Integers and Their Opposites
A scuba diver rose 600 feet to the surface of the water. The integer that represents the diver’s position, in feet, with respect to the water’s surface before rising is
-600
What is the decimal equivalent of -23/20?
-1.15
-23 + 7
-16
-12 - (-12)
0
True or False
-32-34=-66
TRUE
A submarine is underwater. Its position is 645 feet below sea level. It rises in the water 100 feet and then descends 100 feet. What integer represents the change in the submarine’s position in the water?
0
What is the difference between a terminating decimal and a repeating decimal?
A terminating decimal stops and a repeating decimal continues infinitely with a specific pattern
Which sums are positive?
a. -5 + (-2)
b. 5 + (-2)
c. -3 + 4
d. 0 + (-3)
e. -2 + (4)
b. 5 + (-2)
c. -3 + 4
e. -2 + (4)
-7 - 4 - (-6)
-5
The average temperature of Saturn in 218 degrees below zero. What is the absolute value of the integer that represents the temperature?
218
Frank was swimming 9.54 feet below sea level when he spotted a whale. It is estimated that the whale was swimming 67.458 feet below Frank. What was the depth the whale was swimming?
The whale was 76.998 feet below sea level .
DISTANCE CANNOT BE NEGATIVE
The directions on a seed packet say to plant the seeds 1 7/8 inches apart. What is the decimal equivalent of this mixed number?
7/8 = 0.875
1 7/8 = 1.1875
Sandra plays a matching game. In order to advance to the next level, she must score at least 10 points. She scores 18 points for correct matches and -6 points for incorrect matches. Did Sandra make it to the next level?
Sandra scored 12 points
18 + (−6) = 12
The football referee calls a penalty of 5 yards against a team in addition to a loss of 3 yards. If another referee calls an additional penalty of 10 yards, what is the team's net loss in yards as an integer?
-18 is the integer
18 yards would be the total loss
How do you find the additive inverse of a number? Give an example of a number and its additive inverse.
Two numbers that have a sum of 0 are additive inverses, or opposites. 6 and −6
Carleton answered 53 questions incorrectly on a test. Write two different situations that can be represented by the opposite of -53?
(many answers)
answering 53 questions correctly
a temperature of 53 degrees
getting $53.00 as a gift
Nine friends vote on their favorite fruit. Only one person in the group votes for kiwi. Write the fraction as an equivalent decimal. Is the decimal a rational number?
1/9 = 0.1111...
it is rational because the digits repeat.
Ashley’s math average decreased 12 points to 78. Then she completed an extra credit assignment and raised her final average by 5 points. Write an equation to show how Ashley’s average changed. What washer starting average? What was her final average?
−12 + 5 = −7
Ashley’s final average was 83, 7 points less than her starting average of 90.Sample answer: The sum will have the sign of the
Suki solved the following
-8-(-6)=-14
Explain her error AND how to fix it.
-8 - (-6)
-8 + 6
-2
A space shuttle is orbiting the earth at 531084.87 meters above sea level and a submarine is traveling at 432.55 meters below sea level . What is the distance between the two aircrafts?
53184 - 432.55
52752.32
A train is going on a journey. First, it travels east for 50 kilometers. Then, it turns north and travels for 22 kilometers. Next, it goes west for 50 kilometers. Finally, it travels south for a certain number of kilometers. At the end of its journey, it is back at its original location. How many kilometers did it travel in the southward direction?
22 km
Is 0.040040004… a rational number?
No
The decimal has a pattern, but not one that repeats. So the number is not rational.RationalRational
Felix spends $150 each month for his gym membership plus $30 each week for a personal trainer. A new gym charges $255 a month, which includes a weekly session with a personal trainer. Would Felix save money by switching to the new gym?
(remember there are 4 weeks in 1 month)
Felix WOULD save by switching to the new gym. His current gym membership is -270 per month and the new gym membership would be -255 per month
The temperature in Anchorage, Alaska, was -3°C in the afternoon. After the sun went down, the temperature dropped 6 degrees. Write an equation to represent the situation. What was the temperature after the sun went down?
−3 − 6 = −9
The temperature in the late afternoon was −7.5°C. It dropped 5 degrees by early evening and then dropped another 8.5 degrees by midnight. What was the temperature at midnight? L
-21°C