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By the end of this section, you will be able to:
• 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 $\text{base-10}$ 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 .

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.

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. $12+14$

## Solution

• 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 .

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

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

## Model addition of whole numbers

Addition is really just counting. We will model addition with $\text{base-10}$ 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. Then we model the second number with 4 blocks. Count the total number of blocks.

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

Model the addition $2+6.$

## Solution

$2+6$ 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. Model the second number with 6 blocks. Count the total number of blocks There are $8$ blocks in all, so $2+6=8.$

Model: $3+6.$

Model: $5+1.$

When the result is $10$ or more ones blocks, we will exchange the $10$ blocks for one rod.

Model the addition $5+8.$

## Solution

$5+8$ 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. Model the second number with 8 blocks. Count the result. There are more than 10 blocks so we exchange 10 ones blocks for 1 tens rod. 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.

do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
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Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
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Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
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Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
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many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
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after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
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not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
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this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
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how did you get the value of 2000N.What calculations are needed to arrive at it
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Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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