Negative Numbers & Signed Integer Arithmetic (+, −, ×, ÷)
Negative numbers represent values below zero (temperatures, debts, elevation). Mastering sign rules eliminates the #1 cause of lost points in middle school algebra.
🧠 Core Mental Strategies & Shortcuts
➖ Minus a Minus is Plus: a − (−b) = a + b
Subtracting a negative removes a debt, which is identical to adding a positive: 7 − (−4) = 7 + 4 = 11.
✖️ Same Signs Positive, Different Signs Negative
(−) × (−) = (+), while (−) × (+) = (−). For example, (−4) × (−6) = +24.
🌡️ The Number Line Temperature Model
Adding a negative moves left (colder). Subtracting a negative moves right (warmer).
❓ Frequently Asked Questions
Why is a negative times a negative positive?
Think of multiplication as repeated direction: positive is "moving forward", negative is "reversing direction". Reversing twice points you forward again (+).
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