<< Chapter < Page Chapter >> Page >

The temperature in Anchorage, Alaska one morning was 15 degrees. By mid-afternoon the temperature had dropped to 30 degrees below zero. What was the difference in the morning and afternoon temperatures?

The difference in temperatures was 45 degrees.

Got questions? Get instant answers now!

The temperature in Denver was −6 degrees at lunchtime. By sunset the temperature had dropped to −15 degrees. What was the difference in the lunchtime and sunset temperatures?

The difference in temperatures was 9 degrees.

Got questions? Get instant answers now!

Apply a strategy to solve applications with integers.

  1. Read the problem. Make sure all the words and ideas are understood
  2. Identify what we are asked to find.
  3. Write a phrase that gives the information to find it.
  4. Translate the phrase to an expression.
  5. Simplify the expression.
  6. Answer the question with a complete sentence.

The Mustangs football team received three penalties in the third quarter. Each penalty gave them a loss of fifteen yards. What is the number of yards lost?

Solution

Step 1. Read the problem. Make sure all the words and ideas are understood. Step 2. Identify what we are asked to find. the number of yards lost Step 3. Write a phrase that gives the information to find it. three times a 15-yard penalty Step 4. Translate the phrase to an expression. 3 ( −15 ) Step 5. Simplify the expression. −45 Step 6. Answer the question with a complete sentence. The team lost 45 yards.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

The Bears played poorly and had seven penalties in the game. Each penalty resulted in a loss of 15 yards. What is the number of yards lost due to penalties?

The Bears lost 105 yards.

Got questions? Get instant answers now!

Bill uses the ATM on campus because it is convenient. However, each time he uses it he is charged a $2 fee. Last month he used the ATM eight times. How much was his total fee for using the ATM?

A $16 fee was deducted from his checking account.

Got questions? Get instant answers now!

Key concepts

  • Multiplication and Division of Two Signed Numbers
    • Same signs—Product is positive
    • Different signs—Product is negative
  • Strategy for Applications
    1. Identify what you are asked to find.
    2. Write a phrase that gives the information to find it.
    3. Translate the phrase to an expression.
    4. Simplify the expression.
    5. Answer the question with a complete sentence.

Practice makes perfect

Multiply Integers

In the following exercises, multiply.

Divide Integers

In the following exercises, divide.

Simplify Expressions with Integers

In the following exercises, simplify each expression.

5 ( −6 ) + 7 ( −2 ) 3

−47

Got questions? Get instant answers now!

8 ( −4 ) + 5 ( −4 ) 6

Got questions? Get instant answers now!

( 8 11 ) ( 9 12 )

9

Got questions? Get instant answers now!

( 6 11 ) ( 8 13 )

Got questions? Get instant answers now!

65 ÷ ( −5 ) + ( −28 ) ÷ ( −7 )

−9

Got questions? Get instant answers now!

52 ÷ ( −4 ) + ( −32 ) ÷ ( −8 )

Got questions? Get instant answers now!

9 2 [ 3 8 ( −2 ) ]

−29

Got questions? Get instant answers now!

11 3 [ 7 4 ( −2 ) ]

Got questions? Get instant answers now!

( −3 ) 2 24 ÷ ( 8 2 )

5

Got questions? Get instant answers now!

( −4 ) 2 32 ÷ ( 12 4 )

Got questions? Get instant answers now!

Evaluate Variable Expressions with Integers

In the following exercises, evaluate each expression.

y + ( −14 ) when
y = −33
y = 30

−47 16

Got questions? Get instant answers now!

x + ( −21 ) when
x = −27
x = 44

Got questions? Get instant answers now!


a + 3 when a = −7
a + 3 when a = −7

−4 10

Got questions? Get instant answers now!


d + ( −9 ) when d = −8
d + ( −9 ) when d = −8

Got questions? Get instant answers now!

m + n when
m = −15 , n = 7

−8

Got questions? Get instant answers now!

p + q when
p = −9 , q = 17

Got questions? Get instant answers now!

r + s when r = −9 , s = −7

−16

Got questions? Get instant answers now!

t + u when t = −6 , u = −5

Got questions? Get instant answers now!

( x + y ) 2 when
x = −3 , y = 14

121

Got questions? Get instant answers now!

( y + z ) 2 when
y = −3 , z = 15

Got questions? Get instant answers now!

−2 x + 17 when
x = 8
x = −8

1 33

Got questions? Get instant answers now!

−5 y + 14 when
y = 9
y = −9

Got questions? Get instant answers now!

10 3 m when
m = 5
m = −5

−5 25

Got questions? Get instant answers now!

18 4 n when
n = 3
n = −3

Got questions? Get instant answers now!

2 w 2 3 w + 7 when
w = −2

21

Got questions? Get instant answers now!

3 u 2 4 u + 5 when u = −3

Got questions? Get instant answers now!

9 a 2 b 8 when
a = −6 and b = −3

−56

Got questions? Get instant answers now!

