——–——–

0        9

——–——–——–——–——–

3. Add the digits in the hundreds place along with carry forward 1. Since the sum is greater than 9 write the digit 4 under hundred’s place and 1 as carry forward.

1     1

3      5        8          4         7

+1      4         5        6         2

——–——–——–——–——–

4       0         9

——–——–——–——–——–

4. Add the digits in thousand’s place along with carry forward 1. Since the sum is greater than 9 write the digit 0 in thousand’s place and carry forward 1 to ten thousand’s place.

1         1       1

3          5            8           4        7

+1         4           5          6          2

——–——–——–——–——–——–

0           4             0        9

——–——–——–——–——–——–

5. Add the ten thousand’s place along with carry forward 1. write the sum 5 under ten thousand’s place.

1         1            1

3          5            8         4        7

+1         4           5          6        2
——–——–——–——–——–——–

5       0          4        0      9
——–——–——–——–——–——–

Example 3:

Add the 5digit numbers 56148,32751. Find the Sum.

Solution:

5        6       1       4       8

+3         2      7     5       1

——–——–——–——–——–

8       8       8        9    9
——–——–——–——–——–

FAQs on Addition of Five-Digit Numbers

1. From which place will you start adding the numbers?

We will start adding the numbers from units place.

2. What will you do if the sum is greater than 9 in the tens place?

If the sum is greater than 9 put the last digit under tens place and carry forward the other digit to hundreds place.

3. What will you do if there is no carry forward?

write the sum under its place value.

4. Five-digit number consists of how many digits?

The five-digit number consists of five digits.

In this article, we can learn how to calculate the Mode in statistics, its definition, Types of Modes, Advantages, and Example Problems. The purpose of statistics is to make us learn to utilize a restricted sample to make accurate determinations. Statistics deals with the presentation of data, collection of data, and analysis of data or information for a particular purpose.

In statistics to represent the data, we use bar graphs, piecharts, tables, graphs, pictorial representation, and so on. The frequency in statistics tends to represent a set of data by a representative value which would define the entire collection of data. This representative value is known as the measure of central tendency. One such measure of central tendency is the mode of data.

Also, Check Related Articles:

• Mean
• Mean of the Tabulated Data

Mode – Definition

A Mode is defined as the value that appears most frequently in a data set. It is the value that appears the most number of times.  A set of data or values may have one mode, more than one mode, or no mode at all. The central tendency includes the mean, or the average of a set, and the median, the middle value in a set.

Consider an example of mode on statistics is,

Example: Find the mode of a given set of data 4, 3, 3, 6, 7.

Solution: Given the data set is 4, 3, 3, 6, 7.

The mode of the data is 3 because it has a higher frequency it means it will be repeated more time. In this example, the mode value will be repeated two times.

The mode’s main advantage is, it can be applied to any type of data set, and the remaining two central tendencies mean and median can not be applied to nominal data and it is also not affected by outliers. The disadvantage of mode is, it cannot be used for more detailed analysis.

Types of Mode

Based on modes in a data set, Modes are of three types namely:

1. Unimodal
2. Bimodal
3. Trimodal
4. Multimodal

Unimodal: When the given data gas one mode is called Unimodal.

Bimodal: When the given data set has two modes, it is called Bimodal. Consider the example of bimodal is as shown below,

Example: Find the mode of set X = { 1, 2, 3, 3, 4, 4, 4, 5, 6, 6, 6}

Solution: Given the data set is 1, 2, 3, 3, 4, 4, 4, 5, 6, 6, 6

Mode = {4, 6}

The mode of X is 4 and 5 because both 4 and 5 are repeated in the given set those are two modes called bimodal.

Trimodal: When the given data set has three modes, it is called Trimodal. Consider the example of trimodal is as shown below,

Example: Find the mode of the set A = {1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6}

Solution: Given the data set is 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6

Therefore, the Mode is = {2, 5, 6}

The mode of A is 2, 5, 6 because these values repeated, these three modes called Trimodal.

Multimodal: When the given data set has four or more modes is called Multimodal. Consider an example of Multimodal is as shown below,

Example: Find the mean of data set is 2, 3, 4, 5, 5, 5, 7, 6, 9, 9, 9, 12, 12, 12, 10, 1, 1, 1

Solution: Given the data set is 2, 3, 4, 5, 5, 5, 7, 6, 9, 9, 9, 12, 12, 12, 10, 1, 1, 1

Therefore, the Mode is = {5, 9, 12, 1}

The mode of given data is 5, 9, 12, 1 because these values are repeated three times in the data. So, it has more than three modes (or) four modes it is called Multimodal.

