Number line · sign · absolute value
INTEGERS &
NEGATIVES
Integers extend whole-number steps in both directions from zero. Positive integers, negative integers, and zero all live on the same number line, where position tells us order and distance.
Values Around a Reference Point
Negative values describe quantities below a chosen reference point:
- Temperature: −10°C is colder than 0°C.
- Money: If a balance is $5 and $10 is spent, the new balance is −$5.
- Elevation: A location 86 m below sea level can be represented as −86 m.
+
Subtracting a Negative
a − (−b)
=a + b
Subtracting a number means adding its opposite. The opposite of a negative number is positive.
x
Absolute Value
Absolute value measures distance from zero, so it is never negative.
|−5| = 5 · |0| = 0
Number-line lab
Elevator Logic
Equation
0+3=3
Start Floor0
Action Value3
10
9
8
7
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
0
Multiplication Sign Reference
Pos × Pos
= Pos
Neg × Neg
= Pos
Pos × Neg
= Neg
Neg × Pos
= Neg
Same signs produce a positive product; different signs produce a negative product.
Reference & Check
Knowledge Check: Negatives1 / 3
What happens when you subtract a negative number? (e.g., 5 - (-3))
Connect Forward
Signed arithmetic becomes part of the expressions whose operations must be interpreted in a consistent order.