Evaluate numerical expressions involving integers

Key Notes:

1️⃣ Understand Integers

• Integers are whole numbers including positive (+), negative (-), and zero (0).
• Examples: …, -3, -2, -1, 0, 1, 2, 3, …
• 🔹 Positive ➕
• 🔹 Negative ➖

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2️⃣ Order of Operations (BODMAS / PEMDAS) 🧮

• Always follow this order:
  B – Brackets ( )
  O – Orders (powers and roots, e.g., 2²)
  D – Division ÷
  M – Multiplication ×
  A – Addition +
  S – Subtraction –

Example: 5+2×(3−1)=?5 + 2 \times (3 – 1) = ?5+2×(3−1)=?
Step 1: Brackets → 3 – 1 = 2
Step 2: Multiplication → 2 × 2 = 4
Step 3: Addition → 5 + 4 = 9 ✅

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3️⃣ Adding Integers ➕

Same signs: Add and keep the sign

• 5 + 3 = 8
• -5 + -3 = -8

Different signs: Subtract smaller from larger, keep larger number’s sign

• 7 + (-4) → 7 – 4 = 3 ✅
• -7 + 4 → 7 – 4 = 3, sign = – ✅

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4️⃣ Subtracting Integers ➖

Change subtraction to addition of the opposite

a – b = a + (-b)

• Example: 5 – (-3) = 5 + 3 = 8 ✅
• Example: -4 – 6 = -4 + (-6) = -10 ✅

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5️⃣ Multiplying Integers ✖️

Same signs → Positive

• 3 × 4 = 12 ✅
• -3 × -4 = 12 ✅

Different signs → Negative

• -3 × 4 = -12 ✅
• 3 × -4 = -12 ✅

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6️⃣ Dividing Integers ➗

Rules same as multiplication:

• Same signs → Positive
• Different signs → Negative

Example:

• -12 ÷ 3 = -4 ✅
• 12 ÷ -3 = -4 ✅

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7️⃣ Practice Tips ✏️

• Always simplify inside brackets first 🏷️
• Use number lines for visual help 🟢🔴
• Check sign rules carefully ✅

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8️⃣ Quick Tricks ⚡

Double negative → positive: -(-5) = 5

Zero rules:

• 0 + any number = number
• 0 × any number = 0
• Any number ÷ 0 → Not allowed ❌

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9️⃣ Fun Example 🎉

Evaluate: −3+2×(4−7)-3 + 2 \times (4 – 7)−3+2×(4−7)

• Step 1: Brackets → 4 – 7 = -3
• Step 2: Multiply → 2 × -3 = -6
• Step 3: Add → -3 + -6 = -9 ✅