Data Series of Mode

Mode is the value that occurs maximum time in the data set or data series. The series are 3 types:

1. Individual Series – The mode of an individual series is defined as simply finding the value or data that occurs a maximum number of times.
2. Discrete Series – In this mode, the value has higher frequencies.
3. Continuous Series or Frequency distribution Series – In this mode, first we need to find the modal class. Modal class is one of the highest frequency classes.

Mode Formula for grouped Frequency Distribution

In a grouped frequency distribution, the mode calculation is not possible for the frequency. To determine the mode of data in such cases we can calculate the modal class. Mode lies inside the modal class. The grouped frequency distribution mode formula is given as,

The mode of grouped frequency distribution formula is shown as above. In the formula,

where,

f₀ = frequency of the category preceding the modal class

f₁ = frequency of the modal class

f₂ = frequency of the category succeeding the modal class

l = lower limit of the modal class

h = size of the class interval

Ungrouped Frequency Distribution Mode

In Ungrouped data, the observations that occur the most will be the mode of the observation. Observations could also be bimodal or multimodal. With frequency distribution, the observations with the highest frequency will be the modal observation.

Example Problems on Mode

Example 1:

Find the mode of 3, 5, 7, 9, 2, 1?

Solution:

Given the values are 3, 5, 7, 9, 2, 1

Now we are finding the mode of given data.

Mode means high-frequency value. But in this example, no value in the data set is repeated more than one time.

Hence, the set of a given data has no mode value.

Example 2:

Find the mode of the data set {2, 3, 3, 3, 4, 5, 5, 5, 7, 8, 8, 8}

Solution: 

Given the data set is 2, 3, 3, 3, 4, 5, 5, 5, 7, 8, 8, 8

Now we find the mode of the given data set.

Mode = {3, 5, 8}

In this, the mode sets are 3, 5, 8, because the values are 3, 5, 8 are repeated. So it has three mode sets. Three mode sets are called Trimodal.

Hence, the mode of given data is 3, 5, 8.

Example 3:

Marks obtained by 30 students of a class are tabulated below. The highest mark is 25. Find the mode?

Marks Obtained	Number of Students
0 – 5	1
5 – 10	4
10 – 15	7
15 – 20	14
20 – 25	4

Solution:

Given the data in the form of tabular format

The total number of students is 30.

The maximum class frequency is 14 and the class interval corresponding frequency is 15 – 20. So, the modal class is 15 – 20.

The maximum class frequency is 12 and the class interval corresponding to this frequency is 20 – 30. Thus, the modal class is 20 – 30.

The modal class of lower limit (l) = 15

Size of the class interval (h) = 5

Frequency of the modal class (f₁) = 14

Frequency of the category preceding the modal class (f₀) = 1

Frequency of the category succeeding the modal class (f₂)= 7

We know the formula of grouped frequency Mode.

Substituting the given values within the formula we get;

Mean = 15 + ((14 – 1) / (2 x 14 – 1 – 7)) = 15 + ((13) / (6)) = 15 + 2. 166 = 17. 166

Therefore, the mode of a given data set is 17. 166.

Example 4: Find the mode of 5, 5, 5, 6, 7, 15, 15, 15, 28, 49 data set.

Solution: Given the data set is 5, 5, 5, 6, 7, 15, 15, 15, 28, 49

Now, we find the mode of the given data set.

As we know, the data set or values have more than one mode it is the mode. If more than one value occurs which is equal to frequency and number of time compares with other values in the data set.

So, Mode = {5, 15}

Therefore, the mode of the given data set is 5, 15.

Frequently Asked Questions on Mode

1. Define the difference between Mean, Mode, and Median?

The difference between the mean, mode, and median is, the mean of a data set is adding all numbers in the data set and then dividing by the total number of values in the set. The median is the middle value when a data set is ordered from least to greatest, and the mode is the number that occurs most often in a data set.

2. How do you find the mode or modal?

To find the modal, or mode, the best way is to put the numbers in order. After that count how many of each number. If the number appears most often that is the mode.

3. List the types of Modes?

Modes are of four types namely:

1. Unimodal
2. Bimodal
3. Trimodal
4. Multimodal

4. What happens when you have two mode sets?

If we have two numbers are appear most often, then the data or value has two modes. This is called Bimodal. If more than two modes then the data will be called multimodal.

