Integers & Opposites
Rational #'s
Rational #'s
Kristen goes on a cave tour with her family. They climb down to 8 meters below ground level. Then, they climb the opposite of -8 meters back to ground level. What is total number of meters they climbed in either direction?
16 meters
Write all of the positive sums.
-5 + (-2)
5 + (-2)
-3 + 4
0 + (-3)
-2-(-4)
5 + (-2)
-3 + 4
-2-(-4)
Solve 20.25-9 1/2 + 11. Show your work.
21.75 or 21 3/4
Will the sign of the product of two negative numbers be positive or negative?
Positive
No, the quotient should be negative.
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 the journey, it is back at its original location. How many kilometers did it travel in the southward direction?
22
When you add a positive number and a negative number, how can you tell whether the sum will be positive or negative?
The sum will have the sign of the addend with the greater absolute value
Joaquin recorded a temperature of 62 degrees F this morning for science class. The temperature increased 6 1/2 degrees F in the afternoon before decreasing 8.7 degrees F in the evening. What was the evening temperature?
59.8 degrees F
Chase simplified the expression -2 x (5-3), and found -2 x 2 = 4. Is Chase correct? Why or Why not?
No, the factors have different signs so the product should be negative.
Inez says you can plot 4/0 on a number line, but Jeremiah says you cannot. Who is correct? Why
Jeremiah because any number divided by 0 is undefined.
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?
1.875
The temperature in Anchorage, Alaska was -3 degrees Celsius in the afternoon. After the sun went down, the temperature dropped 6 degrees. Write and equation to represent the situation. What was the temperature after the sun went down?
-3-6 = -9
-9
During 7 1/2 months of hibernation, a black bear lost 64.4 pounds. On average, what was the bear's weight change per month?
-8.6 pounds
Find the product of -3/5 x (-1.5).
0.9
Find the quotient of -3/4 / (-8/12)
1 1/8
0.11111111...
Yes, it is rational because it repeats.
Rob borrows $15 from his father, and then he borrows $3 more. How much money does Rob owe his father?
$18
At the beginning of the month, Kim had $65.78. Since then, she has received 3 payments of $32.50 from her babysitting job. Kim's 2 sisters each helped her babysit once during the month, Kim paid them each $8.75. How much money does Kim have now?
$145.78
Jenny has $2.40 deducted from her monthly allowance every time she forgets to do a chore. If she forgets to do her chore 3 times in one month, what will be the change in Jenny's total allowance?
-$7.20
A submarine descends at a rate of 2.6 Km per hour. If the ocean floor is 6.24 km below sea level, how long will it take the submarine to descend to the ocean floor?
2.4 hours
Rochelle needs to pack a picture frame that measures 7 6/11 inches on each side. Will it fit into a box that measures 7.52 inches on each side? Explain.
No
7 6/11 = 7.54, which is greater than 7.52
Suppose y is a positive integer. If x-(-y)=z, will z be greater than or less than x? Explain.
subtracting -y is the same as adding its additive inverse, y.
A scuba diver is swimming 15 feet below the water's surface. The diver swims up slowly at 0.5 feet per second for 4 seconds and then stops to look at an eel. Finally, the diver swims up for 3 more seconds at 0.4 feet per second. What is the diver's new depth?
-11.8 Feet
An airplane descends at a rate of 2,700 feet per minute. Once the airplane stars its descent, what will be its change in elevation after 3 1/2 minutes?
-9450 Feet
A tanker truck fills the gas station’s reservoir at the rate of 121 2 gallons per minute. If the reservoir was empty and it is now 35 gallons full, how long has the tanker been filling the reservoir?
2.8 minutes