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Operations with Integers

Add, subtract, multiply, and divide positive and negative numbers

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Operations with Integers

Adding Integers

Same Signs

Add and keep the sign:

  • 5+3=85 + 3 = 8
  • −5+(−3)=−8-5 + (-3) = -8

Different Signs

Subtract and use the sign of the larger absolute value:

  • 7+(−3)=47 + (-3) = 4
  • −7+3=−4-7 + 3 = -4

Subtracting Integers

Rule: Add the opposite! a−b=a+(−b)a - b = a + (-b)

Examples:

  • 5−8=5+(−8)=−35 - 8 = 5 + (-8) = -3
  • −3−7=−3+(−7)=−10-3 - 7 = -3 + (-7) = -10
  • 4−(−6)=4+6=104 - (-6) = 4 + 6 = 10

Multiplying Integers

Same signs → Positive

  • 5×3=155 \times 3 = 15
  • (−5)×(−3)=15(-5) \times (-3) = 15

Different signs → Negative

  • 5×(−3)=−155 \times (-3) = -15
  • (−5)×3=−15(-5) \times 3 = -15

Dividing Integers

Same rules as multiplication:

  • Same signs → Positive
  • Different signs → Negative

Examples:

  • 12÷3=412 \div 3 = 4
  • (−12)÷(−3)=4(-12) \div (-3) = 4
  • 12÷(−3)=−412 \div (-3) = -4

📚 Practice Problems

1Problem 1easy

❓ Question:

Calculate: −8+5-8 + 5

💡 Show Solution

Solution:

Different signs - subtract and use sign of larger absolute value: ∣−8∣=8,∣5∣=5|-8| = 8, \quad |5| = 5 8−5=38 - 5 = 3

Since -8 has the larger absolute value, the answer is negative.

Answer: −3-3

2Problem 2easy

❓ Question:

Calculate: −8+5-8 + 5

💡 Show Solution

Solution:

Different signs - subtract and use sign of larger absolute value: ∣−8∣=8,∣5∣=5|-8| = 8, \quad |5| = 5 8−5=38 - 5 = 3

Since -8 has the larger absolute value, the answer is negative.

Answer: −3-3

3Problem 3medium

❓ Question:

Calculate: −6×(−4)+8÷(−2)-6 \times (-4) + 8 \div (-2)

💡 Show Solution

Solution:

Follow order of operations:

Step 1: Multiply and divide (left to right) −6×(−4)=24-6 \times (-4) = 24 8÷(−2)=−48 \div (-2) = -4

Step 2: Add 24+(−4)=2024 + (-4) = 20

Answer: 2020

4Problem 4medium

❓ Question:

Calculate: −6×(−4)+8÷(−2)-6 \times (-4) + 8 \div (-2)

💡 Show Solution

Solution:

Follow order of operations:

Step 1: Multiply and divide (left to right) −6×(−4)=24-6 \times (-4) = 24 8÷(−2)=−48 \div (-2) = -4

Step 2: Add 24+(−4)=2024 + (-4) = 20

Answer: 2020

5Problem 5hard

❓ Question:

The temperature at 6 AM was −12°-12°F. It rose 3°3° per hour for 5 hours, then dropped 2°2° per hour for 3 hours. What was the final temperature?

💡 Show Solution

Solution:

Start: −12°-12°

Rose 3°3° per hour for 5 hours: 5×3=15°5 \times 3 = 15° increase −12+15=3°-12 + 15 = 3°

Dropped 2°2° per hour for 3 hours: 3×2=6°3 \times 2 = 6° decrease 3−6=−3°3 - 6 = -3°

Answer: −3°-3°F

6Problem 6hard

❓ Question:

The temperature at 6 AM was −12°-12°F. It rose 3°3° per hour for 5 hours, then dropped 2°2° per hour for 3 hours. What was the final temperature?

💡 Show Solution

Solution:

Start: −12°-12°

Rose 3°3° per hour for 5 hours: 5×3=15°5 \times 3 = 15° increase −12+15=3°-12 + 15 = 3°

Dropped 2°2° per hour for 3 hours: 3×2=6°3 \times 2 = 6° decrease 3−6=−3°3 - 6 = -3°

Answer: −3°-3°F

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📌 Related Topics in Rational Numbers

Multiplying and Dividing FractionsMultiplying and Dividing IntegersRational Number Operations

❓ Frequently Asked Questions

What is Operations with Integers?▾
Add, subtract, multiply, and divide positive and negative numbers
How can I study Operations with Integers effectively?▾
Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Practice with the 6 problems provided, checking solutions as you go. Regular review and active practice are key to retention.
Is this Operations with Integers study guide free?▾
Yes — all study notes, flashcards, and practice problems for Operations with Integers on Study Mondo are free to access. No account is needed.
What course covers Operations with Integers?▾
Operations with Integers is part of the Grade 7 Math course on Study Mondo, specifically in the Rational Numbers section. You can explore the full course for more related topics and practice resources.
Are there practice problems for Operations with Integers?▾
Yes, this page includes 6 practice problems with detailed solutions. Each problem includes a step-by-step explanation to help you understand the approach.