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By the end of this section, you will be able to:
  • Use addition notation
  • Model addition of whole numbers
  • Add whole numbers without models
  • Translate word phrases to math notation
  • Add whole numbers in applications

Before you get started, take this readiness quiz.

  1. What is the number modeled by the base-10 blocks?
    An image consisting of three items. The first item is two squares of 100 blocks each, 10 blocks wide and 10 blocks tall. The second item is one horizontal rod containing 10 blocks. The third item is 5 individual blocks.
    If you missed this problem, review Introduction to Whole Numbers .
  2. Write the number three hundred forty-two thousand six using digits?
    If you missed this problem, review Introduction to Whole Numbers .

Use addition notation

A college student has a part-time job. Last week he worked 3 hours on Monday and 4 hours on Friday. To find the total number of hours he worked last week, he added 3 and 4 .

The operation of addition combines numbers to get a sum    . The notation we use to find the sum of 3 and 4 is:

3 + 4

We read this as three plus four and the result is the sum of three and four. The numbers 3 and 4 are called the addends. A math statement that includes numbers and operations is called an expression.

Addition notation

To describe addition, we can use symbols and words.

Operation Notation Expression Read as Result
Addition + 3 + 4 three plus four the sum of 3 and 4

Translate from math notation to words:

  1. 7 + 1
  2. 12 + 14


  • The expression consists of a plus symbol connecting the addends 7 and 1 . We read this as seven plus one or the sum of seven and one .
  • The expression consists of a plus symbol connecting the addends 12 and 14 . We read this as twelve plus fourteen , or the sum of twelve and fourteen .
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Translate from math notation to words:

  1. 8 + 4
  2. 18 + 11
  • eight plus four; the sum of eight and four
  • eighteen plus eleven; the sum of eighteen and eleven
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Translate from math notation to words:

  1. 21 + 16
  2. 100 + 200
  1. twenty-one plus sixteen; the sum of twenty-one and sixteen
  2. one hundred plus two hundred; the sum of one hundred and two hundred
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Model addition of whole numbers

Addition is really just counting. We will model addition with base-10 blocks. Remember, a block represents 1 and a rod represents 10 . Let’s start by modeling the addition expression we just considered, 3 + 4 .

Each addend is less than 10 , so we can use ones blocks.

We start by modeling the first number with 3 blocks. CNX_BMath_Figure_01_02_019_img-02.png
Then we model the second number with 4 blocks. CNX_BMath_Figure_01_02_019_img-03.png
Count the total number of blocks. CNX_BMath_Figure_01_02_019_img-04.png

There are 7 blocks in all. We use an equal sign (=) to show the sum. A math sentence that shows that two expressions are equal is called an equation. We have shown that. 3 + 4 = 7 .

Doing the Manipulative Mathematics activity “Model Addition of Whole Numbers” will help you develop a better understanding of adding whole numbers.

Model the addition 2 + 6 .


2 + 6 means the sum of 2 and 6

Each addend is less than 10, so we can use ones blocks.

Model the first number with 2 blocks. CNX_BMath_Figure_01_02_016_img-02.png
Model the second number with 6 blocks. CNX_BMath_Figure_01_02_016_img-03.png
Count the total number of blocks CNX_BMath_Figure_01_02_016_img-04.png
There are 8 blocks in all, so 2 + 6 = 8 .
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When the result is 10 or more ones blocks, we will exchange the 10 blocks for one rod.

Model the addition 5 + 8 .


5 + 8 means the sum of 5 and 8 .

Each addend is less than 10, se we can use ones blocks.
Model the first number with 5 blocks. CNX_BMath_Figure_01_02_017_img-02.png
Model the second number with 8 blocks. CNX_BMath_Figure_01_02_017_img-03.png
Count the result. There are more than 10 blocks so we exchange 10 ones blocks for 1 tens rod. CNX_BMath_Figure_01_02_017_img-04.png
Now we have 1 ten and 3 ones, which is 13. 5 + 8 = 13

Notice that we can describe the models as ones blocks and tens rods, or we can simply say ones and tens . From now on, we will use the shorter version but keep in mind that they mean the same thing.

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Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
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s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
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Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
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A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
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Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
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how do you translate this in Algebraic Expressions
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Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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Practice Key Terms 1

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