## Dividing Signed Numbers Just like multiplication, **dividing signed numbers** follows specific sign rules. In the electrical field, you might divide signed numbers when calculating: - Resistance using Ohm’s Law - Current or voltage based on power and resistance - Efficiency ratios - Current over time (to find average current flow) ### Sign Rules for Division |Rule|Example|Result| |---|---|---| |Positive ÷ Positive = Positive|$+12 \div +3$|$+4$| |Negative ÷ Negative = Positive|$-12 \div -3$|$+4$| |Positive ÷ Negative = Negative|$+12 \div -3$|$-4$| |Negative ÷ Positive = Negative|$-12 \div +3$|$-4$| The rules are **identical to multiplication**. ## Example 1: Ohm’s Law Using: $ R = \frac{V}{I} $ If $V = -24$ volts and $I = -6$ amps, then: $ R = \frac{-24}{-6} = +4 \ \Omega $ Even though both values were negative, the result is **positive resistance**, which makes sense physically. ## Example 2: Voltage Direction A sensor outputs a voltage of $-18$ volts and is scaled by a gain of $+3$. To find the base signal: $ \frac{-18}{+3} = -6 \ \text{V} $ This shows that the original signal was inverted. ## Example 3: Power Distribution A battery lost $-60$ watt-hours of energy over $-3$ hours. To find the average power: $ \frac{-60}{-3} = +20 \ \text{watts} $ A negative divided by a negative gives a **positive** result, indicating the system was drawing a consistent load. ## Practice 1. $+18 \div -6 = \ ?$ 2. $-48 \div -8 = \ ?$ 3. $-36 \div +9 = \ ?$ 4. A device discharges $-120$ C of charge over $-4$ seconds. What is the current? ## Summary - Divide the numbers normally - Apply the sign rules: - Same signs → Positive - Different signs → Negative - Signed division appears in **voltage/current ratios**, **power calculations**, and **signal scaling**