Signed Numbers (Integers & Absolute Value)

Why This Matters for Nursing: Temperature changes (dropped 3 degrees), fluid balance (negative 500 mL), and lab value changes all use positive and negative numbers. Understanding how they work prevents critical calculation errors.

What You Need to Know

Integers are whole numbers that can be positive, negative, or zero: - Positive: +1, +2, +3... (or just 1, 2, 3) - Negative: -1, -2, -3... - Zero: 0 (neither positive nor negative)

Absolute value |x| is the distance from zero—always positive: - |5| = 5 - |-5| = 5 - |0| = 0

🧠 Memory Trick

For adding signed numbers: - Same signs → ADD and keep the sign - Different signs → SUBTRACT and keep the sign of the larger absolute value

For subtracting: "Add the opposite" a - b = a + (-b)

"Two negatives make a positive" (when multiplying or dividing)

Rules for Operations

Adding Signed Numbers

Subtracting Signed Numbers

Add the opposite! - 5 - 8 = 5 + (-8) = -3 - -3 - 4 = -3 + (-4) = -7 - -6 - (-2) = -6 + 2 = -4

Multiplying and Dividing

Same signs → Positive result Different signs → Negative result

✏️ Worked Examples

Example 1: Adding Same Signs

Problem: -15 + (-7)

Step 1 — Check the signs. Both numbers are negative. Same signs → add the numbers and keep the negative sign.

Step 2 — Add the absolute values (ignore the signs for now). 15 + 7 = 22.

Step 3 — Apply the sign. Both were negative, so the answer is negative: -22.

Answer: -22

💡 Think of it like debt. If you owe $15 AND you owe another $7, you owe $22 total. Same idea.