5. What are the properties of mode in statistics?

In statistics, the mode is the value that repeatedly occurs in a given set of data. It can also say that the value or number in a data set, which has a high frequency or frequently occurs is called mode or modal value. Mode is one of the three measures of central tendency.

6. What are the merits of Mode?

The mode has many merits, some of them are listed below:

1. Mode is easy to calculate and simple to understand.
2. It is not affected by extremely larger values or smaller values.
3. It can be computed in an open-end frequency table.

Our Roman Numerals Operations Worksheet will help you in practicing and making you efficient in this topic. So our questions are based on roman numerations and their operations. In this Roman Numerals Operations Worksheet, we will solve problems on adding roman numerals, subtracting roman numerals, multiplying roman numerals, and dividing roman numerals. Become a pro by practicing mathematical operations on Roman numerals using our worksheet for free.

Also, Check:

• Worksheet on Roman Numeration
• Worksheet on Comparison of Roman Numerals

1. Solve the following and Add the Roman Numerals

(i) XXVIII + LV

(ii) CV + CLXV

(iii) CLXXXIX + MCXXIV

(iv) XXXVII + XLIV

Solution:

For adding any two Roman numerical we to covert given numbers Roman numerals into Hindi-Arabic numbers.

(i) XXVIII + LV

Let’s solve the equation by initially converting it into Hindu-Arabic numbers.

To do so let’s split our numeral XXVIII = 2(X) + V + 3(I)

As we know what our above numerals stands for let’s substitute them with respective integers = 2(10) + 5 + 3(1)

Add all those integers = 28

Now So the same  LV = L + V

= 50 + 5

= 55

Now that we have values of XXVIII and LV, we can solve them by adding the obtained values.

So, XXVII + LV = 28 + 55

= 83.

(ii) CV + CLXV

Let’s solve the equation by initially converting it into Hindu-Arabic numbers.

To do so let’s split our numeral CV = C + V

As we know what our above numerals stands for let’s substitute them with respective integers = 100 + 5

Add all those integers = 105

Now do the same as above CLXV = C +L +X + V

= 100 + 50 + 10 + 5

= 165

Now that we have values of CV and CLXV, we can solve them by adding the obtained values.

So, CV + CLXV = 105 + 165

= 270.

(iii)CLXXXIX + MCXXIV

Let’s solve the equation by initially converting it into Hindu-Arabic numbers.

To do so let’s split our numeral CLXXXIX = C + L + 3(X) + IX

As we know what our above numerals stands for let’s substitute them with respective integers= 100 + 50 + 3(10) + (10-9)

Add all those integers = 189

Now do same as above MCXXIV = M + C + 2(X) + IV

= 1000 + 100 + 2(10) + (5-1)

= 1124.

Now that we have values of CLXXXIX and MCXXIV, we can solve them by adding the obtained values.

So, CLXXXIX + MCXXIV = 189 + 1124

= 1313.

(iv) XXXVII + XLIV

Let’s solve the equation by initially converting it into Hindu-Arabic numbers.

To do so let’s split our numeral XXXVII = 3(X) + V + 2(I)

As we know what our above numerals stands for let’s substitute them with respective integers= 3(10) + 5 + 2(1)

Add all those integers  = 37

Now do the same as above XLIV = XL + IV +

= (50 – 10) + (5 – 1)

= 44.

Now that we have values of CLXXXIX and MCXXIV, we can solve them by adding the obtained values.

So, XXXVII + XLIV = 37 + 44

= 81.

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2. Solve given equations by subtracting roman numerals.

(i) CXCII – LXXIX

(ii) MMMCCXI – CCVIII

(iii) XXVIII – XXIV

(iv) CC – VV

Solution:

For subtracting any two Roman numerical we to covert given numbers Roman numerals into Hindu-Arabic numbers.

(i) CXCII – LXXIX

Let’s solve the equation by initially converting it into Hindu-Arabic numbers.

To do so let’s split our numeral LXXIX = L + 2(X) + (X – 1)

As we know what our above numerals stands for let’s substitute them with respective integers =(50)+2(10)+(10-1)

Now let’s add integers = 79

Now do the same as above CXCII = C + XC +2(1)

= 100 + (100 – 10) + 2(1)

= 192

Now that we have values of LXXIX and CXCII, we can solve the equation by subtracting the obtained values.

So, CXCII – LXXIX = 192 – 79

= 270.

