Properties of Real Numbers

Commutative Properties

• a + b = b + a
• Example: 7 + 3 = 3 + 7
• When we add two numbers, order doesn't matter.

• ab = ba
• Example: 3 * 5 = 5 * 3
• When we multiply two numbers, order doesn't matter.

Associative Properties

• (a + b) + c = a + (b + c)
• Example: (2 + 4) + 8 = 2 + (4 + 8)
• When we add three numbers, it does not matter which two we add first.

• (ab)c = a(bc)
• Example: (3 * 7) * 5 = 3 * (7 * 5)
• When we multiple three numbers, it does not matter which two we multiple first.

Distributive Property

• a(b + c) = ab + ac
• Example: 2 * (3 + 5) = 2 * 3 + 2 * 5
• When we multiply a number by a sum of two numbers, we get the same result as multiplying the number by each of the terms and then adding the products.
• (b + c)a = ab + ac
• Example: (4 + 5) * 2 = 2 * 4 + 2 * 5