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Understanding Mathematical Properties: Commutative, Associative, Distributive

Learn about the commutative property, associative property, and distributive property in mathematics. Understand how the order of addends or factors can affect sums or products. Examples and hints provided for easy comprehension.

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Understanding Mathematical Properties: Commutative, Associative, Distributive

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  1. Mathematical Properties

  2. Commutative Property If the order of the addends (+) or factors (x) is changed, the sum (+) or product (x) does not change. Examples: 2 + 3 = 3 + 2 5 = 5 4 · 6 = 6 · 4 24 = 24 *Hint:* You commute back and forth to school. Numbers can do the same.

  3. Associative Property The way that the addends or factors are grouped, does not change the sum or product. Examples: (2 + 3) + 5 = 2 + (3 + 5) 5 + 5 = 2 + 8 10 = 10 (4 • 2) • 6 = 4 • (2 • 6) 8 • 6 = 4 • 12 48 = 48 *Hint: You associate with different people. Numbers can do the same.

  4. Distributive Property Multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. Example: 6(4 + 2) = (6 • 4) + (6 • 2) 6 • 6 = 24 + 12 36 = 36 *Hint: You distribute papers to classmates. Numbers can do the same.

  5. Associative Prop. Mult. Commutative Prop. Addition Examples Commutative Prop. Mult. Distributive Property Associative Prop. Add 1 x (5 x 9) = (1 x 5) x 9 4 + b = b +4 m x n = n x m 6(y + z) = 6y + 6z 2 + (4 + 5) = (2 + 4) + 5 6 x (7 x 8) = (6 x 7) x 8 5 + 7 = 7 + 5 3(6 + 9) = (3 x 6) + (3 x 9) (9 + 8) + 3 = 9 + (8 + 3) Associative Prop. Mult. Commutative Prop. Addition Distributive Property Associative Prop. Add

  6. Identity Property of Addition/Subtraction Any number added to or subtracted by zero is that number. Examples: 0 + 6 = 6 0 + 1,324,450 = 1,324,450 176 – 0 = 176

  7. Identity Property of Multiplication Any number multiplied by 1 is that number. Examples: 8 · 1 = 8 2,378.953 x 1 = 2,378.953

  8. Zero Property of Multiplication Any number multiplied by zero (0) is zero (0). Examples: 15 · 0 = 0 7,238.463 · 0 = 0

  9. More Examples commutative • ab = ba • 17 + 34 = 34 + 17 • (x + m) + p = x + (m + p) • 8 · 1 = 8 • 10 · (5 + 3) = (10 · 5) + (10 · 3) • 7 + ( 3 + 6) = (7 + 3) + 6 • 0 + 435 = 435 **8. 4(b + 2) = 4b + 8 commutative associative Identity Property of Multiplication Distributive Property associative Identity Property of Addition Distributive Property

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