7 m 4 n 2 when
m = −4 and n = −9

Got questions? Get instant answers now!

Translate English Phrases to Algebraic Expressions

In the following exercises, translate to an algebraic expression and simplify if possible.

the sum of 3 and −15 , increased by 7

( 3 + ( −15 ) ) + 7 ; 5

Got questions? Get instant answers now!

the sum of −8 and −9 , increased by 23

Got questions? Get instant answers now!

the difference of 10 and −18

10 ( −18 ) ; 28

Got questions? Get instant answers now!

the difference of −5 and −30

−5 ( −30 ) ; 25

Got questions? Get instant answers now!

subtract −6 from −13

Got questions? Get instant answers now!

the product of −3 and 15

−3 · 15 ; 45

Got questions? Get instant answers now!

the product of −4 and 16

Got questions? Get instant answers now!

the quotient of −60 and −20

−60 ÷ ( −20 ) ; 3

Got questions? Get instant answers now!

the quotient of −40 and −20

Got questions? Get instant answers now!

the quotient of −6 and the sum of a and b

−6 a + b

Got questions? Get instant answers now!

the quotient of −7 and the sum of m and n

Got questions? Get instant answers now!

the product of −10 and the difference of p and q

−10 ( p q )

Got questions? Get instant answers now!

the product of −13 and the difference of c and d

Got questions? Get instant answers now!

Use Integers in Applications

In the following exercises, solve.

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

96 °

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

Football At the first down, the Chargers had the ball on their 25 yard line. On the next three downs, they lost 6 yards, gained 10 yards, and lost 8 yards. What was the yard line at the end of the fourth down?

21

Got questions? Get instant answers now!

Football At the first down, the Steelers had the ball on their 30 yard line. On the next three downs, they gained 9 yards, lost 14 yards, and lost 2 yards. What was the yard line at the end of the fourth down?

Got questions? Get instant answers now!

Checking Account Mayra has $124 in her checking account. She writes a check for $152. What is the new balance in her checking account?

$28

Got questions? Get instant answers now!

Checking Account Selina has $165 in her checking account. She writes a check for $207. What is the new balance in her checking account?

Got questions? Get instant answers now!

Checking Account Diontre has a balance of $38 in his checking account. He deposits $225 to the account. What is the new balance?

$187

Got questions? Get instant answers now!

Checking Account Reymonte has a balance of $49 in his checking account. He deposits $281 to the account. What is the new balance?

Got questions? Get instant answers now!

Everyday math

Stock market Javier owns 300 shares of stock in one company. On Tuesday, the stock price dropped $12 per share. What was the total effect on Javier’s portfolio?

$3600

Got questions? Get instant answers now!

Weight loss In the first week of a diet program, eight women lost an average of 3 pounds each. What was the total weight change for the eight women?

Got questions? Get instant answers now!

Writing exercises

In your own words, state the rules for multiplying integers.

Answers may vary

Got questions? Get instant answers now!

In your own words, state the rules for dividing integers.

Got questions? Get instant answers now!

Why is 2 4 ( −2 ) 4 ?

Answers may vary

Got questions? Get instant answers now!

Why is 4 3 = ( −4 ) 3 ?

Got questions? Get instant answers now!

Self check

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

A table is shown that is composed of four columns and seven rows. The titles of the columns are “I can …”, “Confidently”, “With some help” and “No – I don’t get it!”. The first column reads “multiple integers.”, “divide integers.”, “simplify expressions with integers.”, “evaluate variable expressions with integers.”, “translate English phrases to algebraic expressions.” and “use integers in applications.”

On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?

Questions & Answers

What are the factors that affect demand for a commodity
Florence Reply
differentiate between demand and supply giving examples
Lambiv Reply
differentiated between demand and supply using examples
Lambiv
what is labour ?
Lambiv
how will I do?
Venny Reply
how is the graph works?I don't fully understand
Rezat Reply
information
Eliyee
devaluation
Eliyee
t
WARKISA
hi guys good evening to all
Lambiv
multiple choice question
Aster Reply
appreciation
Eliyee
explain perfect market
Lindiwe Reply
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
Ezea
What is ceteris paribus?
Shukri Reply
other things being equal
AI-Robot
When MP₁ becomes negative, TP start to decline. Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Kelo
yes,thank you
Shukri
Can I ask you other question?
Shukri
what is monopoly mean?
Habtamu Reply
What is different between quantity demand and demand?
Shukri Reply
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Lilia Reply
what is the difference between economic growth and development
Fiker Reply
Economic growth as an increase in the production and consumption of goods and services within an economy.but Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
Abdisa Reply
any question about economics?
Awais Reply
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50. A,Calculate quantities of x and y which maximize utility. B,Calculate value of Lagrange multiplier. C,Calculate quantities of X and Y consumed with a given price. D,alculate optimum level of output .
Feyisa Reply
Answer
Feyisa
c
Jabir
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
Gsbwnw Reply
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
Abdureman
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask