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Simplify Expressions with Integers

In the following exercises, simplify each expression.

  1. 15 6
  2. 15 + ( −6 )

  1. 9
  2. 9

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  1. 12 9
  2. 12 + ( −9 )

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  1. 44 28
  2. 44 + ( −28 )

  1. 16
  2. 16

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  1. 35 16
  2. 35 + ( −16 )

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  1. 8 ( −9 )
  2. 8 + 9

  1. 17
  2. 17

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  1. 4 ( −4 )
  2. 4 + 4
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  1. 27 ( −18 )
  2. 27 + 18
  1. 45
  2. 45
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  1. 46 ( −37 )
  2. 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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−16 ( −4 + 1 ) 7

−20

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−15 ( −6 + 4 ) 3

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( 2 7 ) ( 3 8 )

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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5 · 7 8 · 2 4 · 9

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Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression for the given values.

x 6 when

  1. x = 3
  2. x = −3

  1. −3
  2. −9
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x 4 when

  1. x = 5
  2. x = −5

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5 y when

  1. y = 2
  2. y = −2

  1. 3
  2. 7
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8 y when

  1. y = 3
  2. y = −3

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4 x 2 15 x + 1 when x = 3

−8

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5 x 2 14 x + 7 when x = 2

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−12 5 x 2 when x = 6

−192

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−19 4 x 2 when x = 5

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Translate Word Phrases to Algebraic Expressions

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

  1. The difference of 3 and −10
  2. Subtract −20 from 45
  1. −3 − (−10) = 13
  2. 45 − (−20) = 65
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  1. The difference of 8 and −12
  2. Subtract −13 from 50
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  1. The difference of −6 and 9
  2. Subtract −12 from −16
  1. −6 − 9 = −15
  2. −16 − (−12) = −4
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  1. The difference of −8 and 9
  2. Subtract 15 from 19
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  1. 8 less than −17
  2. 24 minus 37
  1. −17 − 8 = −25
  2. −24 − 37 = −61
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  1. 5 less than −14
  2. −13 minus 42
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  1. 21 less than 6
  2. 31 subtracted from −19
  1. 6 − 21 = −15
  2. −19 − 31 = −50
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  1. 34 less than 7
  2. 29 subtracted from −50
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Subtract Integers in Applications

In the following exercises, solve the following applications.

Temperature One morning, the temperature in Urbana, Illinois, was 28° Fahrenheit. By evening, the temperature had dropped 38° Fahrenheit. What was the temperature that evening?

−10°

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Temperature On Thursday, the temperature in Spincich Lake, Michigan, was 22° Fahrenheit. By Friday, the temperature had dropped 35° Fahrenheit. What was the temperature on Friday?

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Temperature On January 15, the high temperature in Anaheim, California, was 84° Fahrenheit. That same day, the high temperature in Embarrass, Minnesota was −12° Fahrenheit. What was the difference between the temperature in Anaheim and the temperature in Embarrass?

96°

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Temperature On January 21, the high temperature in Palm Springs, California, was 89°, and the high temperature in Whitefield, New Hampshire was −31° . What was the difference between the temperature in Palm Springs and the temperature in Whitefield?

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Football At the first down, the Warriors football team had the ball on their 30-yard line. On the next three downs, they gained 2 yards, lost 7 yards, and lost 4 yards. What was the yard line at the end of the third down?

21-yard line

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Football At the first down, the Barons football team had the ball on their 20-yard line. On the next three downs, they lost 8 yards, gained 5 yards, and lost 6 yards. What was the yard line at the end of the third down?

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Checking Account John has $148 in his checking account. He writes a check for $83. What is the new balance in his checking account?

$65

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Checking Account Ellie has $426 in her checking account. She writes a check for $152. What is the new balance in her checking account?

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Checking Account Gina has $210 in her checking account. She writes a check for $250. What is the new balance in her checking account?

−$40

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Checking Account Frank has $94 in his checking account. He writes a check for $110. What is the new balance in his checking account?

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Checking Account Bill has a balance of −$14 in his checking account. He deposits $40 to the account. What is the new balance?