(ii) MMMCCXI – CCVIII

Let’s solve the equation by initially converting it into Hindu-Arabic numbers.

To do so let’s split our numeral MMMCCXI = 3(M) + 2(C) + X + I

As we know what our above numerals stands for let’s substitute them with respective integers= 3(1000) + 2(100) + 10 + 1

Now let’s add integers  = 3211

Now do the same as above CCVIII = 2(C) + V +3(1)

= 2(100) + 5 + 3(1)

= 208

Now that we have values of MMMCCXI and CCVIII, we can solve our equation by subtracting the obtained values.

So, MMMCCXI – CCVIII = 3211 – 208

= 3003.

(iii) XXVIII – XXIV

Let’s solve the equation by initially converting it into Hindu-Arabic numbers.

To do so let’s split our numeral XXVIII = 2(X) + V + 3(I)

As we know what our above numerals stand for let’s substitute them with respective integers = 2(10) + 5 + 3(1)

Now let’s add integers = 28

Now do the same as above XXIV = 2(X) + IV

= 2(10) + (5 – 1)

= 24

Now that we have values of XXVIII and XXIV, we can solve the equation by subtracting the obtained values.

So, XXVIII – XXIV = 28 – 24

= 4.

(iv) CC –VV

Let’s solve the equation by initially converting it into Hindu-Arabic numbers.

To do so let’s split our numeral CC = 2(C)

As we know what our above numerals stand for let’s substitute them with respective integers = 2(100)

Now let’s add integers = 200

Now do the same as above VV = 2(V)

= 2(5)

= 10

Now that we have values of CC and VV, we can solve by subtracting the obtained values.

So, CC – VV = 200 – 10

= 190.

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3. Solve given equations by multiplying roman numerals.

(i) CC * CV

(ii) CLX * CLV

(iii) MCV * LX

(iv) LXI * CXIII

Solution:

For multiplying any two Roman numerical we need to convert the given numbers Roman numerals into Hindu-Arabic numbers.

(i) CC * CV

Let’s solve the equation by initially converting it into Hindu-Arabic numbers.

To do so let’s split our numeral CC = 2(C)

As we know what our above numerals stands for let’s substitute them with respective integers = 2(100)

Solve the equation = 200

Now do the same as above CV = C + V

= 100 + 5

= 105

Now that we have values of CC and VV, we can our equation solve by multiplying the obtained values.

So, CC * CV = 200 * 105

= 21000.

(ii) CLX * CLV

Let’s solve the equation by initially converting it into Hindu-Arabic numbers.

To do so let’s split our numeral CLX = C + L + X

As we know what our above numerals stands for let’s substitute them with respective integers = 100 + 50 + 10

Solve the above equation = 160

Now do the same as above CLV = C + L + V

= 100 + 50 + 5

= 155

Now that we have values of CLX and CLV, we can solve our equation by multiplying the obtained values.

So, CLX * CLV = 160 * 155

= 24800.

(iii) MCV * LX

Let’s solve the equation by initially converting it into Hindu-Arabic numbers.

To do so let’s split our numeral MCV = M + C + V

As we know what our above numerals stands for let’s substitute them with respective integers = 1000 + 100 + 10

Solve the above equation = 1110

Now do same as above LX = L + X

= 50 + 1

= 51

Now that we have values of MCV and LX, we can solve our equation by multiplying the obtained values.

So, MCV * LX = 1110 * 51

= 56610.

(iv) LXI * CXIII

Let’s solve the equation by initially converting it into Hindu-Arabic numbers.

To do so let’s split our numeral LXI = L + X + I

As we know what our above numerals stands for let’s substitute them with respective integers = 50 + 10 + 1

Now solve the above equation = 61

Now do same as above CXIII = C + X + 3(1)

= 100 + 10 + 3(1)

= 53

Now that we have values of LXI and CXIII, we can solve our equation by multiplying the obtained values.

So, LXI * CXIII = 61 * 53

= 3233.

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4. Solve given equations by dividing roman numerals.

(i) CCL / XXV

(ii) MMM / L

(iii) CXXV / XXV

(iv) MCXI / XI

Solution:

For dividing any two Roman numerical we have to covert the given numbers Roman numerals into Hindi-Arabic numbers.

(i) CCL / XXV

Let’s solve the equation by initially converting it into Hindu-Arabic numbers.

To do so let’s split our numeral CCL= 2(C) + L.

