Multiplying Rational Numbers
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Multiplying Integers: The Sign Battle
What happens when you multiply -3 × -4? If you're thinking the answer is negative, prepare to be surprised. When integers multiply, their signs wage a battle with very specific rules — and the outcome isn't always what you'd expect.
Think of positive integers as your allies and negative integers as enemies. When they multiply, they follow the ancient rule: "The enemy of my enemy is my friend."
The Four Sign Battles
Working Through the Battle
Let's see this in action with a real temperature problem. If the temperature drops 3 degrees every hour for 5 hours, what's the total change?
Step 1: Identify the signs
• Drop = negative = -3
• Hours = positive = 5
Step 2: Apply sign rules (Enemy × Ally = Enemy)
Step 3: Calculate: (-3) × 5 = -15
Answer: The temperature drops 15 degrees total
💡 The Sign Shortcut
Here's the mathematical magic: Same signs always give positive results, different signs always give negative results.
- Same:(+) × (+) = (+) and (-) × (-) = (+)
- Different:(+) × (-) = (-) and (-) × (+) = (-)
🔑 Key Takeaway
Remember that surprising result from -3 × -4? It equals +12! When two negatives multiply, they create a positive — just like how the enemy of your enemy becomes your friend. Master these sign rules, and integer multiplication becomes as predictable as clockwork.
Sample questions
Skills in this topic
- Multiply integers using sign rules
- Multiply positive and negative fractions
- Multiply positive and negative decimals
- Evaluate exponents with negative bases
- Solve real-world multiplication problems with rational numbers
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