| Closure | a + b is a real number | ab is a real number |
| Identity | a + 0 = a, 0 + a = a | a × 1 = a, 1 × a = a |
| Inverse | a + (-a) = 0 | a × 1/a = 1, a ≠ 0 |
| Commutative | a + b = b + a | ab = ba |
| Associative | (a + b) + c = a + (b + c) | (ab)c = a(bc) |
| Distributive | |
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Take a look at the exercises below and then identify which property of real numbers is illustrated?
a. 5 × (-2) = (-2) × 5
This is the commutative property of multiplication
b. 4 + (-4) = 0
This is the inverse property of addition
c. 1 + (3 + 7) = (1 + 3) + 7
This is the associative property of addition
d. 9 + (-4 × 1) = 9 + -4
This is the identity property of multiplication
e. (3 + 7)8 = 8 × 3 + 8 × 7
This is the distributive property
f. 10 × 1/10 = 1
This is the inverse property of multiplication