# Properties of real numbers

 Properties of real numbers Let a, b, and c represent real numbers Property Addition Multiplication 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 a(b + c) = ab + ac

## Identifying properties of real numbers using the summary table above

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 × × 7

This is the distributive property

f. 10 × 1/10 1

This is the inverse property of multiplication

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