As we know what our above numerals stand for let’s substitute them with respective integers = 2(100) + 50.

Now solve the above equation = 250.

Now do same as above XXV= 2(X) + V.

= 2(10) + 5

= 25

Now that we have values of CCL and XXV, we can solve our equation by dividing the obtained values.

So, CCL / XXV = 250 / 25

= 10.

(ii) MMM / L

Let’s solve the equation by initially converting it into Hindu-Arabic numbers.

To do so let’s split our numeral MMM= 3(M).

As we know what our above numerals stand for let’s substitute them with respective integers = 3(1000).

Now solve the above equation = 3000.

Now do the same as above L= 50.

Now that we have values of MMM and L, we can solve our equation by dividing the obtained values.

So, MMM / L= 3000 / 50.

= 60

(iii) CXXV / XXV

Let’s solve the equation by initially converting it into Hindu-Arabic numbers.

To do so let’s split our numeral CXXV = C + 2(X) + V.

As we know what our above numerals stand for let’s substitute them with respective integers = 100 + 2(10) + 5.

Now solve the above equation = 125.

Now do same as above XXV= 2(X) + V.

= 2(10) + 5

= 25

Now that we have values of CXXV and XXV, we can solve our equation by dividing the obtained values.

So, CXXV / XXV = 125 / 25

= 5

(iv) MCXI / XI

Let’s solve the equation by initially converting it into Hindu-Arabic numbers.

To do so let’s split our numeral MCXI = M+ C + X + I.

As we know what our above numerals stand for let’s substitute them with respective integers = 1000 +100 + 10 + 1.

Now solve the above equation = 1111.

Now do same as above XI = 11

Now that we have values of MCXI and XI, we can solve our equation by dividing the obtained values.

So, MCXI / XI = 1111 / 11

= 101.

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Our Roman Numerals Worksheet will help you in practicing and making you efficient in this topic. So our questions are based on roman numerations and rules that are used in solving them. In this Roman Numerals Comparison Worksheet, you will solve problems related to the comparison of two roman numerals, find the largest and smallest roman numeral among the given roman numbers. Look no further and begin practicing using our Worksheet on Comparing Roman Numerals.

Also, Read: Worksheet on Roman Numeration

Rules for Converting Roman Numerals to Numbers

We have to follow certain rules while converting roman numbers into Hindi – Arabic numerals as mentioned below

• When a roman number is given we have initially split the given number into digit, double-digit, triple-digit, quadruple-digit symbols
• Find the largest Roman numeral by using the decimal value.
• Now if the largest numeral appears first then we have to count how many times it is repeated. Remember a number can’t be repeated more than three times.
• Now if the number is repeated, multiply its value by the number of times it is repeated.
• Now add the value of roman to the value of a decimal number.
• If in case largest numeral appears second then subtract the value of the number before its value.

Rules for Converting Numbers to Roman Numerals

We have certain rules to covert Hindu-Arabic numbers into roman numerical as mentioned below.

• Each symbol can only be repeated three times.
• We have to split the given number into units form.
• Always remember if a smaller number is placed before a larger number, the number has the effect of addition. Which means the smaller number must be added to the larger number.
• And if a smaller number is placed after a larger number then we have to perform subtraction, which means we have to subtract a smaller number from a larger number

1. Compare and find the largest Roman numeral.

(i). MDCCCLXXIX, MDXXVI

(ii)CDXI, MDCCXI

(iii)MCMLX, DCCXLIII

(iv)CLVII, XXIV

(v)XXXVIII, XXV

Solution:

To the largest numeral among given numerals, we have to initially convert those roman numerals into Hindu-Arabic numbers.

We have to repeat the above steps till we get our number.

Now let’s solve our problems.

(i) MDCCCLXXIX, MDXXVI

First let’s covert MDCCCLXXIX = M + D + 3(C) + L + 2(X) + IX

= 1000 + 500 + 3(100) + 50 + 2(10) + 9

= 1879

Now, MDXXVI = M + D + 2(X) + VI

= 1000 + 500 + 2(10) + 6

= 1526

Now that we know MDCCCLXXIX = 1879 & MDXXVI = 1526

Since 1879 is greater than 1526

Answer:  MDCCCLXXIX is larger than MDXXVI

(ii) CDXI, MDCCXI

First let’s covert CDXI = CD + XI

= (1000-100) + 10 + 1

= 911

Now, MDCCXI = M + D + 2(C) + X + I

= 1000 + 500 + 2(100) + 10 + 1

= 1711

Now that we know CDXI = 911 & MDCCXI = 1711

Since 1711 is greater than 911

Answer:  MDCCXI is larger than CDXI

(iii). MCMLX, DCCXLIII

First let’s covert MCMLX = M + CM + L + X

= 1000 + (1000- 100) + 50 + 10

= 1960

Now, DCCXLIII = D + 2(C) + XL + 3(I)

