Absolute Value and Opposites
Marcus dives from the surface of the ocean to a reef 18 meters below sea level. What integer represents Marcus’s location relative to the surface? How far does Marcus have to go to return to the surface?
-18, 18 meters
what is the decimal equivalent of 7/20
.35
When you add a positive number and a negative number, how can you tell whether the sum will be positive or negative?
The sign will be that of the bigger number (addend)
Will the sign of the product of two negative numbers be negative or positive? Explain.
Positive
Kareem heats a beaker of water to a boil. Then he records that the water temperature decreases from 100°C to 19°C in 5 2/5 minutes. What was the average change in temperature each minute
-15 degrees
What property is shown here
2 + 3 = 3 + 2
2 x 3 = 3 x 2
Commutative
The temperature of the water in Emily’s fish tank was 78°F on Sunday. The water temperature changed by -3° on Monday, and then by 3°on Tuesday. What integer represents the temperature change of the water from Sunday to Tuesday? What was the water temperature on Tuesday?
0, 78
Is 1.272727... a rational number? explain
Yes, it is a repeating decimal. Rational numbers are terminating and repeating decimals.
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
Solve -2 × (5 - 3)
-4
To win a trivia game, Nevan must score 90 points. Each correct answer is worth 1 3/4 points, and each incorrect answer is worth -14 points. If he gets 58 questions correct and 22 questions incorrect, does Nevan win? How many points does he score?
Yes he scored 96 points.
What property is shown here:
(2 + 3) + 4 = 2 + (3 + 4)
(2 x 3) x 4 = 2 x (3 x 4).
Associative
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 to return to ground level. What is total number of meters they climbed (in either direction)?
16
-3/11 Find the decimal Equivalent
-.2727....
what is the rule for subtracting integers
Keep the sign of the first number
Change to addition
Flip the sign of the second number
An airplane descends at a rate of 2,700 feet per minute. Once the airplane starts its descent, what will be its change in elevation after 3 1/2 minutes?
−9,450 feet
At the beginning of the month, Kimberly had $65.78. Since then, she has received three payments of $32.50 from her babysitting job. Kimberly’s 2 sisters each helped her babysit once during the month, so Kimberly paid them each $8.75. If Kimberly did not spend any money, how much money does she have now?
$145.78
What Property is shown here
a(b + c) = ab + ac.
distributive
what is the absolute value of -5
5
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
Joaquin recorded a temperature of 62°F this morning for science class. The temperature increased 6 1/2°F in the afternoon before decreasing 8.7°F in the evening. What was the evening temperature?
59.8
Inez says you can plot 4/0 on a number line, but Jeremiah says you cannot. Who is correct? Explain
Jeremiah
Any number divided by zero is not a rational number and cannot be represented on a number line
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
What property is shown here
5 + 0 = 5 and 5 x 1 = 5
The identity property. This property refers to numbers that don't change the value of another number when combined. In addition, the identity is 0, and in multiplication, the identity is 1.
Define Absolute Value
Distance from zero
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
- 4 1/2 + 3 1/4. What is the sum?
-1 1/4
Jenna works in an ice cream shop. When she starts her shift, the tub of chocolate ice cream is 2/3 full. When she finishes her shift 6 1/2 hours later, there is only 1/6 of the tub left. What was the average hourly change in tub fullness?
-1/13
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? Round to the nearest tenth
−8.6 pounds
What Property tell us
5 x 0 = 0, or n x 0 = 0
Zero Product. Think about the word product (Means Multiplication)