Integers in Real Life
A submarine is 9 feet below sea level. What integer represents its position?
−9
Below sea level is represented by a negative integer
Which is greater: −7 or −3?
−3
−3 is farther left on the number line.
What number lies halfway between −2 and −1 on a number line?
−1.5 (or −1½)
Halfway between −2 and −1.
What does the absolute value of a number tell you?
Its distance from zero on a number line.
Distance cannot be negative.
Which is best represented by a positive integer: a debt, an elevation above sea level, or a temperature below 0°F?
An elevation above sea level
Above sea level means a positive elevation.
Order these temperatures from warmest to coldest: −6°F, −1°F, −15°F, −9°F.
−1°F, −6°F, −9°F, −15°F
Greatest to least.
Which quadrant contains the point (4, −3)?
Quadrant IV
Positive x, negative y.
Evaluate |−6|.
6
The number −6 is 6 units from zero.
The temperature changes from −8°F in the morning to 17°F in the afternoon. What is the difference?
25°F
17 − (−8) = 25
Complete the inequality: −4.5 ___ −2.
<
−4.5 is farther left than −2.
Starting at the origin, how do you plot (−5, 4)?
Move left 5, then up 4.
x first, then y.
True or false: |−4| > |4|. Explain.
False
Both absolute values equal 4.
A student borrows $4 from each of 3 friends. They earn $12 and repay everyone. What is their final balance?
$0
Three debts of $4 total −$12; −12 + 12 = 0.
Which is larger: 0.75 or 3/8? Explain.
0.75
3/8 = 0.375, so 0.75 > 0.375.
A park is at (5, 4) and a school is at (5, −4). What is the difference in their y-coordinates?
8 units
4 − (−4) = 8.
Which statement is true:
|7.2| = |−7.2| or |−7.2| = −7.2?
|7.2| = |−7.2|
Both equal 7.2.
Create a real-world situation represented by −12. Explain what zero means in your situation.
Sample: A diver is 12 feet below sea level; zero is sea level.
Accept other accurate situations with a meaningful zero.
A student says −5½ > −3 because 5½ is farther from zero. Identify and correct the error.
−5½ < −3
For negative numbers, farther left means smaller; absolute value is not the signed value.
A student plots (2, −4) by moving left 2 and up 4. Explain the mistake and give the correct directions.
Move right 2 and down 4.
Positive x is right; negative y is down.
A scuba diver is 48 feet below sea level and a hiker is 175 feet above sea level. How far apart are they in elevation?
223 feet
175 − (−48) = 223 feet.