Lecture on Operations with Real Numbers (Integers)

Introduction to Integers

• Integers include positive and negative whole numbers.
• Examples: -3, -2, -1, 0, 1, 2, 3, etc.

Adding Integers

• Same Sign: Add the numbers and keep the sign.
• Different Signs: Subtract the absolute values and keep the sign of the number with the larger absolute value.
• Absolute Value: Always positive; it represents the distance a number is from zero.
  • Example: | -3 | = 3; | 3 | = 3

Examples of Adding Integers

1. -3 + -8
   • Both negative
   • Add absolute values: 3 + 8 = 11
   • Result: -11
2. 18 + 89
   • Both positive
   • Add: 18 + 89 = 107
   • Result: 107
3. -23 + 85
   • Different signs
   • Subtract: 85 - 23 = 62
   • 85 is larger and positive
   • Result: 62
4. 8 + -3
   • Different signs
   • Subtract: 8 - 3 = 5
   • 8 is larger and positive
   • Result: 5
5. -26 + -18
   • Both negative
   • Add: 26 + 18 = 44
   • Result: -44
6. 28 + -32
   • Different signs
   • Subtract: 32 - 28 = 4
   • 32 is larger and negative
   • Result: -4

Subtracting Integers

• Rule: Keep Change Change
  • Keep the sign of the first number.
  • Change subtraction to addition.
  • Change the sign of the second number.

Examples of Subtracting Integers

1. 7 - 5
   • Keep 7, change to 7 + (-5)
   • Different signs: Subtract 7 - 5 = 2
   • 7 is larger and positive
   • Result: 2
2. 5 - 9
   • Keep 5, change to 5 + (-9)
   • Different signs: Subtract 9 - 5 = 4
   • 9 is larger and negative
   • Result: -4
3. -9 - (-13)
   • Keep -9, change to -9 + 13
   • Different signs: Subtract 13 - 9 = 4
   • 13 is larger and positive
   • Result: 4
4. 17 - -26
   • Keep 17, change to 17 + 26
   • Same signs: Add 17 + 26 = 43
   • Result: 43
5. -18 - 5
   • Keep -18, change to -18 + (-5)
   • Both negative
   • Add: 18 + 5 = 23
   • Result: -23
6. -23 - 37
   • Keep -23, change to -23 + (-37)
   • Both negative
   • Add: 23 + 37 = 60
   • Result: -60