= 500 + 2(100) + (50-10) + 3(1)

= 743

Now that we know MCMLX = 1960 & DCCXLIII = 743

Since 1960 is greater than 743

Answer:  MCMLX is larger than DCCXLIII

(iv). CLVII, XXIV

First let’s covert CLVII = C + L + V + I + I

= 100 + 50 + 5 + 1 +1

= 157

Now XXIV = X + X + IV

= 10 + 10 + 4

= 24.

Now that we know CLVII = 157 & XXIV = 24

Since 157 is greater than 24

Answer:  CLVII is larger than XXIV

(v). XXXVIII, XXV

First let’s covert: CLVII = 3(X) + V +3( I)

= 30 + 5 + 3

= 38

XXV = 2(V)

= 10 + 10 + 5

= 25.

Now that we know CLVII = 38 & XXV = 25

Since 38 is greater than 22

Answer:  CLVII is larger than XXV

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2. Compare and find the smallest Roman numeral.

(i). CMLVI, DLXXII

(ii). LXXXVI, XI

(iii). CXXV, XXV

(iv). CC, VI

(v). CCL, XXVI

Solution:

Now let’s solve our problems.
To the smallest numeral among given numerals, we have to initially convert those roman numerals into Hindu-Arabic numbers.

(i). CMLVI, DLXXII

First let’s covert CMLVI = CM + L + V + I

= 900+ 50 + 5 + 1

= 956

Now, DLXXII = D+ L + 2(X) + 2(I)

= 500 + 50 +2(10) + 2(1)

= 572

Now that we know CMLVI = 956 & DLXXII = 572

Since 572is smaller than 956

Answer:  DLXXII is smaller than CMLVI

(ii). LXXXVI, XI

First let’s covert LXXXVI = L + 3(X) + V + I

= 50 + 30 + 5 + 1

= 86

Now, XI = X + I

= 10 + 1

= 11

Now that we know LXXXVI = 86 & XI = 11

Since 11 is smaller than 86

Answer:  XI is smaller than LXXXVI

(iii). CXXV, XXV.

First let’s covert CXXV = C + 2(X) + V

= 100+ 2(10) + 5

= 125

Now XXV = 2(X) + V

= 2(10) + 5

= 25

Now that we know CXXV = 125 & XXV = 25

Since 25 is smaller than 125

Answer:  XXV is smaller than CXXV

(iv). CC, VI.

First let’s covert CC = 2(C)

= 2(100)

= 200

Now LLVI = 2(L) + V + I

= 2(50) + 5 + 1

= 106

Now that we know CC = 200 & LLVI = 106

Since 106 is smaller than 200

Answer:  LLVI is smaller than CC

(v). CCL, XXVI

First let’s covert CCL = 2(C) + L

= 2(100) + 50

= 250

Now, XXVI = 2(X) + V + I

= 2(10) + 5 + 1

= 26

Now that we know CCL = 250 & XXVI = 26

Since 26 is smaller than 250

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3.Compare and fill in the blank with correct sign (<, >, =)

(i). MMVI ____ MLIX

(ii) XXVIII ____ LV

(iii) 105 ___ CV

(iv) CLXV ___ 165

(v) CLXXXIX ___ MCXXIV

Solution:

To compare any two Roman numerical or any two Hindu-Arabic numbers first we need to find decimal value for those numbers.

(i) MMMVI____ MLIX

First let’s covert MMMVI = 3(M) + V + I

= 3(1000) + 5 + 1

= 3006

MLIX = M + L + IX

= 1000 + 50 + (10 – 1)

= 1059

Now that we know MMMVI = 3006 & MLIX = 1059

As we know 3006 is greater than 1059.

So MMMVI is greater than MLIX

Answer: MMXVI > MLIX

(ii) XXVIII____ LV

First let’s covert XXVIII = 2(X) + V + 3(I)

= 2(10) + 5 + 3(1)

= 28

LV = L + V

= 50 + 5

= 55

Now that we know XXVIII = 28 & LX = 55

As we know 28 is smaller than 55.

