<< Chapter < Page Chapter >> Page >
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to add whole numbers. By the end of this module, students should be able to understand the addition process, add whole numbers, and use the calculator to add one whole number to another.

Section overview

  • Addition
  • Addition Visualized on the Number Line
  • The Addition Process
  • Addition Involving Carrying
  • Calculators


Suppose we have two collections of objects that we combine together to form a third collection. For example,

A group of four dots is combine with a group of three dots to yield seven dots.

We are combining a collection of four objects with a collection of three objects to obtain a collection of seven objects.


The process of combining two or more objects (real or intuitive) to form a third, the total, is called addition .

In addition, the numbers being added are called addends or terms , and the total is called the sum . The plus symbol (+) is used to indicate addition, and the equal symbol (=) is used to represent the word "equal." For example, 4 + 3 = 7 size 12{4+3=7} {} means "four added to three equals seven."

Addition visualized on the number line

Addition is easily visualized on the number line. Let's visualize the addition of 4 and 3 using the number line.

To find 4 + 3 size 12{4+3} {} ,

  1. Start at 0.
  2. Move to the right 4 units. We are now located at 4.
  3. From 4, move to the right 3 units. We are now located at 7.

Thus, 4 + 3 = 7 size 12{4+3=7} {} .

A number line from 0 to 11. An arrow is drawn from 0 to 4, and is labeled 4. An arrow is drawn from 4 to 7 to a dot on the 7, and is labeled 3. There is a plus sign in between the two arrows.

The addition process

We'll study the process of addition by considering the sum of 25 and 43.

25 + 43 ̲ means Vertical math. 2 tens + 5 ones over 4 tens + 3 ones = 6 tens + 8 ones

We write this as 68.

We can suggest the following procedure for adding whole numbers using this example.

The process of adding whole numbers

To add whole numbers ,

The process:

  1. Write the numbers vertically, placing corresponding positions in the same column.

    25 + 43 ̲

  2. Add the digits in each column. Start at the right (in the ones position) and move to the left, placing the sum at the bottom.

    25 + 43 ̲ 68

Got questions? Get instant answers now!
Confusion and incorrect sums can occur when the numbers are not aligned in columns properly. Avoid writing such additions as
25 + 43 ̲
25 + 43 ̲

Sample set a

Add 276 and 103.

276 + 103 ̲ 379 6 + 3 = 9 . 7 + 0 = 7 . 2 + 1 = 3 . alignl { stack { size 12{6+3=9 "." } {} #size 12{7+0=7 "." } {} # size 12{2+1=3 "." } {}} } {}

Got questions? Get instant answers now!

Add 1459 and 130

1459 + 130 ̲ 1589 9 + 0 = 9 . 5 + 3 = 8 . 4 + 1 = 5 . 1 + 0 = 1 . alignl { stack { size 12{9+0=9 "." } {} #size 12{5+3=9 "." } {} # size 12{4+1=5 "." } {} #size 12{1+0=1 "." } {} } } {}

Got questions? Get instant answers now!

In each of these examples, each individual sum does not exceed 9. We will examine individual sums that exceed 9 in the next section.

Practice set a

Perform each addition. Show the expanded form in problems 1 and 2.

Add 4,026 and 1,501.


Vertical addition. 4 thousands + 0 hundreds + 2 tens + 6 ones, over 1 thousand + 5 hundreds + 0 tens + 1 one = 5 thousands + 5 hundreds + 2 tens + 7 ones.

Got questions? Get instant answers now!

Add 231,045 and 36,121.


Got questions? Get instant answers now!

Addition involving carrying

It often happens in addition that the sum of the digits in a column will exceed 9. This happens when we add 18 and 34. We show this in expanded form as follows.

18 + 34 is separated into 1 ten + 8 ones over 3 tens + 4 ones. The sum of the ones column exceeds nine. The sum is 4 tens + 12 ones, which is separated into 4 tens  + 1 ten + 2 ones. This is simplified to 5 tens + 2 ones, which is simplified to 52.

Notice that when we add the 8 ones to the 4 ones we get 12 ones. We then convert the 12 ones to 1 ten and 2 ones. In vertical addition, we show this conversion by carrying the ten to the tens column. We write a 1 at the top of the tens column to indicate the carry. This same example is shown in a shorter form as follows:

18 + 34 = 52. Above the tens column is a carried one. 8 + 4 = 12 Write 2, carry 1 ten to the top of the next column to the left.

Sample set b

Perform the following additions. Use the process of carrying when needed.

Questions & Answers

how can chip be made from sand
Eke Reply
are nano particles real
Missy Reply
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
has a lot of application modern world
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
In the number 779,844,205 how many ten millions are there?
From 1973 to 1979, in the United States, there was an increase of 166.6% of Ph.D. social scien­tists to 52,000. How many were there in 1973?
Khizar Reply
7hours 36 min - 4hours 50 min
Tanis Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now

Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Fundamentals of mathematics' conversation and receive update notifications?