Day 3: Multiplying & Dividing Integers ✖️➗
Middle Stage (Grades 6, 7 & 8) | Apex Institute of Maths and Sciences
🎯 1. Concept: The Sign Rules
Welcome to Day 3! You already know how to add and subtract integers. Today, we look at Multiplication and Division. Here is the great news: The rules are exactly the same for both!
You don’t need to worry about which number is bigger anymore. You only need to look at the signs (+ or -) and follow the Two Golden Sign Rules:
💡 2. The Golden Sign Rules
Rule 1: SAME Signs = Positive Result (+)
- Positive × Positive = Positive (Example: 3 × 4 = 12)
- Negative × Negative = Positive (Example: -3 × -4 = 12)
Trick: “The enemy of my enemy is my friend!” Two negatives cancel each other out.
Rule 2: DIFFERENT Signs = Negative Result (-)
- Positive × Negative = Negative (Example: 3 × -4 = -12)
- Negative × Positive = Negative (Example: -3 × 4 = -12)
Trick: The negative sign is powerful; if there’s only one, it takes over the answer!
*These exact same rules apply to division! (-20 ÷ -4 = 5) and (-20 ÷ 4 = -5).
🌍 3. Math in Our Daily Life
Multiplying negatives happens in real life when we deal with recurring losses!
Scenario 1 (Subscriptions): Imagine a streaming service charges you ₹200 a month. This is a change to your bank of -200. If you pay this for 4 months, what is the total change?
Calculation: 4 months × (-200) = -800. Your account lost ₹800.
Scenario 2 (Submarines): A submarine dives down to -600 meters. It took 3 minutes to reach that depth. How fast was it diving per minute?
Calculation: -600 meters ÷ 3 minutes = -200 meters per minute.
📝 4. Application Tasks
Grab your math journal and try these tasks:
- Task A: The Cheat Sheet: Take a colorful piece of paper and draw a “Sign Rules” cheat sheet for multiplying and dividing. Stick it near your study table!
- Task B: The Video Game: In a video game, you lose 5 points (-5) every time you hit a red wall. If you hit the wall 6 times, write the multiplication equation to find your total score change.
- Task C: The Tricky Challenge: What do you get if you multiply (-1) × (-1)? What if you multiply (-1) × (-1) × (-1)? Try it!
✅ 5. Day 3 Practice Test
Let’s master the Sign Rules! Select the correct answers below and click submit to check your score.