So XXVIII is smaller than LX

Answer: MMXVI < MLIX

(iii) 105___ CV

To compare any two digits they have to be in the same format, so let’s covert Hindu-Arabic number 105 into roman numerals.

So 105 = 100 + 5

= CV

Answer: 105 = CV

(iv). CLXV ___ 165

To compare any two digits they have to be in same format, so let’s convert roman numerical CLXV into -Arabic number.

As we already know steps to convert any given roman numerical to Hindu-Arabic digit let’s follow those steps and find out.

Let’s covert CLXV = C + L + V + X

= 100 + 50 + 10 + 5

= 165

Answer: CLXV = 165

(v). CLXXXIX____ MCXXIV

Following above mentioned steps and rules

First let’s covert CLXXXIX = C + L + 3(X) + IV

= 100 + 50 + 3(10) + (5-1)

= 189

MCXXIV = M + C + 2(X) + IV

= 1000 + 100 + 2 (10) + (5 – 1)

= 1124

Now that we know CLXXXIX = 189 & MCXXIV = 1124

As we know 189 is smaller than 1124.

So CLXXXIX is smaller than MCXXIV

Answer: CLXXXIX < MCXXIV

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If you are interested to know how to add four-digit numbers, then this article helps you to get more information regarding the addition of 4-digit numbers. Certain rules have to be followed while adding four-digit Numbers. You can have a better understanding by checking the solved examples.

The addition is the process of calculating the sum of two or more numbers. When adding line up the numbers according to the place value. The numbers which we add are called addends and total is the sum. Adding 0 to sum doesn’t change the sum. Changing the order of addends doesn’t change the sum.

Also, Check: Facts about Addition

How to Add 4-Digit Numbers? | Adding 4-digit Numbers Steps

Follow the steps listed below to add four-digit numbers easily. They are along the lines

• Lineup the numbers according to the place value.
• Add the numbers from units place The sum is placed under unit digit.
• If the sum is>9, Write the one’s digit under the units and carry forward its tens digit to the tens place.
• Add the tens digit. If they are any carry forward add it along.
• Add the hundreds digit. If they are any carry forward add it along.
• Add the thousands digit. If there are any carryforward add it along.

Addition of 4-Digit Numbers Examples

Example 1:

Add 25 and 34?

Solution:

2  5

+3  4
——–

5   9

——–

Here 2,5,3,4 are called operands. 59 is the sum.

Example 2:

Add 8564 and 6693?

Solution:

Th        H         T          O

1              1

8           5         6         4

+6          6         9          3
——–——–——–——–——–—

15            2             5         7

——–——–——–——–——–—

Here we added the addends 4,3 and the sum 7 is placed under one’s digit. We added the addends 6, 9 sum is 15. We write 5 under tens place and carry forward 1 to the hundreds digit. Add the hundreds digit along with the carry forward 1.Place the sum 2 under the hundred’s digit and carry forward 1 to the thousands digit. Add the thousand’s digit along with carryforward 1. Now the sum is 15.

Example 3:

4       5        6        3

+2      4        1         6

——–——–——–——–——–

6        9       7          9

——–——–——–——–——–

1. Sum of ones=3+6=9
2. Sum of tens=6+1=7
3. Sum of hundreds=5+4=9
4. Sum of thousands=4+2=6.Hence sum=6979.

Example 4:

6          7          8          5

+3         2            1        3

——–——–——–——–——–

9         9       9        8

——–——–——–——–——–

1)Sum of ones=5+3=8

2)Sum of tens=8+1=9

3)Sum of Hundreds=7+2=9

4)Sum of thousands=6+3=9

Hence the sum=9998.

Example 5:

3        4       6        7

+0       0       0       0
——–——–——–——–

3          4        6       7
——–——–——–——–

Therefore, adding 0 to a number does not change the number.

Example 6:

1    1

4    8     9    6

+6    3    4     3

——–——–——–

1 1    2    3    9

——–——–——

Start adding the digits from right to left. Add the units place and the sum is placed under units digit. Add the tens digit and the sum is placed under the tens digit. Since the sum is greater than 9 place tens digit under tens and carry forward 1 to the hundreds digit. Add the hundreds digit along with 1 which is carry forwarded. Place the sum under hundreds digit. Since the sum is greater than 9. Place 2 under hundreds digit and carry forward 1 to the thousands place. Add the thousand’s place. Place the sum under Thousands place.

How to Check the Answer of an Addition Sum?

