Apply multiplication and division rules

Key notes:

✖️ Multiplication Rules

  • 🔢 Multiply the numbers normally → then place the decimal if needed.
  • ➕ Positive × Positive = Positive 🙂
  • ➖ Negative × Negative = Positive 😎
  • ➕➖ Positive × Negative = Negative 🙁
  • 🔁 Order doesn’t matter (Commutative Law):
    a × b = b × a

➗ Division Rules

  • 🔢 Divide the numbers normally, then place the decimal correctly.
  • ➕ Positive ÷ Positive = Positive 🙂
  • ➖ Negative ÷ Negative = Positive 😎
  • ➕➖ Positive ÷ Negative = Negative 🙁
  • ⚠️ Never divide by zero (0) → ❌ not possible!

📏 Zero Rules

  • 🔥 Any number × 0 = 0
  • ➗ 0 ÷ any number ≠ 0 (it = 0)
    Example: 0 ÷ 5 = 0
  • ❌ Division by 0 = not defined

🔄 Rules for Large Numbers

  • ✳️ Use factoring to simplify big multiplications/divisions.
    Example:
    20 × 15 = (2 × 10) × (3 × 5)

📐 Rules with Fractions

  • ✖️ Multiply fractions:
    Multiply top × top and bottom × bottom.
    Example: 2/3 × 4/5 = 8/15
  • ➗ Divide fractions:
    Flip the second fraction (reciprocal) and multiply. 🔄
    Example: 3/4 ÷ 2/5 = 3/4 × 5/2

🔢 Rules with Integers

  • 🔹 Same signs → positive result 🙂
  • 🔹 Different signs → negative result 🙃
  • 🔹 Use a number line to visualize if needed.

💡 Estimation Rules

  • 🧮 Round numbers to make calculations easier:
    Example: 198 × 5 ≈ 200 × 5 = 1000

🎯 Word Problem Tips

📌 Identify operation (× or ÷) from keywords:

  • “Each,” “Every,” “Times” → Multiply ✖️
  • “Share,” “Per,” “Split” → Divide ➗

📝 Write the equation before solving.

Learn with an example

🎈 The number line shows an unknown number, a.

Is 4a positive or negative?

  • positive
  • negative
  • Determine if a is positive or negative.
  • The unknown number a is to the left of 0. So, a is negative.
  • Determine if 4a is positive or negative.
  • In the expression 4a, 4 is positive and a is negative. The product of a positive number and a negative number is negative. So, 4a is negative.

🎈 The number line shows an unknown number, q.

Is 2q positive or negative?

  • positive
  • negative
  • Determine if q is positive or negative.
  • The unknown number q is to the right of 0. So, q is positive.
  • Determine if 2q is positive or negative.
  • In the expression 2q, 2 is positive and q is positive. The product of two positive numbers is positive. So, 2q is positive.

🎈 The number line shows an unknown number, b.

Is 3b positive or negative?

  • positive
  • negative
  • Determine if b is positive or negative.
  • The unknown number b is to the right of 0. So, b is positive.
  • Determine if 3b is positive or negative.
  • In the expression 3b, 3 is positive and b is positive. The product of two positive numbers is positive. So, 3b is positive.

Let’s practice!🖊️