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Translate into an expression with integers:

The football team had a gain of 5 yards.

5 yards

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Translate into an expression with integers:

The scuba diver was 30 feet below the surface of the water.

−30 feet

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Key concepts

  • Opposite Notation
    • a means the opposite of the number a
    • The notation a is read the opposite of a .
  • Absolute Value Notation
    • The absolute value of a number n is written as | n | .
    • | n | 0 for all numbers.

Practice makes perfect

Locate Positive and Negative Numbers on the Number Line

In the following exercises, locate and label the given points on a number line.

Order Positive and Negative Numbers on the Number Line

In the following exercises, order each of the following pairs of numbers, using < or >.

  1. 9 __ 4
  2. −3 __ 6
  3. −8 __ −2
  4. 1 __ −10

  1. >
  2. <
  3. <
  4. >
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  1. 6 __ 2 ;
  2. −7 __ 4 ;
  3. −9 __ −1 ;
  4. 9 __ −3
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  1. −5 __ 1 ;
  2. −4 __ −9 ;
  3. 6 __ 10 ;
  4. 3 __ −8
  1. <
  2. >
  3. <
  4. >
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  1. −7 __ 3 ;
  2. −10 __ −5 ;
  3. 2 __ −6 ;
  4. 8 __ 9
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Find Opposites

In the following exercises, find the opposite of each number.

  1. 2
  2. −6
  1. −2
  2. 6
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  1. −8
  2. 1
  1. 8
  2. −1
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In the following exercises, simplify.

In the following exercises, evaluate.

m when

  1. m = 3
  2. m = −3

  1. −3
  2. 3
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p when

  1. p = 6
  2. p = −6

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c when

  1. c = 12
  2. c = −12

  1. −12;
  2. 12
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d when

  1. d = 21
  2. d = −21

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Simplify Expressions with Absolute Value

In the following exercises, simplify each absolute value expression.

  1. | 7 |
  2. | −25 |
  3. | 0 |
  1. 7
  2. 25
  3. 0
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  1. | 5 |
  2. | 20 |
  3. | −19 |
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  1. | −32 |
  2. | −18 |
  3. | 16 |
  1. 32
  2. 18
  3. 16
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  1. | −41 |
  2. | −40 |
  3. | 22 |
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In the following exercises, evaluate each absolute value expression.

  1. | x | when x = −28
  2. | u | when u = −15
  1. 28
  2. 15
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  1. | y | when y = −37
  2. | z | when z = −24
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  1. | p | when p = 19
  2. | q | when q = −33
  1. −19
  2. −33
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  1. | a | when a = 60
  2. | b | when b = −12
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In the following exercises, fill in < , > , or = to compare each expression.

  1. −6 __ | −6 |
  2. | −3 | __ −3
  1. <
  2. =
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  1. −8 __ | −8 |
  2. | −2 | __ −2
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  1. | −3 | __ | −3 |
  2. 4 __ | −4 |
  1. >
  2. >
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  1. | −5 | __ | −5 |
  2. 9 __ | −9 |
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In the following exercises, simplify each expression.

| 15 7 | | 14 6 |

0

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| 17 8 | | 13 4 |

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18 | 2 ( 8 3 ) |

8

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15 | 3 ( 8 5 ) |

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8 ( 14 2 | −2 | )

80

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Translate Word Phrases into Expressions with Integers

Translate each phrase into an expression with integers. Do not simplify .

  1. the opposite of 8
  2. the opposite of −6
  3. negative three
  4. 4 minus negative 3
  1. −8
  2. −(−6), or 6
  3. −3
  4. 4−(−3)
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  1. the opposite of 11
  2. the opposite of −4
  3. negative nine
  4. 8 minus negative 2
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  1. the opposite of 20
  2. the opposite of −5
  3. negative twelve
  4. 18 minus negative 7
  1. −20
  2. −(−5), or 5
  3. −12
  4. 18−(−7)
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  1. the opposite of 15
  2. the opposite of −9
  3. negative sixty
  4. 12 minus 5
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a temperature of 6 degrees below zero

−6 degrees

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a temperature of 14 degrees below zero

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an elevation of 40 feet below sea level

−40 feet

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an elevation of 65 feet below sea level

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a football play loss of 12 yards

−12 yards

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a football play gain of 4 yards

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a golf score one above par

+1

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a golf score of 3 below par

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Everyday math

Elevation The highest elevation in the United States is Mount McKinley, Alaska, at 20,320 feet above sea level. The lowest elevation is Death Valley, California, at 282 feet below sea level. Use integers to write the elevation of:

  1. Mount McKinley
  2. Death Valley

  1. 20,320 feet
  2. −282 feet
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Extreme temperatures The highest recorded temperature on Earth is 58° Celsius, recorded in the Sahara Desert in 1922. The lowest recorded temperature is 90° below 0° Celsius, recorded in Antarctica in 1983. Use integers to write the:

  1. highest recorded temperature
  2. lowest recorded temperature

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State budgets In June, 2011, the state of Pennsylvania estimated it would have a budget surplus of $540 million. That same month, Texas estimated it would have a budget deficit of $27 billion. Use integers to write the budget:

  1. surplus
  2. deficit

  1. $540 million
  2. −$27 billion
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College enrollments Across the United States, community college enrollment grew by 1,400,000 students from 2007 to 2010 . In California, community college enrollment declined by 110,171 students from 2009 to 2010 . Use integers to write the change in enrollment:

  1. growth
  2. decline

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Writing exercises

Give an example of a negative number from your life experience.

Sample answer: I have experienced negative temperatures.

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What are the three uses of the “−” sign in algebra? Explain how they differ.

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Self check

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

.

If most of your checks were:

…confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific.

…with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?

…no—I don’t get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.

Questions & Answers

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
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
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
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
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
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
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
Privacy Information Security Software Version 1.1a
Good
how do you translate this in Algebraic Expressions
linda 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
Practice Key Terms 4

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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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