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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