<< Chapter < Page Chapter >> Page >
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 with Zero
  • 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.

A number line with has marks for the numbers -2 to 7. An arrow is drawn from 0 to 2, and from 2 to 5.

Thus, 2 + 3 = 5 size 12{"2 "+" 3 "=" 5"} {} .

Summarizing, we have

( 2 positive units ) + ( 3 positive units ) = ( 5 positive units ) size 12{ \( "2 positive units" \) + \( "3 positive units" \) = \( "5 positive units" \) } {}

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.

A number line with has marks for the numbers -7 to 2. An arrow is drawn from 0 to -2, and from -2 to -5.

Thus, ( 2 ) + ( 3 ) = 5 size 12{ \( - 2 \) + \( - 3 \) = - 5} {} .

Summarizing, we have

( 2 negative units ) + ( 3 negative units ) = ( 5 negative units ) size 12{ \( "2 negative units" \) + \( "3 negative units" \) = \( "5 negative units" \) } {}

Observing these two examples, we can suggest these relationships:

( positive number ) + ( positive number ) = ( positive number ) size 12{ \( "positive number" \) + \( "positive number" \) = \( "positive number" \) } {}

( negative number ) + ( negative number ) = ( negative number ) size 12{ \( "negative number" \) + \( "negative number" \) = \( "negative number" \) } {}

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 size 12{3+7} {}

| 3 | = 3 | 7 | = 7 Add these absolute values.

3 + 7 = 10

The common sign is “+.”

Thus, 3 + 7 = + 10 size 12{"3 "+" 7 "= +"10"} {} , or 3 + 7 = 10 size 12{"3 "+" 7 "=" 10"} {} .

Got questions? Get instant answers now!

( 4 ) + ( 9 ) size 12{ \( - 4 \) + \( - 9 \) } {}

| - 4 | = 4 | - 9 | = 9 Add these absolute values.

4 + 9 = 13

The common sign is “ - .“

Thus, ( 4 ) + ( 9 ) = 13 size 12{ \( - 4 \) + \( - 9 \) = - "13"} {} .

Got questions? Get instant answers now!

Practice set a

Find the sums.

8 + 6 size 12{"8 "+" 6"} {}

14

Got questions? Get instant answers now!

41 + 11 size 12{"41 "+" 11"} {}

52

Got questions? Get instant answers now!

( - 4 ) + ( - 8 ) size 12{ \( "-4" \) + \( "–8" \) } {}

-12

Got questions? Get instant answers now!

36 + 9 size 12{ left ( - "36" right )+ left ( - 9 right )} {}

-45

Got questions? Get instant answers now!

14 + 20 size 12{ - "14"+ left ( - "20" right )} {}

-34

Got questions? Get instant answers now!

2 3 + 5 3 size 12{ - { {2} over {3} } + left ( - { {5} over {3} } right )} {}

7 3 size 12{- { {7} over {3} } } {}

Got questions? Get instant answers now!

- 2 . 8 + ( - 4 . 6 ) size 12{"–2" "." 8+ \( " –4" "." 6 \) } {}

7 . 4 size 12{-7 "." 4} {}

Got questions? Get instant answers now!

0 + ( 16 ) size 12{0+ \( - "16" \) } {}

16 size 12{-"16"} {}

Got questions? Get instant answers now!

Addition with zero

Addition with zero

Notice that
( 0 ) + ( a positive number ) = ( that same positive number ) size 12{ \( 0 \) + \( "a positive number" \) = \( "that same positive number" \) } {} .
( 0 ) + ( a negative number ) = ( that same negative number ) size 12{ \( 0 \) + \( "a negative number" \) = \( "that same negative number" \) } {} .

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 2 + ( - 6 ) size 12{"2 "+ \( " –6" \) } {} , 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.

A number line with has marks for the numbers -5 to 4. An arrow is drawn from 2 to -4, and from 0 to 2.

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.

7 + ( - 2 ) size 12{"7 "+ \( "–2" \) } {}

| 7 | = 7 Larger absolute value. Sign is positive.       | - 2 | = 2 Smaller absolute value.

Subtract absolute values: 7 - 2 = 5 size 12{"7 – 2 "=" 5"} {} .

Attach the proper sign: "+."

Thus, 7 + ( - 2 ) = + 5 size 12{"7 "+ \( "–2" \) = +5} {} or 7 + ( - 2 ) = 5 size 12{"7 "+ \( " –2" \) =" 5"} {} .

Got questions? Get instant answers now!

3 + ( - 11 ) size 12{"3 "+ \( "–11" \) } {}

| 3 | = 3 Smaller absolute value.       | - 11 | = 11 Larger absolute value. Sign is negative.

Subtract absolute values: 11 - 3 = 8 size 12{"11 – 3 "=" 8"} {} .

Attach the proper sign: " - ."

Thus, 3 + ( - 11 ) = - 8 size 12{3+ \( "–11" \) =" –8"} {} .

Got questions? Get instant answers now!

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 + 25 size 12{"–12 "+" 25"} {} .

| - 12 | = 12 Smaller absolute value.       | 25 | = 25 Larger absolute value. Sign is positive.

Subtract absolute values: 25 - 12 = 16 size 12{"25 – 12 "=" 16"} {} .

Attach the proper sign: "+."

Thus, - 12 + 25 = 13 size 12{"–12 "+" 25 "=" 13"} {} .

Got questions? Get instant answers now!

Practice set b

Find the sums.

4 + ( - 3 ) size 12{"4 "+ \( "–3" \) } {}

1

Got questions? Get instant answers now!

