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Identify the property being described in each of the following statements:

1. Identify the property being described in each of the following statements:. ( i ). This property means the numbers can be swapped. Commutative: a + b = b + a. (ii). This property refers to grouping. Associative: a + ( b + c ) = ( a + b ) + c. (iii).

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Identify the property being described in each of the following statements:

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  1. 1. Identify the property being described in each of the following statements: (i) This property means the numbers can be swapped. Commutative: a + b = b + a (ii) This property refers to grouping. Associative: a + (b + c) = (a + b) + c (iii) This property multiplies the value outside the brackets with each of the terms in the brackets. Distributive: a × (b + c) = a × b + a × c

  2. 1. Identify the property being described in each of the following statements: (iv) This property says that, changing the grouping of numbers that are either being added or multiplied does not change the value of it. Associative: a + (b + c) = (a + b) + c (v) This property says the brackets can be moved. Associative: a + (b + c) = (a + b) + c

  3. 2. Use the numbers and the property in each of the questions below to create an equation and verify that the property is true for each of the following: (i) Property: Commutative property of addition Numbers: 7 and 11 a + b = b + a 7 + 11 = 11 + 7 18 = 18

  4. 2. Use the numbers and the property in each of the questions below to create an equation and verify that the property is true for each of the following: (ii) Property: Commutative property of multiplication Numbers: 15 and 6 a × b = b × a 15 × 6 = 6 × 15 90 = 90

  5. 2. Use the numbers and the property in each of the questions below to create an equation and verify that the property is true for each of the following: (iii) Property: Associative property of addition Numbers: 9, 11 and 4 a + (b + c) = (a + b) + c 9 + (11 + 4) = (9 + 11) + 4 9 + 15 = 20 + 4 24 = 24

  6. 2. Use the numbers and the property in each of the questions below to create an equation and verify that the property is true for each of the following: (iv) Property: Distributive property of addition Numbers: 12, 2 and 4 a × (b + c) = a × b + a × c 12 × (2 + 4) = 12 × 2 + 12 × 4 12 × 6 = 24 + 48 72 = 72

  7. 3. Rewrite the following expressions in a different way to get the same answer: (i) 2 + (6 + 8) = (2 + 6) + 8 Verify: 2 + (6 + 8) = 2 +14 = 16 (2 + 6) + 8 = 8 + 8 = 16 (ii) 5 × (8 × 3) = (5 × 8) × 3 Verify: 5 × (8 × 3) = 5 × 24 = 120 (5 × 8) × 3 = 40 × 3 = 120

  8. 3. Rewrite the following expressions in a different way to get the same answer: (iii) 4(9 – 2) = 4 × 9 – 4 × 2 Verify: 4(9 – 2) = 4(7) = 28 4 × 9 – 4 × 2 = 36 – 8 = 28 (iv) (2 × 3) + (4 × 6) = (6) + (24) Verify: (2 × 3) + (4 × 6) = 6 + 24 = 30 (6) + (24) = 30

  9. 3. Rewrite the following expressions in a different way to get the same answer: (v) (9 + 3) + 5 = 9 + (3 + 5) Verify: (9 + 3) + 5 = 12 + 5 = 17 9 + (3 + 5) = 9 + 8 = 17 (vi) (6 × 7) × 9 = 6 × (7 × 9) Verify: (6 × 7) × 9 = 42 × 9 = 378 6 × (7 × 9) = 6 × 63 = 378

  10. 4. Rewrite the expression using the distributive property of multiplication and then solve each expression: (i) (ii) (9 – 2) × 2 5 × (5 + 7) = 5 × 5 + 5 × 7 = 9 × 2 – 2 × 2 = 25 + 35 = 18 – 4 = 60 = 14 (iii) (2 + 7) × (–3) = (2 × –3) + (7 × –3) = –6 + (–21) = –6 – 21 = –27

  11. 5. Determine which property of multiplication is shown in each of the following (commutative, associative or distributive). (i) (5 × 7) × 4 = 5 × (7 × 4) Associative (ii) 10 × 8 = 8 × 10 Commutative (iii) 9 × 2 = 2 × (2 + 7) Associative and Commutative (because the 2 has moved to the start)

  12. 5. Determine which property of multiplication is shown in each of the following (commutative, associative or distributive). (iv) 4 × (5 + 6) = (4 × 5) + (4 × 6) Distributive (v) (10 × 3) + (10 × 0) = 10 × (3 + 0) Distributive

  13. 6. Using the associative and commutative properties of addition, write (at least three) expressions equivalent to the expression (4x + 2y) + 3z. 3z + (4x + 2y) 3z + (2y + 4x) (2y + 4x) + 3z 4x + (2y + 3z) 4x + (3z +2y) 2y + (4x + 3z)

  14. 6. Pick one of the expressions above that shows the commutative property of addition. Clearly explain how this property was used. (4x + 2y) + 3z = 3z + (4x + 2y) The commutative property says we can swap numbers around and still get the same answer.

  15. 6. (iii) Pick one of the expressions that show the associative property of addition. Clearly explain how this property was used. (4 + 2) + 3 = 4 + (2 + 3) The associative property says that it doesn’t matter how we group the numbers (i.e. which is calculated first).

  16. 7. A soccer uniform costs €13 for the jersey, €11 for shorts, and €8 for socks. Write two equivalent expressions for the total cost of 12 uniforms, then find the cost. 12 × (13 + 11 + 8) = (12 × 13) + (12 × 11) + (12 × 8) 12 × 32 = 156 + 132 + 96 €384 = €384

  17. 8. The price of an apple is n. The number of apples bought by three different people is x, y and z. Write two equivalent expressions to represent the total cost of all the apples bought by the three people. Whatpropertydidyou use? n × (x + y + z) = (n × x) + (n × y) + (n × z) Distributive Property

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