Integers & Absolute Value — Practice
Below zero is a direction, and how far from zero is a separate question.
What these questions 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
Which is smaller, -8 or -3?
- -8
- -3
- They are equal
- Cannot tell
Worked answer
-8
-8 sits further left on the number line
Problem 2
Which is larger, -1 or 0?
- 0
- -1
- They are equal
- Cannot tell
Worked answer
0
0 is to the right of -1
Problem 3
Work out |-7|.
Worked answer
7
Seven steps from zero
Problem 4
Work out |12|.
Worked answer
12
Twelve steps from zero
Problem 5
Give the opposite of -5.
Worked answer
5
5
Problem 6
Work out -(-9).
Worked answer
9
Two minuses cancel
Problem 7
Work out |-12| + |5|.
Worked answer
17
12 + 5 = 17
Problem 8
Work out |-9| - |-4|.
Worked answer
5
9 - 4 = 5
Problem 9
Put -4, 2, -7, 0 in order, smallest first, separated by commas.
Worked answer
-7,-4,0,2
Left to right: -7, -4, 0, 2
Problem 10
Put 3, -1, -6, 1 in order, smallest first.
Worked answer
-6,-1,1,3
-6, -1, 1, 3
Problem 11
The temperature is -3° and falls 5°. What is it now?
Worked answer
-8
-3 - 5 = -8
Problem 12
A submarine is at -120 m and rises 45 m. What is its depth now?
Worked answer
-75
-120 + 45 = -75
Problem 13
Which is furthest from zero: -9, 4, or -2?
- -9
- 4
- -2
- They are equal
Worked answer
-9
|-9| = 9, the largest distance
Problem 14
A bank balance of -$40 means a debt. After paying in $65, what is the balance?
Worked answer
25
-40 + 65 = 25
Problem 15
Which statement is true?
- -5 < -2
- -5 > -2
- |-5| < |-2|
- -5 = 5
Worked answer
-5 < -2
-5 is further left, so smaller
But |-5| = 5 is the larger distance
Problem 16
Work out |-3| × |-4|.
Worked answer
12
3 × 4 = 12