$26

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Checking Account Patty has a balance of −$23 in her checking account. She deposits $80 to the account. What is the new balance?

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Everyday math

Camping Rene is on an Alpine hike. The temperature is 7 ° . Rene’s sleeping bag is rated “comfortable to 20 °”. How much can the temperature change before it is too cold for Rene’s sleeping bag?

13°

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Scuba Diving Shelly’s scuba watch is guaranteed to be watertight to −100 feet . She is diving at −45 feet on the face of an underwater canyon. By how many feet can she change her depth before her watch is no longer guaranteed?

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Writing exercises

Explain why the difference of 9 and −6 is 15 .

Sample answer: On a number line, 9 is 15 units away from −6.

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Why is the result of subtracting 3 ( −4 ) the same as the result of adding 3 + 4 ?

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Self check

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

.

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

Questions & Answers

how does the planets on our solar system orbit
cheten Reply
how many Messier objects are there in space
satish Reply
did you g8ve certificate
Richard Reply
what are astronomy
Issan Reply
Astronomy (from Ancient Greek ἀστρονομία (astronomía) 'science that studies the laws of the stars') is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution.
Rafael
vjuvu
Elgoog
what is big bang theory?
Rosemary
what type of activity astronomer do?
Rosemary
No
Richard
the big bang theory is a theory which states that all matter was compressed together in one place the matter got so unstable it exploded releasing All its contents in the form of hydrogen
Roaul
I want to be an astronomer. That's my dream
Astrit
Who named the the whole galaxy?
Shola Reply
solar Univers
GPOWER
what is space
Richard
what is the dark matter
Richard
what are the factors upon which the atmosphere is stratified
Nicholas Reply
is the big bang the sun
Folakemi Reply
no
Sokak
bigbang is the beginning of the universe
Sokak
but thats just a theory
Sokak
nothing will happen, don't worry brother.
Vansh
what does comet means
GANGAIN Reply
these are Rocky substances between mars and jupiter
GANGAIN
Comets are cosmic snowballs of frozen gases , rock and dust that orbit the sun. They are mostly found between the orbits of Venus and Mercury.
Aarya
hllo
John
hi
John
qt rrt
John
r u there
John
hey can anyone guide me abt international astronomy olympiad
sahil
how can we learn right and true ?
Govinda Reply
why the moon is always appear in an elliptical shape
Gatjuol Reply
Because when astroid hit the Earth then a piece of elliptical shape of the earth was separated which is now called moon.
Hemen
what's see level?
lidiya Reply
Did you mean eye sight or sea level
Minal
oh sorry it's sea level
lidiya
according to the theory of astronomers why the moon is always appear in an elliptical orbit?
Gatjuol
hi !!! I am new in astronomy.... I have so many questions in mind .... all of scientists of the word they just give opinion only. but they never think true or false ... i respect all of them... I believes whole universe depending on true ...থিউরি
Govinda
hello
Jackson
hi
Elyana
we're all stars and galaxies a part of sun. how can science prove thx with respect old ancient times picture or books..or anything with respect to present time .but we r a part of that universe
w astronomy and cosmology!
Michele
another theory of universe except big ban
Albash Reply
how was universe born
Asmit Reply
there many theory to born universe but what is the reality of big bang theory to born universe
Asmit
what is the exact value of π?
Nagalakshmi
by big bang
universal
there are many theories regarding this it's on you believe any theory that you think is true ex. eternal inflation theory, oscillation model theory, multiple universe theory the big bang theory etc.
Aarya
I think after Big Bang!
Michele
from where on earth could u observe all the stars during the during the course of an year
Karuna Reply
I think it couldn't possible on earth
Nagalakshmi
in this time i don't Know
Michele
is that so. the question was in the end of this chapter
Karuna
in theory, you could see them all from the equator (though over the course of a year, not at pne time). stars are measured in "declination", which is how far N or S of the equator (90* to -90*). Polaris is the North star, and is ALMOST 90* (+89*). So it would just barely creep over the horizon.
Christopher
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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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