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Use Negatives and Opposites of Integers

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


9 ___ 4
−3 ___ 6
−8 ___ −2
1 ___ −10

> < < >

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−7 ___ 3
−10 ___ −5
2 ___ −6
8 ___ 9

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


2
−6

−2 6

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In the following exercises, simplify.

In the following exercises, evaluate.

c when
c = 12
c = −12

−12 12

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d when
d = 21
d = −21

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Simplify Expressions with Absolute Value

In the following exercises, simplify.


| −32 |
| 0 |
| 16 |

32 0 16

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| 0 |
| −40 |
| 22 |

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In the following exercises, fill in<,>, or = for each of the following pairs of numbers.


−6 ___ | −6 |
| −3 | ___ −3

< =

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| −5 | ___ | −5 |
9 ___ | −9 |

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In the following exercises, simplify.

( −5 ) and | −5 |

5 , −5

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| −9 | and ( −9 )

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| 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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18 | 3 ( 8 5 ) |

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In the following exercises, evaluate.


| p | when p = 19
| q | when q = −33

−19 −33

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| a | when a = 60
| b | when b = −12

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Add Integers

In the following exercises, simplify each expression.

−14 + ( −12 ) + 4

−22

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135 + ( −110 ) + 83

108

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6 −38 + 27 + ( −8 ) + 126

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Subtract Integers

In the following exercises, simplify.


44 28
44 + ( −28 )

16 16

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35 16
35 + ( −16 )

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27 ( −18 )
27 + 18

45 45

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46 ( −37 )
46 + 37

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In the following exercises, simplify each expression.

−103 ( −52 )

−51

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−14 ( −27 ) + 9

22

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( 2 7 ) ( 3 8 ) ( 2 )

0

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( 1 8 ) ( 2 9 )

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( 6 8 ) ( 2 4 )

4

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( 4 5 ) ( 7 8 )

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25 [ 10 ( 3 12 ) ]

6

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32 [ 5 ( 15 20 ) ]

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6.3 4.3 7.2

−8

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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:

Mount McKinley.
Death Valley.

20,329 −282

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Extreme temperatures The highest recorded temperature on Earth was 58 ° Celsius, recorded in the Sahara Desert in 1922. The lowest recorded temperature was 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 of:

Pennsylvania.
Texas.

$540 million $27 billion

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College enrollments Across the United States, community college enrollment grew by 1,400,000 students from Fall 2007 to Fall 2010. In California, community college enrollment declined by 110,171 students from Fall 2009 to Fall 2010.

Use integers to write the change in enrollment:

  1. in the U.S. from Fall 2007 to Fall 2010.
  2. in California from Fall 2009 to Fall 2010.
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Stock Market The week of September 15, 2008 was one of the most volatile weeks ever for the US stock market. The closing numbers of the Dow Jones Industrial Average each day were:

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

What was the overall change for the week? Was it positive or negative?

−32

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Stock Market During the week of June 22, 2009, the closing numbers of the Dow Jones Industrial Average each day were:

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

What was the overall change for the week? Was it positive or negative?

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Writing exercises

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

Answers may vary

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

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

Answers may vary

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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.

A table is shown with four columns and five rows. The column titles, from left to right, are “I can …”, “Confidently”, “With some help” and “No – I don’t get it!” The first column includes the phrases “use negatives and opposites of integers.”, “Simplify: expressions with absolute value.”, “add integers.” and “subtract integers.”

What does this checklist tell you about your mastery of this section? What steps will you take to improve?

