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POD

POD. b = 5, c= 3, d=7. basic. advanced. 4b + 6. (10c ÷b) 2 + d. (10(3) ÷5) 2 + 7. 4(5) + 6. (30 ÷5) 2 + 7. 20 + 6. (6) 2 + 7. 26. 36 + 7. 43. POD. b = 5, c= 3, d=7. basic. advanced. (b 2 × 4 + 44) ÷ (4c). b + 4c × d. (5 2 × 4 + 44) ÷ (4 × 3). 5 + 4(3) × 7.

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POD

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  1. POD b= 5, c= 3, d=7 basic advanced 4b + 6 (10c ÷b)2 + d (10(3) ÷5)2 + 7 4(5) + 6 (30 ÷5)2 + 7 20 + 6 (6)2 + 7 26 36 + 7 43

  2. POD b= 5, c= 3, d=7 basic advanced (b2 × 4 + 44) ÷ (4c) b + 4c × d (52 × 4 + 44) ÷ (4 × 3) 5 + 4(3) × 7 (25 × 4 + 44) ÷ (4 × 3) 5 + 12 × 7 (100 + 44) ÷ (4 × 3) 5 + 84 (144) ÷ (4 × 3) 89 (144) ÷ (12) 12

  3. POD State whether the conjecture is true or false. If false, provide a counterexample. Subtraction of whole numbers is associative False (8−5) − 3 ≠ 8 − (5−3)

  4. Properties of Operations The Commutative Property states that the order in which numbers are added or multiplied does not change the sum or product. a + b = b + a a × b = b × a

  5. The Associative Property states that the way in which numbers are grouped when they are added or multiplied does not change the sum or product. a + (b+c) = (a+ b) + c a × (b×c) = (a × b) × c

  6. The Additive Identity Property states that when 0 is added to any number, the sum is the number. a + 0 = a 0 + a = a

  7. The Multiplicative Identity Property states that when any number is multiplied by 1, the product is the number. a × 1 = a 1 × a = a

  8. The Multiplicative Property of Zero states that when any number is multiplied by 0, the product is 0. a × 0 = 0 0 × a = 0

  9. The Distributive Property states that to multiply a sum or difference by a number, multiply each term inside the parenthesis by the number outside the parenthesis. a( b + c ) = ab + ac a( b – c ) = ab − ac

  10. 2 ( y + 2) = 2(y) +2(2) = 2y + 4 The expressions 2(y+2) and 2y+4 are equivalent expressions. No matter what y is, these expressions have the same value.

  11. Whiteboard time Name the property shown by the statement: 2 × (5 × n) = (2 × 5) × n Associative Property

  12. Whiteboard time Name the property shown by the statement: 42 + b + y = 42 + y + b Commutative Property

  13. Whiteboard time Name the property shown by the statement: 3c + 0 = 3c Additive Identity Property

  14. Whiteboard time Name the property shown by the statement: 3m × 0 × 5m = 0 Multiplicative Property of Zero

  15. Whiteboard time Name the property shown by the statement: 7c + 0 = 7c Additive Identity Property

  16. Whiteboard time Name the property shown by the statement: (3 × m) × 2 = 2 × (3 × m) Commutative Property

  17. Whiteboard time Name the property shown by the statement: 8(-9 + 4) = 8(-9) + 8(4) Distributive Property

  18. Whiteboard time Use the distributive property and evaluate: 5(-9 + 11) 5(-9) + 5(11) -45 + 55 10

  19. Whiteboard time Use the distributive property and evaluate: 7(10 − 5) 7(10) − 7(5) 70 − 35 35

  20. Whiteboard time Use the distributive property and evaluate: 6(p − 5) 6(p) − 6(5) 6p − 30

  21. Simplify each expression (7 + g) + 5 (7 + g) + 5 = (g + 7) + 5 Commutative Property of Multiplication = g + (7 + 5) Associative Property of Multiplication = g + 12

  22. Simplify each expression (m × 11) × m (m × 11) × m = (11 × m) × m Commutative Property of Multiplication = 11 × (m × m) Associative Property of Multiplication = 11 × m2 = 11m2

  23. Simplify each expression a  (9 b) a  (9 b) = (a  9) b Associative Property of Multiplication (9  a) b commutative Property of Multiplication 9  (a b) Associative Property of Multiplication = 9ab

  24. Simplify each expression 9c + (8+3c) 9c + (8+3c) = 9c + (3c +8) commutative Property of Multiplication (9c + 3c) +8 Associative Property of Multiplication 12c +8

  25. Simplify each expression 6 + (d + 8) 6 + (d + 8)= 6 +(8 + d) commutative Property of Multiplication (6+8) +d Associative Property of Multiplication 14 + d

  26. Simplify each expression 4 × (3c × 2) 4 × (3c × 2)= 4 × (2× 3c) commutative Property of Multiplication (4 × 2) × 3c Associative Property of Multiplication 8 × 3c (8 × 3) × c Associative Property of Multiplication 24 × c 24c

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