Additive and multiplicative properties of rational numbers.9th class mathematics(9th class New Book)

| Addition Property | Description |
|----------------------|--------------------------------|
|Closure. |a+b € R
| Commutative | a + b = b + a |
| Associative | (a + b) + c = a + (b + c) |
| Identity | 0 is the additive identity
| Inverse | Each a has an inverse (-a) such that a + (-a) = 0
| Multiplication Property | Description |
|-------------------------|-----------------------------------------------|
| Closure | If a and b are rational, then a * b is rational |

| Commutative | a * b = b * a

| Associative | (a * b) * c = a * (b * c)

| Identity | The number 1 is the multiplicative identity (a * 1 = a) |

| Inverse | Every nonzero rational number a has an inverse 1/a such that a * (1/a) = 1 |

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