Integer Properties

Identity Property

Identity Property has two types:

Definition: For any real number (a), (a + 0 = a).
Examples:
1. (9 + 0 = 9)
  - Adding zero to nine returns nine.
2. (0 + (-100) = -100)
  - Adding zero to negative one hundred returns negative one hundred.
Conclusion: Adding zero to any real number results in the number itself. Zero is known as the additive identity.

Definition: For any real number (a), (a \times 1 = a).
Examples:
1. ((-21) \times 1 = -21)
  - Multiplying negative twenty-one by one returns negative twenty-one.
2. (1 \times 50 = 50)
  - Multiplying fifty by one returns fifty.
Conclusion: Multiplying one by any real number results in the number itself. One is known as the multiplicative identity.

Inverse Property is another type of integer property:

Definition: For any real number (a), there exists another real number (-a) such that (a + (-a) = 0).
Examples:
1. (5 + (-5) = 0)
  - Five added to its additive inverse (-5) results in zero.
2. ((-\frac{2}{3}) + (\frac{2}{3}) = 0)
  - Negative two-thirds added to its additive inverse (two-thirds) results in zero.
Conclusion: Adding a number to its additive inverse results in zero.

Definition: For any non-zero real number (a), there exists another real number (\frac{1}{a}) such that (a \times \frac{1}{a} = 1).
Examples:
1. (12 \times \frac{1}{12} = 1)
  - Twelve multiplied by its multiplicative inverse (one-twelfth) results in one.
2. ((-\frac{2}{3}) \times (-\frac{3}{2}) = 1)
  - Negative two-thirds multiplied by its multiplicative inverse (-three-halves) results in one.
Conclusion: Multiplying a number by its multiplicative inverse results in one.

Practice: To effectively understand and learn mathematics, continuous practice is essential.