Answer:
<u>Associative Property Law</u>
Applies to <em>addition </em>and <em>multiplication </em>only.
Grouping of numbers by parentheses in a different way does not affect their sum or product.
Addition: (a + b) + c = a + (b + c) = (a + c) + b
Multiplication: (a × b) × c = a × (b × c) = (a × c) × b
<u>Commutative Property Law</u>
Applies to addition and multiplication only.
Changing the order or position of two numbers does not change the end result.
Addition: a + b = b + a
Multiplication: a × b = b × a
<u>Distributive Property</u>
Distributive multiplication over addition and subtraction:
Addition: a(b + c) = ab + ac
Subtraction: a(b - c) = ab - ac
<u>Identity Property of Addition</u>
Also known as the <em>identity property of zero</em>. Adding 0 to any number does not change the number, i.e. the number keeps its identity.
a + 0 = a = 0 + a
<u>Identity Property of Multiplication</u>
Also known as the <em>identity property of one</em>. Multiplying any number by 1 does not change the number, i.e. the number keeps its identity.
a × 1 = a = 1 × a
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4 + 3(9 + 2)
4 + (3 × 9) + (3 × 2) distributive property
4 + 27 + 6
4 + 6 + 27 commutative property of addition
10 + 27
37
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(4 × 5) × ¹/₄
4 × (5 × ¹/₄) associative property of multiplication
4 × (¹/₄ × 5) commutative property of multiplication
(4 × ¹/₄) × 5 associative property of multiplication
1 × 5 identity property of multiplication
5
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(0 + 3) + 17
0 + (3 + 17) associative property of addition
0 + 20 identity property of addition
20
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8 + 3(1 - 2)
8 + (3 × 1) - (3 × 2) distributive property
8 + 3 - 6
11 - 6
5