1. From the sum subtract the first addend.

To check this consider the previous example where the addends are 6785 and 3213. The sum is 9998.

9  9  9  8

-6  7  8  5
——–——–

3 2  1 3
——–——–

2. We can subtract the second addend from the sum to get the first addend.

9   9   9   8

-3   2   1   3

——–——–
6    7   8  5
——–——–

FAQ’S on Addition of Four-Digit Numbers

1. Adding 0 to the sum of the four-digit number changes its value?

Adding 0 to the sum of the four-digit value doesn’t change its value.

2. How do you check the sum of two operands is correct?

By Subtracting the first operand from the Sum, we get the second operand.

3. What is the sign of Addition?

+ is the sign of Addition.

4. When adding a 4-digit number when will you carry forward the digit?

If the sum is >9 carry forward the digit.

Are you looking for the information regarding Addition? Here you can find complete information regarding Addition such as Definition, Related Terms, Facts. Get to know the interesting facts about addition in no time and learn how to apply them to your real-time math problems. You can understand the basic addition facts clearly with our clear-cut explanations provided.

Also, Read: Addition of Integers

Addition

When two or more numbers are added together it is called addition. The numbers that are added are called addends and the result to addition is called the sum. In an addition sentence, the addends are added to find the sum. The symbol used to indicate addition is plus(+). The addition of small numbers can be done using your fingers too.

For Example 2+2=4, 5+2=7, 3+3=6.

Addition Sentence

It is a mathematical expression that shows two or more values added together is called Addition Sentence. For example,

3+2=5

3,2 are addends

5 is the sum.

Basic Facts about Addition

Learn all about the Addition Facts by checking out the below points. They are as such

• The addition of small numbers can be done horizontally. 2+3+1=6, 4+2+1=7
• The addition of large numbers can be done vertically under the place value chart.
•  A zero added to a number can not change the place value of a number.
• A zero added to any number does not change the sum. For example, 5+3=8, Here the sum is 8. Adding 0 to 8 doesn’t change the sum.
• If you add one to a number it gives the successor of the number as a sum.
• In an addition, changing the order of addends does not change the sum. For example 2+5+3=10,5+3+2=10,3+2+5=10.
• When adding more than two numbers we can add any two numbers it does not change the sum.
• To find the missing addend in the addition, Subtract the given addend from the sum.

Facts about Addition Examples

1. Add the Numbers 9532+2153+342?

Solution:

1. Write the numbers one below another as per places of the digits.
2. Start adding numbers from units place. The sum is placed under one digit. If the sum is greater than 9,        write the one’s digit under the ones and carry forward its tens digit to the tens column.
3. Add the tens digit. If there was a carry forward digit add it along.

Th   H      T       O

9     5      3       2

2     1      5        3

+1      3      4      2

——–——–——–——–
13      0        2          7

——–——–——–——–

2. Add Zero to 564?

Solution:

564

+0

——–

564

——–

3. Add 1 to 745?

Solution:

745

+  1

——–

746

——–

Here 745,1 are addends

746 is the successor.

4. 15+(85+5)=15+90 

15+(85+5)=15+90 = 105 (or)

we can add any two numbers i.e. 15,5 or 85,5

(15+5)+85=105.

5. Find the missing addend in the below example?

3  5

+——–

5     7

——–

Solution:

For finding the missing addend, subtract the given addend from the sum.

5    7

– 3  5

——–

2    2

——–

Addition Facts Examples

1. In a Basket, if there are 30 red balls and 10 blue balls. How many balls were there in the basket?

Add 30 red balls and 10 blue balls. There are 40 balls in the basket.

2. In a garden there are 25 red roses and 10 orange roses. How many roses were there in the garden?

Add 25 red roses and 10 orange roses. There are 35 roses in the garden.

3. In a class there are 50 boys and 50 girls. How many students were there in the class?

Add 50 boys and 50 girls. There are 100 students in the class.

4. In a Box there are 2o blue color chocolates and 40 red color chocolates. How many chocolates were there in the box?

There are 60 chocolates in the box.

FAQ’s on Addition Facts

1. Which sign is used for an addition?

The ‘+’ sign is used for an addition.

2. What we call the result after adding two numbers?

The result after adding two numbers is called a sum.

3. What is meant by addition?

Adding two or more numbers is called addition.

4. What are addends?

The numbers that are added are called addends.

5. Will the sum changes when 0 is added to the number?

The sum does not change, when zero is added.

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