Integers & Absolute Value — Challenge
Below zero is a direction, and how far from zero is a separate question.
What these problems cover
These questions use 2 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Absolute value — |x| — distance from zero, always positive or zero.
- Number line — A line with numbers increasing to the right.
Problem 1
On a winter day the high temperature was 16 degrees higher than the low temperature. The low was -9 degrees. What was the high temperature?
- -25
- -7
- 7
- 16
- 25
Worked answer
7
Higher means add: the high is -9+16.
Starting at -9 and moving 16 to the right on the number line passes zero and lands on 7 degrees.
Problem 2
A submarine at an elevation of -120 metres rises 85 metres. What is its new elevation in metres?
- -205
- -35
- -45
- 35
- 205
Worked answer
-35
Rising means adding: -120+85.
Because 120 is larger than 85, the result is still below sea level: -120+85 = -35 metres.
Problem 3
An account holds $40 and a withdrawal of $65 is allowed to overdraw it. What is the balance in dollars afterwards?
- -105
- -25
- -15
- 25
- 105
Worked answer
-25
A withdrawal subtracts: 40-65.
Subtracting a larger number from a smaller one gives a negative result: 40-65 = -25 dollars, meaning the account is 25 dollars overdrawn.
Problem 4
What is |-7|+(-3)?
- -10
- -4
- 4
- 10
- -21
Worked answer
4
The absolute value bars give the distance from zero, which is never negative: |-7| = 7.
Then 7+(-3) = 7-3 = 4.
Problem 5
What is -6+2+(-11)+0?
- -19
- -15
- -9
- 15
- 19
Worked answer
-15
Add the negatives together: -6+(-11) = -17.
Then add the positives: -17+2+0 = -15.
Problem 6
A lift starts on floor -3, goes up 7 floors, then down 2 floors. Which floor does it end on?
- -12
- -2
- 2
- 8
- 12
Worked answer
2
Up adds and down subtracts, so the journey is -3+7-2.
-3+7 = 4, and 4-2 = 2, so the lift ends on floor 2.
Problem 7
At noon the temperature was -3°. It rose 7° by 3 p.m., then fell 12° by midnight. What was the midnight temperature?
- -8°
- -2°
- 8°
- 4°
- -16°
Worked answer
-8°
Start at -3 and rise 7: -3 + 7 = 4. Now fall 12 from there: 4 - 12 = -8. So it was -8° at midnight — colder than it started, because the fall was larger than the rise.
Problem 8
Which of these is the largest?
- |-7|
- -9
- |3|
- -|5|
- 6
Worked answer
|-7|
Work each one out first: |-7| = 7, -9 stays -9, |3| = 3, -|5| = -5, and 6 is 6. Now compare: 7, -9, 3, -5, 6. The largest is 7. Note that -9 has the biggest digits and is the smallest value of all.