Multiplying Integers
(-15)(-3)
What is 45?
38 ÷ (-19)
What is -2?
-5 + -8
What is -13?
-5 + (-4)
What is -9?
The record high temperature for Massachusetts is 104 degrees Fahrenheit. The record low is -18 degrees Fahrenheit. What is the difference between high and low?
What is 122 degrees Fahrenheit?
The problem has 1 important component. It is the phrase "difference between high and low."
Difference between high and low is the same as subtracting the smaller number from the bigger number.
104 - -18 = 104 + 18 = 122
The difference between high and low is 122 degrees Fahrenheit.
(8)(-12)
What is -96?
26/-13
What is -2?
-3 + 12
What is 9?
-52 + (-48)
What is -100?
A football team loses 6 yards on one play and then loses 10 yards on the next play. How many yards did they lose on the two plays?
What is -16?
-15(9)
What is -135?
-63/-21
What is 3?
-1500 + 525 + -350
What is -1325?
-90 + (-20)
What is -110?
Sylvia checked the balance in her bank account early in the morning and saw that she had 98 dollars. In the afternoon, she noticed that there was an overdraft of 6 dollars in the account for unpaid bills. How much were the unpaid bills?
What is $104?
The problem has 1 important component. It is the word "Overdraft."
An overdraft occurs when the bank gives you money to cover the amount you did not have at the time the bills were paid. In this case, what you did not have is 6 dollars. Since the bank gave it to you, you owe it to the bank. Therefore, you owe 6 dollars to the bank and this can be expressed as -6.
The amount of unpaid bills is the difference between what you had that morning (98) and what you have this afternoon (-6).
98 - -6 = 98 + 6 = 104 dollars
The amount of unpaid bills is 104 dollars
A test has 20 questions. The test awards 3 points if the answer is correct and takes away 1 point if the answer is incorrect. A student answered 5 questions incorrectly. How many points did the student lose?
What is -5 points?
For each incorrect answer, the student earns -1 point.
After answering 5 questions incorrectly the student earns -1 × 5 = -5.
The students lost 5 points.
A penalty in Meteor-Mania is -5 seconds. A penalty in Cosmic Calamity is -7 seconds. Yolanda had penalties totaling -25 seconds in a game of Meteor-Mania and -35 seconds in a game of Cosmic Calamity. In which game did Yolanda receive more penalties? Justify your answer.
What is Yolanda received the same number of penalties in each game?
Step 1 :
To find the number of times Yolanda received penalties in Meteor-Mania, divide the total penalties by penalties per time.
-25 ÷ (-5) = 5
In the game of Meteor-Mania, she received penalties 5 times
Step 2 :
To find the number of times Yolanda received penalties in Cosmic Calamity, divide the total penalties by penalties per time.
-35 ÷ (-7) = 5
In the game of Cosmic Calamity, she received penalties 5 times.
Step 3 :
Compare the number of times she received penalties in both the games.
5 = 5
Yolanda received the same number of penalties in each game
In 2002, Tiger Woods won the Masters Tournament. His scores were 2, 3, 6 and 1 for four rounds. What was his final score?
What is -12?
-2 + -3 + -6 + -1
-5 + -6 + -1
-11 + -1
-12
An airplane takes off and then climbs 2500 feet. After 20 minutes, the airplane descends 150 feet. What is the airplane's current height?
What is 2350 feet?
The problem has 2 important components shown in bold below.
An airplane takes off and then climbs 2500 feet. After 20 minutes, the airplane descends 150 feet. What is the airplane's current height?
Climbs 2500 feet can be represented with +2500
Descends 150 feet can be represented with - 150
We get +2500 - 150 = +2500 + -150 = 2350
The airplane is now at a height of 2350 feet.
The price of one share of a stock fell 4 dollars each day for 8 days. How much value did one share of the stock lose?
What is -32?
Each day, one share of the stock goes down by 4 dollars. We can represent this situation with the integer -4.
After 8 days, one share of a stock has gone down by -4 × 8 = -32
One share of a stock is now worth 32 dollars less.
A credit card company charges a late fee of 25 dollars each time a customer fails to pay on time. A customer missed the payment 4 times last year. At the customer's request and out of courtesy, the credit card company decides to cancel all late fees for that year. Write a numerical expression to show how much money was return.
What is -25 × 4?
The amount of late fee the bank charged last year was -25 × 4
In order to return the money, the bank can do this math: -25 × -4
Notice how the number 4 became negative. This is necessary so the amount of money the customer gets back is a positive number.
A machine is used to get water out of the ground. The water is located at 165 feet below ground level. If the machine plans on digging the same amount for 6 days, what is the change in the location of the bottom of the hole each day?
What is -27.5?
Equation:
-165 ÷ 6
A local bookstore has 30 copies of a bestseller when it opens on Monday morning. On Monday, it sells 6 copies of the book. On Tuesday, it sells 3 copies. On Wednesday, it receives a shipment containing 24 copies of the books and also sells 8 copies. How many books does the store have at the end of Wednesday?
What is 37 books?
30 + -6 + -3 + 24 + -8
24 + -3 + 24 + -8
21+ 24 + -8
45 + -8
37 books
You are 5 dollars in debt. You borrow 12 dollars more. What is the total amount of your debt?
What is $17?
The problem has 2 important components shown in bold below.
You are 5 dollars in debt. You borrow 12 dollars more. What is the total amount of your debt?
5 dollars in debt can be represented by -5
Borrow 12 more can be represented by - 12
We get -5 - 12 = -5 + -12 = -17
The amount of your debt is 17 dollars.
Jimmy answers questions in two different online Olympic trivia quizzes. In each quiz, he loses points when he gives an incorrect answer. The table shows the points lost for each wrong answer in each quiz and Jimmy’s total points lost in each quiz. In which quiz did he have more wrong answers?
What is winter quiz?
Step 1 :
To find the number of incorrect answers in the winter quiz, divide the total points lost by the number of points lost per the wrong answer.
-33 ÷ (-3) = 11
Step 2 :
Find the number of incorrect answers Jimmy gave in the summer quiz. Divide the total points lost by the number of points lost per the wrong answer.
-56 ÷ (-7) = 8
Step 3 :
Compare the numbers of wrong answers.
11 > 8
So, Jimmy had more wrong answers in the winter quiz.