# 10.4 Addition of signed numbers

 Page 1 / 1
This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to add signed numbers. By the end of the module students should be able to add numbers with like signs and with unlike signs and be able to use the calculator for addition of signed numbers.

## Section overview

• Addition of Numbers with Like Signs
• Addition of Numbers with Unlike Signs
• Calculators

## Addition of numbers with like signs

The addition of the two positive numbers 2 and 3 is performed on the number line as follows.

Begin at 0, the origin.

Since 2 is positive, move 2 units to the right.

Since 3 is positive, move 3 more units to the right.

We are now located at 5.

Thus, $\text{2}+\text{3}=\text{5}$ .

Summarizing, we have

$\left(\text{2 positive units}\right)+\left(\text{3 positive units}\right)=\left(\text{5 positive units}\right)$

The addition of the two negative numbers -2 and -3 is performed on the number line as follows.

Begin at 0, the origin.

Since -2 is negative, move 2 units to the left.

Since -3 is negative, move 3 more units to the left.

We are now located at -5.

Thus, $\left(-2\right)+\left(-3\right)=-5$ .

Summarizing, we have

$\left(\text{2 negative units}\right)+\left(\text{3 negative units}\right)=\left(\text{5 negative units}\right)$

Observing these two examples, we can suggest these relationships:

$\left(\text{positive number}\right)+\left(\text{positive number}\right)=\left(\text{positive number}\right)$

$\left(\text{negative number}\right)+\left(\text{negative number}\right)=\left(\text{negative number}\right)$

## Adding numbers with the same sign

Addition of numbers with like sign:
To add two real numbers that have the same sign, add the absolute values of the numbers and associate with the sum the common sign.

## Sample set a

Find the sums.

$3+7$

$\left(\begin{array}{ccc}|3|& =& 3\\ |7|& =& 7\end{array}}$ Add these absolute values.

$3+7=10$

The common sign is “+.”

Thus, $\text{3}+\text{7}=+\text{10}$ , or $\text{3}+\text{7}=\text{10}$ .

$\left(-4\right)+\left(-9\right)$

$\left(\begin{array}{ccc}|-4|& =& 4\\ |-9|& =& 9\end{array}}$ Add these absolute values.

$4+9=13$

The common sign is “ $-$ .“

Thus, $\left(-4\right)+\left(-9\right)=-\text{13}$ .

## Practice set a

Find the sums.

$\text{8}+\text{6}$

14

$\text{41}+\text{11}$

52

$\left(-4\right)+\left(-8\right)$

-12

$\left(-\text{36}\right)+\left(-9\right)$

-45

$-\text{14}+\left(-\text{20}\right)$

-34

$-\frac{2}{3}+\left(-\frac{5}{3}\right)$

$-\frac{7}{3}$

$-2\text{.}8+\left(-4\text{.}6\right)$

$-7\text{.}4$

$0+\left(-\text{16}\right)$

$-\text{16}$

Notice that
$\left(0\right)+\left(\text{a positive number}\right)=\left(\text{that same positive number}\right)$ .
$\left(0\right)+\left(\text{a negative number}\right)=\left(\text{that same negative number}\right)$ .

## The additive identity is zero

Since adding zero to a real number leaves that number unchanged, zero is called the additive identity .

## Addition of numbers with unlike signs

The addition $\text{2}+\left(-6\right)$ , two numbers with unlike signs , can also be illustrated using the number line.

Begin at 0, the origin.

Since 2 is positive, move 2 units to the right.

Since -6 is negative, move, from 2, 6 units to the left.

We are now located at -4.

We can suggest a rule for adding two numbers that have unlike signs by noting that if the signs are disregarded, 4 can be obtained by subtracting 2 from 6. But 2 and 6 are precisely the absolute values of 2 and -6. Also, notice that the sign of the number with the larger absolute value is negative and that the sign of the resulting sum is negative.

## Adding numbers with unlike signs

Addition of numbers with unlike signs: To add two real numbers that have unlike signs , subtract the smaller absolute value from the larger absolute value and associate with this difference the sign of the number with the larger absolute value.

## Sample set b

Find the following sums.

$\text{7}+\left(-2\right)$

$\underset{\text{value. Sign is positive.}}{\underset{\text{Larger absolute}}{\underbrace{|7|=7}}}$       $\underset{\text{value.}}{\underset{\text{Smaller absolute}}{\underbrace{|-2|=2}}}$

Subtract absolute values: $7-2=\text{5}$ .

Attach the proper sign: "+."

Thus, $\text{7}+\left(-2\right)=+5$ or $\text{7}+\left(-2\right)=\text{5}$ .

$\text{3}+\left(-11\right)$

$\underset{\text{value.}}{\underset{\text{Smaller absolute}}{\underbrace{|3|=3}}}$       $\underset{\text{value. Sign is negative.}}{\underset{\text{Larger absolute}}{\underbrace{|-11|=11}}}$

Subtract absolute values: $11-3=\text{8}$ .

Attach the proper sign: " $-$ ."

Thus, $3+\left(-11\right)=-8$ .

The morning temperature on a winter's day in Lake Tahoe was -12 degrees. The afternoon temperature was 25 degrees warmer. What was the afternoon temperature?

We need to find $-12+\text{25}$ .

$\underset{\text{value.}}{\underset{\text{Smaller absolute}}{\underbrace{|-12|=12}}}$       $\underset{\text{value. Sign is positive.}}{\underset{\text{Larger absolute}}{\underbrace{|25|=25}}}$

Subtract absolute values: $25-12=\text{16}$ .

Attach the proper sign: "+."

Thus, $-12+\text{25}=\text{13}$ .

## Practice set b

Find the sums.

$\text{4}+\left(-3\right)$

1

$-3+5$

2

$\text{15}+\left(-\text{18}\right)$

-3

$0+\left(-6\right)$

-6

$-\text{26}+\text{12}$

-14

$\text{35}+\left(-\text{78}\right)$

-43

$\text{15}+\left(-10\right)$

5

$1\text{.}5+\left(-2\right)$

-0.5

$-8+0$

-8

$\text{0}+\left(0\text{.}\text{57}\right)$

0.57

$-\text{879}+\text{454}$

-425

## Calculators

Calculators having the key can be used for finding sums of signed numbers.

## Sample set c

Use a calculator to find the sum of -147 and 84.

 Display Reads Type 147 147 Press -147 This key changes the sign of a number. It is different than $-$ . Press + -147 Type 84 84 Press = -63

## Practice set c

Use a calculator to find each sum.

$\text{673}+\left(-721\right)$

-48

$-8,261+\text{2,206}$

-6,085

$-1,345\text{.}6+\left(-6,648\text{.}1\right)$

-7,993.7

## Exercises

Find the sums in the following 27 problems. If possible, use a calculator to check each result.

$4+\text{12}$

16

$8+6$

$\left(-3\right)+\left(-\text{12}\right)$

-15

$\left(-6\right)+\left(-\text{20}\right)$

$\text{10}+\left(-2\right)$

8

$8+\left(-\text{15}\right)$

$-\text{16}+\left(-9\right)$

-25

$-\text{22}+\left(-1\right)$

$0+\left(-\text{12}\right)$

-12

$0+\left(-4\right)$

$0+\left(\text{24}\right)$

24

$-6+1+\left(-7\right)$

$-5+\left(-\text{12}\right)+\left(-4\right)$

-21

$-5+5$

$-7+7$

0

$-\text{14}+\text{14}$

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

0

$9+\left(-9\right)$

$\text{84}+\left(-\text{61}\right)$

23

$\text{13}+\left(-\text{56}\right)$

$\text{452}+\left(-\text{124}\right)$

328

$\text{636}+\left(-\text{989}\right)$

$1,\text{811}+\left(-\text{935}\right)$

876

$-\text{373}+\left(-\text{14}\right)$

$-1,\text{211}+\left(-\text{44}\right)$

-1,255

$-\text{47}\text{.}\text{03}+\left(-\text{22}\text{.}\text{71}\right)$

$-1\text{.}\text{998}+\left(-4\text{.}\text{086}\right)$

-6.084

In order for a small business to break even on a project, it must have sales of $21,000. If the amount of sales was$15,000, by how much money did this company fall short?

Suppose a person has $56 in his checking account. He deposits$100 into his checking account by using the automatic teller machine. He then writes a check for $84.50. If an error causes the deposit not to be listed into this person’s account, what is this person’s checking balance? -$28.50

A person borrows $7 on Monday and then$12 on Tuesday. How much has this person borrowed?

A person borrows $11 on Monday and then pays back$8 on Tuesday. How much does this person owe?

\$3.00

## Exercises for review

( [link] ) Find the reciprocal of $8\frac{5}{6}$ .

( [link] ) Find the value of $\frac{5}{\text{12}}+\frac{7}{\text{18}}-\frac{1}{3}$ .

$\frac{\text{17}}{\text{36}}$

( [link] ) Round 0.01628 to the nearest tenth.

( [link] ) Convert 62% to a fraction.

$\frac{\text{62}}{\text{100}}=\frac{\text{31}}{\text{50}}$

( [link] ) Find the value of $\mid -\text{12}\mid$ .

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?
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
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.
what is nano technology
what is system testing?
preparation of nanomaterial
how to synthesize TiO2 nanoparticles by chemical methods
Zubear
what's the program
Jordan
?
Jordan
what chemical
Jordan
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
7hours 36 min - 4hours 50 min