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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

what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
how did I we'll learn this
Noor Reply
f(x)= 2|x+5| find f(-6)
Prince Reply
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
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
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
Prasenjit
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?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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