# 3.2 Add integers  (Page 2/4)

 Page 2 / 4

Now let’s see what happens when the signs are different.

Model: $-5+3.$

## Solution

 Interpret the expression. $-5+3$ means the sum of $-5$ and $3$ . Model the first number. Start with 5 negatives. Model the second number. Add 3 positives. Remove any neutral pairs. Count the result. The sum of −5 and 3 is −2. $-5+3=-2$

Notice that there were more negatives than positives, so the result is negative.

Model the expression, and then simplify:

$2+\left(-4\right)$

2

Model the expression, and then simplify:

$2+\left(-5\right)$

−3

Model: $5+\left(-3\right).$

## Solution

 Interpret the expression. $5+\left(-3\right)$ means the sum of $5$ and $-3$ . Model the first number. Start with 5 positives. Model the second number. Add 3 negatives. Remove any neutral pairs. Count the result. The sum of 5 and −3 is 2. $5+\left(-3\right)=2$

Model the expression, and then simplify:

$\left(-2\right)+4$

−2

Model the expression:

$\left(-2\right)+5$

3

## Modeling addition of positive and negative integers

1. ⓐ 4 + 2
2. ⓑ −3 + 6
3. ⓒ 4 + (−5)
4. ⓓ -2 + (−3)

 ⓐ $4+2$ Start with 4 positives. Add two positives. How many do you have? $6\phantom{\rule{0.6em}{0ex}}$ $4+2=6$
 ⓑ $-3+6$ Start with 3 negatives. Add 6 positives. Remove neutral pairs. How many are left? $3\phantom{\rule{0.6em}{0ex}}-3+6=3$
 ⓒ $4+\left(-5\right)$ Start with 4 negatives. Add 5 negatives. Remove neutral pairs. How many are left? $-1\phantom{\rule{0.6em}{0ex}}4+\left(-5\right)=-1$
 ⓓ $-2+\left(-3\right)$ Start with 2 negatives. Add 3 negatives. How many do you have? $-5\phantom{\rule{0.6em}{0ex}}-2+\left(-3\right)=-5$

1. ⓐ 3 + 4
2. ⓑ −1 + 4
3. ⓒ 4 + (−6)
4. ⓓ−2 + (−2)

1. ⓐ 5 + 1
2. ⓑ −3 + 7
3. ⓒ 2 + (−8)
4. ⓓ −3 + (−4)

## Simplify expressions with integers

Now that you have modeled adding small positive and negative integers, you can visualize the model in your mind to simplify expressions    with any integers.

For example, if you want to add $37+\left(-53\right),$ you don’t have to count out $37$ blue counters and $53$ red counters.

Picture $37$ blue counters with $53$ red counters lined up underneath. Since there would be more negative counters than positive counters, the sum would be negative. Because $53-37=16,$ there are $16$ more negative counters.

$37+\left(-53\right)=-16$

Let’s try another one. We’ll add $-74+\left(-27\right).$ Imagine $74$ red counters and $27$ more red counters, so we have $101$ red counters all together. This means the sum is $\text{−101.}$

$-74+\left(-27\right)=-101$
 $5+3$ $-5+\left(-3\right)$ both positive, sum positive both negative, sum negative When the signs are the same, the counters would be all the same color, so add them. $-5+3$ $5+\left(-3\right)$ different signs, more negatives different signs, more positives Sum negative sum positive When the signs are different, some counters would make neutral pairs; subtract to see how many are left.

Simplify:

1. $\phantom{\rule{0.2em}{0ex}}19+\left(-47\right)\phantom{\rule{1em}{0ex}}$
2. $\phantom{\rule{0.2em}{0ex}}-32+40$

## Solution

ⓐ Since the signs are different, we subtract $19$ from $47.$ The answer will be negative because there are more negatives than positives.

$\begin{array}{c}19+\left(-47\right)\\ -28\end{array}$

ⓑ The signs are different so we subtract $32$ from $40.$ The answer will be positive because there are more positives than negatives

$\begin{array}{c}-32+40\\ 8\end{array}$

Simplify each expression:

1. $\phantom{\rule{0.2em}{0ex}}15+\left(-32\right)\phantom{\rule{1em}{0ex}}$
2. $\phantom{\rule{0.2em}{0ex}}-19+76$
1. ⓐ −17
2. ⓑ 57

Simplify each expression:

1. $\phantom{\rule{0.2em}{0ex}}-55+9\phantom{\rule{1em}{0ex}}$
2. $\phantom{\rule{0.2em}{0ex}}43+\left(-17\right)$

1. ⓐ −46
2. ⓑ 26

Simplify: $-14+\left(-36\right).$

## Solution

Since the signs are the same, we add. The answer will be negative because there are only negatives.

$\begin{array}{c}-14+\left(-36\right)\\ -50\end{array}$

Simplify the expression:

$-31+\left(-19\right)$

−50

Simplify the expression:

$-42+\left(-28\right)$

−70

anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
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
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
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.
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?
of graphene you mean?
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
Porter
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.
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
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.
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.
What is the expressiin for seven less than four times the number of nickels
How do i figure this problem out.
how do you translate this in Algebraic Expressions
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?