Day 3: Multiplying & Dividing Integers | Middle Stage | Apex Institute of Maths and Sciences

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Day 3: Multiplying & Dividing Integers | Middle Stage | Apex Institute of Maths and Sciences

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.

1. According to the rules, a Negative number multiplied by a Negative number gives a…
Solution: SAME signs result in a Positive! The two negatives cancel each other out.
2. A Positive number multiplied by a Negative number gives a…
Solution: DIFFERENT signs result in a Negative! The one negative sign takes over the answer.
3. What is (-5) × (-4)?
Solution: 5 × 4 is 20. Since both signs are negative (same signs), the answer is positive 20.
4. What is 7 × (-3)?
Solution: 7 × 3 is 21. Since the signs are different (one positive, one negative), the answer is -21.
5. What is (-36) ÷ 6?
Solution: 36 ÷ 6 is 6. The signs are different (negative divided by positive), so the answer is -6.
6. What is (-40) ÷ (-8)?
Solution: 40 ÷ 8 is 5. Since both signs are the same (negative), the answer becomes positive 5.
7. In a game, you lose 3 points every time you drop the ball. You drop it 4 times. What is your total score change?
Solution: Losing 3 points is -3. You do it 4 times. (-3) × 4 = -12.
8. What is (-8) × 0?
Solution: The zero rule always wins! Any number multiplied by 0 is exactly 0.
9. What is (-1) × (-1)?
Solution: 1 × 1 is 1. A negative times a negative makes a positive. Answer is 1.
10. Tricky Question: What is (-2) × (-2) × (-2)?
Solution: Do it in steps! First: (-2) × (-2) = +4. Next: multiply that +4 by the last (-2). 4 × (-2) = -8.
⚠️ Please answer all 10 questions before submitting!
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