Questions & Answers

Can you explain further
Monica Reply
How do you find divisible numbers without a calculator?
Jacob Reply
TAKE OFF THE LAST DIGIT AND MULTIPLY IT 9. SUBTRACT IT THE DIGITS YOU HAVE LEFT. IF THE ANSWER DIVIDES BY 13(OR IS ZERO), THEN YOUR ORIGINAL NUMBER WILL ALSO DIVIDE BY 13!IS DIVISIBLE BY 13
BAINAMA
When she graduates college, Linda will owe $43,000 in student loans. The interest rate on the federal loans is 4.5% and the rate on the private bank loans is 2%. The total interest she owes for one year was $1,585. What is the amount of each loan?
Ariana Reply
Sean took the bus from Seattle to Boise, a distance of 506 miles. If the trip took 7 2/3 hours, what was the speed of the bus?
Kirisma Reply
66miles/hour
snigdha
How did you work it out?
Esther
s=mi/hr 2/3~0.67 s=506mi/7.67hr = ~66 mi/hr
Orlando
hello, I have algebra phobia. Subtracting negative numbers always seem to get me confused.
Alicia Reply
what do you need help in?
Felix
subtracting a negative....is adding!!
Heather
look at the numbers if they have different signs, it's like subtracting....but you keep the sign of the largest number...
Felix
for example.... -19 + 7.... different signs...subtract.... 12 keep the sign of the "largest" number 19 is bigger than 7.... 19 has the negative sign... Therefore, -12 is your answer...
Felix
—12
Niazmohammad
Thanks Felix.l also get confused with signs.
Esther
Thank you for this
Shatey
ty
Graham
think about it like you lost $19 (-19), then found $7(+7). Totally you lost just $12 (-12)
Annushka
I used to struggle a lot with negative numbers and math in general what I typically do is look at it in terms of money I have -$5 in my account I then take out 5 more dollars how much do I have in my account well-$10 ... I also for a long time would draw it out on a number line to visualize it
Meg
practicing with smaller numbers to understand then working with larger numbers helps too and the song/rhyme same sign add and keep opposite signs subtract keep the sign of the bigger # then you'll be exact
Meg
Bruce drives his car for his job. The equation R=0.575m+42 models the relation between the amount in dollars, R, that he is reimbursed and the number of miles, m, he drives in one day. Find the amount Bruce is reimbursed on a day when he drives 220 miles
John Reply
168.50=R
Heather
john is 5years older than wanjiru.the sum of their years is27years.what is the age of each
achol Reply
46
mustee
j 17 w 11
Joseph
john is 16. wanjiru is 11.
Felix
27-5=22 22÷2=11 11+5=16
Joyce
where's the answers?
Ed Reply
I don't see where the answers are.
Ed
Cindy and Richard leave their dorm in Charleston at the same time. Cindy rides her bicycle north at a speed of 18 miles per hour. Richard rides his bicycle south at a speed of 14 miles per hour. How long will it take them to be 96 miles apart?
Maddy Reply
3
Christopher
18t+14t=96 32t=96 32/96 3
Christopher
show that a^n-b^2n is divisible by a-b
Florence Reply
What does 3 times your weight right now
Cherokee Reply
Use algebra to combine 39×5 and the half sum of travel of 59+30
Cherokee
What is the segment of 13? Explain
Cherokee
my weight is 49. So 3 times is 147
Cherokee
kg to lbs you goin to convert 2.2 or one if the same unit your going to time your body weight by 3. example if my body weight is 210lb. what would be my weight if I was 3 times as much in kg. that's you do 210 x3 = 630lb. then 630 x 2.2= .... hope this helps
tyler
How to convert grams to pounds?
paul
What is the lcm of 340
Kendra Reply
Yes
Cherokee
How many numbers each equal to y must be taken to make 15xy
Malik Reply
15x
Martin
15x
Asamoah
15x
Hugo
1y
Tom
1y x 15y
Tom
find the equation whose roots are 1 and 2
Adda Reply
(x - 2)(x -1)=0 so equation is x^2-x+2=0
Ranu
I believe it's x^2-3x+2
NerdNamedGerg
because the X's multiply by the -2 and the -1 and than combine like terms
NerdNamedGerg
find the equation whose roots are -1 and 4
Adda
Ans = ×^2-3×+2
Gee
find the equation whose roots are -2 and -1
Adda
(×+1)(×-4) = x^2-3×-4
Gee
yeah
Asamoah
Quadratic equations involving factorization
Winner Reply
there's a chatting option in the app wow
Nana
That's cool cool
Nana
Nice to meet you all
Nana
you too.
Joan
😃
Nana
Hey you all there are several Free Apps that can really help you to better solve type Equations.
Debra
Debra, which apps specifically. ..?
Nana
am having a course in elementary algebra ,any recommendations ?
samuel
Samuel Addai, me too at ucc elementary algebra as part of my core subjects in science
Nana
me too as part of my core subjects in R M E
Ken
at ABETIFI COLLEGE OF EDUCATION
Ken
ok great. Good to know.
Joan
5x + 1/3= 2x + 1/2
sanam
Plz solve this
sanam
5x - 3x = 1/2 - 1/3 2x = 1/6 x = 1/12
Ranu
Thks ranu
sanam
Please help me solve this 10x+14=-2x+38
Erica
the previous equation should be 3x = 1/6 x=1/18
Sriram
for the new one 10x + 2x = 38 - 14
Sriram
12x = 24 x=2
Sriram
10x + 14 = -2x +38 10x + 2x = 38 - 14 12x = 24 divide both sides by the coefficient of x, which is 12 therefore × = 2
vida
Practice Key Terms 3

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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