Evaluate numerical expressions involving integers

Key Notes :

🔹 What are Integers?

• Integers are whole numbers and their negatives.
• Examples: …, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 …

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🔹 What is a Numerical Expression?

• A numerical expression is a combination of numbers and mathematical operations ( +, −, ×, ÷, brackets, exponents).
• Example: 3+(−5)×2

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🔹 Order of Operations (BODMAS Rule)

To evaluate expressions correctly, follow BODMAS:

• B → Brackets (first solve inside brackets)
• O → Orders (powers, squares, roots, etc.)
• D → Division
• M → Multiplication
• A → Addition
• S → Subtraction

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🔹 Rules of Integers

Addition

• (+) + (+) = +
• (−) + (−) = −
• (−) + (+) → subtract and keep the sign of bigger number

Subtraction

• a−b=a+(−b)

Multiplication & Division

• (+) × (+) = +
• (−) × (−) = +
• (+) × (−) = −
• (−) × (+) = −

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🔹 Examples

Example 1:

Evaluate: 5+(−3)

• 👉 5−3=2

Example 2:

Evaluate: (−6)−(−8)

• 👉 −6+8=2

Example 3:

Evaluate: (−4)×(−7)

• 👉 +28

Example 4:

Evaluate: 12÷(−3)

• 👉 −4

Example 5:

Evaluate: [3+(−2)]×(−4)

• 👉 Inside bracket: 3−2=1
• 👉 Multiply: 1×(−4)=−4

Example 6:

Evaluate: (−2)²+(−3)³

• 👉 (−2)²=4
• 👉 (−3)³=−27
• 👉 4+(−27)=−23

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🔹 Key Points to Remember

• Always apply BODMAS when more than one operation is involved.
• Be careful with signs while adding, subtracting, multiplying, and dividing.
• Use brackets to simplify step by step.
• Negative × Negative = Positive; Positive × Negative = Negative.

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✅ Practice Questions for Students

1. Evaluate: (−5)+(−8)+12
2. Evaluate: 15−(−9)
3. Evaluate: (−7)×(−6)÷(−2)
4. Evaluate: [10−(−5)]×(−3)
5. Evaluate: (−4)³+(2)²

Learn with Example

Let’s practice!🖊️