## Subtracting Signed Numbers Subtracting signed numbers is a natural extension of adding them. The key idea is: **Subtraction is the same as adding the opposite.** This rule helps simplify all signed subtraction problems, and it's widely used in voltage calculations, phase shifts, and comparing values in electrical diagnostics. ### The Rule To subtract a signed number: $A - B = A + (-B)$ That means: - **Keep the first number as is** - **Change the subtraction sign to addition** - **Flip the sign of the second number** Then use the rules for **adding signed numbers**. ### Example 1 $+6 - (+4)$ Rewrite as: $+6 + (-4) = +2$ ### Example 2 $-7 - (+3)$ Rewrite as: $-7 + (-3) = -10$ ### Example 3 $-5 - (-8)$ Rewrite as: $-5 + (+8) = +3$ Notice: - Subtracting a negative is the same as **adding** a positive. ## Visualizing with a Number Line You can think of subtraction as **movement** on the number line: - Subtracting a positive → move **left** - Subtracting a negative → move **right** Example: Start at $-2$, subtract $-3$: $-2 - (-3) = -2 + 3 = +1$ Move right → you land at 1. ## Electrical Example: Net Voltage Drop A circuit sees a voltage increase of +12 V, followed by a drop of −7 V. The voltage change is: $ +12 - (-7) = +12 + (+7) = +19 \ \text{V} $ Another case: If a battery reads +10 V and a load causes a +4 V drop, the net voltage becomes: $ +10 - (+4) = +6 \ \text{V} $ ## Practice 1. $+9 - (+3) = \ ?$ 2. $-6 - (-2) = \ ?$ 3. $-4 - (+5) = \ ?$ 4. $+7 - (-3) = \ ?$ ## Summary - Subtraction becomes **adding the opposite** - Flip the sign of the second number, then add - This method is critical in **voltage**, **current**, and **measurement difference** calculations in the field