3 + 5 size 12{ - 3+5} {}

2

Got questions? Get instant answers now!

15 + ( 18 ) size 12{"15"+ \( - "18" \) } {}

-3

Got questions? Get instant answers now!

0 + ( 6 ) size 12{0+ \( - 6 \) } {}

-6

Got questions? Get instant answers now!

26 + 12 size 12{ - "26"+"12"} {}

-14

Got questions? Get instant answers now!

35 + ( 78 ) size 12{"35"+ \( - "78" \) } {}

-43

Got questions? Get instant answers now!

15 + ( - 10 ) size 12{"15 "+ \( "–10" \) } {}

5

Got questions? Get instant answers now!

1 . 5 + ( 2 ) size 12{1 "." 5+ \( - 2 \) } {}

-0.5

Got questions? Get instant answers now!

8 + 0 size 12{ - 8+0} {}

-8

Got questions? Get instant answers now!

0 + ( 0 . 57 ) size 12{"0 "+ \( 0 "." "57" \) } {}

0.57

Got questions? Get instant answers now!

879 + 454 size 12{ - "879"+"454"} {}

-425

Got questions? Get instant answers now!

Calculators

Calculators having the A square with a plus and minus sign. 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 A square with a plus and minus sign. -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.

673 + ( - 721 ) size 12{"673 "+ \( "–721" \) } {}

-48

Got questions? Get instant answers now!

- 8,261 + 2,206 size 12{"–8,261 "+" 2,206"} {}

-6,085

Got questions? Get instant answers now!

- 1,345 . 6 + ( - 6,648 . 1 ) size 12{"–1,345" "." 6+ \( "–6,648" "." 1 \) } {}

-7,993.7

Got questions? Get instant answers now!

Exercises

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

4 + 12 size 12{4+"12"} {}

16

Got questions? Get instant answers now!

3 + 12 size 12{ left (-3 right )+ left (-"12" right )} {}

-15

Got questions? Get instant answers now!

6 + 20 size 12{ left (-6 right )+ left (-"20" right )} {}

Got questions? Get instant answers now!

10 + 2 size 12{"10"+ left (-2 right )} {}

8

Got questions? Get instant answers now!

8 + 15 size 12{8+ left (-"15" right )} {}

Got questions? Get instant answers now!

16 + 9 size 12{-"16"+ left (-9 right )} {}

-25

Got questions? Get instant answers now!

22 + 1 size 12{-"22"+ left (-1 right )} {}

Got questions? Get instant answers now!

0 + 12 size 12{0+ left (-"12" right )} {}

-12

Got questions? Get instant answers now!

0 + 4 size 12{0+ left (-4 right )} {}

Got questions? Get instant answers now!

0 + 24 size 12{0+ left ("24" right )} {}

24

Got questions? Get instant answers now!

6 + 1 + 7 size 12{-6+1+ left (-7 right )} {}

Got questions? Get instant answers now!

5 + 12 + 4 size 12{-5+ left (-"12" right )+ left (-4 right )} {}

-21

Got questions? Get instant answers now!

5 + 5 size 12{-5+5} {}

Got questions? Get instant answers now!

7 + 7 size 12{-7+7} {}

0

Got questions? Get instant answers now!

14 + 14 size 12{-"14"+"14"} {}

Got questions? Get instant answers now!

4 + 4 size 12{4+ left (-4 right )} {}

0

Got questions? Get instant answers now!

9 + 9 size 12{9+ left (-9 right )} {}

Got questions? Get instant answers now!

84 + 61 size 12{"84"+ left (-"61" right )} {}

23

Got questions? Get instant answers now!

13 + 56 size 12{"13"+ left (-"56" right )} {}

Got questions? Get instant answers now!

452 + 124 size 12{"452"+ left (-"124" right )} {}

328

Got questions? Get instant answers now!

636 + 989 size 12{"636"+ left (-"989" right )} {}

Got questions? Get instant answers now!

1, 811 + ( 935 ) size 12{1,"811"+ \( -"935" \) } {}

876

Got questions? Get instant answers now!

373 + 14 size 12{-"373"+ left (-"14" right )} {}

Got questions? Get instant answers now!

1, 211 + 44 size 12{-1,"211"+ left (-"44" right )} {}

-1,255

Got questions? Get instant answers now!

47 . 03 + 22 . 71 size 12{-"47" "." "03"+ left (-"22" "." "71" right )} {}

Got questions? Get instant answers now!

1 . 998 + 4 . 086 size 12{-1 "." "998"+ left (-4 "." "086" right )} {}

-6.084

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

$3.00

Got questions? Get instant answers now!

Exercises for review

( [link] ) Find the reciprocal of 8 5 6 size 12{8 { {5} over {6} } } {} .

Got questions? Get instant answers now!

( [link] ) Find the value of 5 12 + 7 18 1 3 size 12{ { {5} over {"12"} } + { {7} over {"18"} } - { {1} over {3} } } {} .

17 36 size 12{ { {"17"} over {"36"} } } {}

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

62 100 = 31 50 size 12{ { {"62"} over {"100"} } = { {"31"} over {"50"} } } {}

Got questions? Get instant answers now!

( [link] ) Find the value of 12 size 12{ lline -"12" rline } {} .

Got questions? Get instant answers now!

Questions & Answers

what does nano mean?
Anassong Reply
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?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
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
Abhijith Reply
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?
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
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
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
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.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
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
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Berger describes sociologists as concerned with
Mueller Reply
7hours 36 min - 4hours 50 min
Tanis Reply

Get the best Algebra and trigonometry course in your pocket!





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?

Ask