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Lesson Directive // Negative NumbersREF_CORE

The Number Line

−(-(−a-a))==aa

Hover over a variable in the formula above, or see glossary below:

aa
Positive Value
Real Number

Negative numbers lie to the left of zero on the number line. Adding a positive number moves right; adding a negative number moves left.

INSIGHT: Subtracting is the same as adding a negative: $5 - 3 = 5 + (-3)$.

Sign Rules for Multiplication

Positive × Positive = Positive. Negative × Negative = Positive. Positive × Negative = Negative.

INSIGHT: Two negatives cancel out — mathematically and intuitively.

Absolute Value

The absolute value |a| is the distance of a from zero on the number line, always non-negative: |-5| = 5.

INSIGHT: Distance is never negative — that is what absolute value captures.
Detailed Theory & ReferencesEXT_DOC

Negative Numbers and Signed Arithmetic

Negative numbers extend the counting numbers into values less than zero. They are fundamental to algebra, physics, finance, and computing.

The Number Line

⋯−3,−2,−1,0,+1,+2,+3⋯\cdots -3, -2, -1, 0, +1, +2, +3 \cdots

Addition and Subtraction Rules

OperationInterpretation
a+ba + bMove bb units right
a+(−b)a + (-b)Move bb units left (same as a−ba - b)
a−(−b)a - (-b)Move bb units right (same as a+ba + b)

Multiplication Sign Rules

SignsProduct
(+)(+)(+)(+)Positive
(−)(−)(-)(-) Positive
(+)(−)(+)(-)Negative

Absolute Value

∣a∣={aif a≥0−aif a<0|a| = \begin{cases} a & \text{if } a \geq 0 \\ -a & \text{if } a < 0 \end{cases}

References

AI NOTICE

AI Assistance Disclaimer: This module uses AI-assisted educational models and interactive visual representations to help explain scientific and mathematical concepts. For formal research or academic evaluation, please verify formulas and data against standard primary reference materials.