Evaluate numerical expressions involving integers

key notes :

🔢 Integers

• Integers include positive numbers, negative numbers, and zero.
  Example: … −5, −2, 0, 3, 7 …

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🧮 Order of Operations (BODMAS / PEMDAS)

To evaluate any numerical expression, always follow the correct order:

B → Brackets 🟩

Evaluate inside (), {}, or [] first.

O → Orders (Powers/Exponents)

Example: 3²=9

D/M → Division & Multiplication (Left to right)

A/S → Addition & Subtraction (Left to right)

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➕➖✖️➗ Adding Integers

• Same signs: Add the values, keep the sign.
  Example: −3 + (−5) = −8
• Different signs: Subtract the values, keep the sign of the larger number.
  Example: −7 + 4 = −3

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➖ Subtracting Integers

Change subtraction to addition by adding the opposite:
👉 a−b=a+(−b)

Example: 8 − (−3) = 8 + 3 = 11

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✖️ Multiplying & Dividing Integers

Operation	Result
(+) × (+)	+
(−) × (−)	+
(+) × (−)	−
(−) × (+)	−

Same rules apply for division.

Example:

• −6×−2=12
• 15÷−3=−5

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🧠 Simplifying Expressions Step-by-Step

Always:

1. Apply BODMAS.
2. Work left to right.
3. Keep track of signs.

Example:
Evaluate: 6−[3−(8−12)]

Step 1: Inside inner bracket → 8−12 = −4
Step 2: Next bracket → 3−(−4) = 3+4 = 7
Step 3: Final → 6−7 = −1

Answer: −1

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📘 Common Mistakes to Avoid

• Ignoring minus signs near brackets.
• Forgetting to use left-to-right rules for multiplication/division.
• Not converting subtraction to addition of the opposite.

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📝 Practice Examples

1. −5+12−7=?
2. 3×(−4)+8=?
3. (15÷−3)×(−2)=?
4. [6−(2−9)]÷7=?

Learn with an example

Let’s Practice!