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The temperature in Chicago at 5 A.M. was 10 degrees below zero Celsius. Six hours later, it had warmed up 14 degrees Celsius. What is the temperature at 11 A.M.?

4 degrees Celsius

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A scuba diver was swimming 16 feet below the surface and then dove down another 17 feet. What is her new depth?

−33 feet

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A football team took possession of the football on their 42-yard line. In the next three plays, they lost 6 yards, gained 4 yards, and then lost 8 yards. On what yard line was the ball at the end of those three plays?

Solution

We are asked to find the yard line the ball was on at the end of three plays.

Write a word phrase for the position of the ball. Start at 42, then lose 6, gain 4, lose 8.
Translate to math notation. 42−6+4−8
Simplify. 32
Write a sentence to answer the question. At the end of the three plays, the ball is on the 32-yard line.
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The Bears took possession of the football on their 20-yard line. In the next three plays, they lost 9 yards, gained 7 yards, then lost 4 yards. On what yard line was the ball at the end of those three plays?

14-yard line

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The Chargers began with the football on their 25-yard line. They gained 5 yards, lost 8 yards and then gained 15 yards on the next three plays. Where was the ball at the end of these plays?

37-yard line

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Key concepts

  • Addition of Positive and Negative Integers
    5 + 3 −5 + ( −3 )
    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 + ( −3 )
    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.

Practice makes perfect

Model Addition of Integers

In the following exercises, model the expression to simplify.

Simplify Expressions with Integers

In the following exercises, simplify each expression.

−14 + ( −12 ) + 4

−22

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135 + ( −110 ) + 83

108

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−32 + 24 + ( −6 ) + 10

−4

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−38 + 27 + ( −8 ) + 12

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Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

x + 8 when

  1. x = −26
  2. x = −95

  1. ⓐ −18
  2. ⓑ −87

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y + 9 when

  1. y = −29
  2. y = −84

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y + ( −14 ) when

  1. y = −33
  2. y = 30

  1. ⓐ −47
  2. ⓑ 16

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x + ( −21 ) when

  1. x = −27
  2. x = 44

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When a = −7 , evaluate:

  1. a + 3
  2. a + 3

  1. ⓐ −4
  2. ⓑ 10

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When b = −11 , evaluate:

  1. b + 6
  2. b + 6

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When c = −9 , evaluate:

  1. c + ( −4 )
  2. c + ( −4 )

  1. ⓐ −13
  2. ⓑ 5

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When d = −8 , evaluate:

  1. d + ( −9 )
  2. d + ( −9 )

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m + n when, m = −15 , n = 7

−8

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p + q when, p = −9 , q = 17

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r −3 s when, r = 16 , s = 2

10

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2 t + u when, t = −6 , u = −5

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( a + b ) 2 when, a = −7 , b = 15

64

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( c + d ) 2 when, c = −5 , d = 14

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( x + y ) 2 when, x = −3 , y = 14

121

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( y + z ) 2 when, y = −3 , z = 15

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Translate Word Phrases to Algebraic Expressions

In the following exercises, translate each phrase into an algebraic expression and then simplify.

The sum of −14 and 5

−14 + 5 = −9

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8 more than −2

−2 + 8 = 6

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−10 added to −15

−15 + (−10) = −25

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6 more than the sum of −1 and −12

[−1 + (−12)] + 6 = −7

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3 more than the sum of −2 and −8

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the sum of 10 and −19 , increased by 4

[10 + (−19)] + 4 = −5

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the sum of 12 and −15 , increased by 1

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Add Integers in Applications

In the following exercises, solve.

Temperature The temperature in St. Paul, Minnesota was −19 °F at sunrise. By noon the temperature had risen 26°F. What was the temperature at noon?

7°F

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Temperature The temperature in Chicago was −15 °F at 6 am. By afternoon the temperature had risen 28°F. What was the afternoon temperature?

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Credit Cards Lupe owes $73 on her credit card. Then she charges $45 more. What is the new balance?

−$118

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Credit Cards Frank owes $212 on his credit card. Then he charges $105 more. What is the new balance?

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Weight Loss Angie lost 3 pounds the first week of her diet. Over the next three weeks, she lost 2 pounds, gained 1 pound, and then lost 4 pounds. What was the change in her weight over the four weeks?

−8 pounds

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Weight Loss April lost 5 pounds the first week of her diet. Over the next three weeks, she lost 3 pounds, gained 2 pounds, and then lost 1 pound. What was the change in her weight over the four weeks?

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Football The Rams took possession of the football on their own 35-yard line. In the next three plays, they lost 12 yards, gained 8 yards, then lost 6 yards. On what yard line was the ball at the end of those three plays?

25-yard line

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Football The Cowboys began with the ball on their own 20-yard line. They gained 15 yards, lost 3 yards and then gained 6 yards on the next three plays. Where was the ball at the end of these plays?

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Calories Lisbeth walked from her house to get a frozen yogurt, and then she walked home. By walking for a total of 20 minutes, she burned 90 calories. The frozen yogurt she ate was 110 calories. What was her total calorie gain or loss?

20 calories

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Calories Ozzie rode his bike for 30 minutes, burning 168 calories. Then he had a 140-calorie iced blended mocha. Represent the change in calories as an integer?

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Everyday math

Stock Market The week of September 15, 2008, was one of the most volatile weeks ever for the U.S. stock market. The change in the Dow Jones Industrial Average each day was:

Monday −504 Tuesday + 142 Wednesday −449 Thursday + 410 Friday + 369

What was the overall change for the week?

−32

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Stock Market During the week of June 22, 2009, the change in the Dow Jones Industrial Average each day was:

Monday −201 Tuesday −16 Wednesday −23 Thursday + 172 Friday −34

What was the overall change for the week?

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Writing exercises

Explain why the sum of −8 and 2 is negative, but the sum of 8 and −2 and is positive.

Sample answer: In the first case, there are more negatives so the sum is negative. In the second case, there are more positives so the sum is positive.

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Give an example from your life experience of adding two negative numbers.

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Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

.

After reviewing this checklist, what will you do to become confident for all objectives?

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
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.
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
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
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
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?
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
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.
Kimberly Reply
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
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
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)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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