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Identity and Equality Products

Identity and Equality Products. · Additive Identity For any number a, 0 + a = a · Additive Inverse Two numbers with a sum of zero, a + (-a) = 0 · Multiplicative Identity The product of any number and 1 is equal to the number, n ( 1) = n

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Identity and Equality Products

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  1. Identity and Equality Products ·Additive Identity For any number a, 0 + a = a ·Additive Inverse Two numbers with a sum of zero, a + (-a) = 0 ·Multiplicative Identity The product of any number and 1 is equal to the number, n ( 1) = n ·Multiplicative Property of Zero The product of any number and 0 is equal to 0, m(0) = 0 ·Multiplicative Inverses or Reciprocals Two numbers whose product is 1, (1/x)(x) = 1 ·Reflexive Any quantity is equal to itself For any number a, a = a ·Symmetric If one quantity equals a second quantity, then the second quantity equals the first For any numbers a and b, if a = b, then b = a ·Transitive If one quantity equals a second quantity and the second quantity equals a third quantity, then the first quantity equals the third quantity For any numbers a,b, and c, if a = b, and b = c, then a = c ·Substitution A quantity may be substituted for its equal in any expression If a = b, then a may be replaced by b in any expression If n = 15, then 3n = 3(15)

  2. Evaluate 2[(3)(2) - 5] + 3(1/3) Name the property for each step · = 2(6 - 5) + 3(1/3) Substitution 3(2) = 6 · = 2(1) + 3(1/3) Substitution 6 - 5 = 1 · = 2 + 3(1/3) Multiplicative Identity 2(1) = 2 · = 2 + 1 Multiplicative Inverse 3(1/3) = 1 · = 3 Substitution 2 + 1 = 3 Evaluate 8 + [15 - 3(5)] Name the property for each step · = 8 + (15 - 15) Substitution · = 8 + 0 Substitution · = 8 Additive Identity

  3. Distributive Property For any numbers a, b, and c, a( b + c) = ab + ac and (b + c)a = ba + ca and a(b - c) = ab - ac and (b - c)a = ba - ca 15(99) = 15(100 - 1) OR 15(99) = 15(100) - 15(1) = 15(90) + 15(9) = 1500 - 15 = 1350 + 135 = 1485 = 1485

  4. 5(g - 9) = 5g - 5(9) = 5g - 45 3(x2 + x - 1) = 3x2 + 3x - 3 2( 8 + n) = 2(8) + 2n = 16 + 2n -6(r - 3s - t) = -6r -6(-3s) -6(-t) = -6r + 18s + 6t Simplify 15x + 18x = x(15 + 18) = 33x 10n + 3n2 + 9n2 = 10n + (3 + 9)n2 = 10n + 12n2 6t - 4t = t(6 - 4) = 2t

  5. Commutative and Associative Properties ·Commutative Property The order in which you add or multiply numbers does not change their sum or product. For any numbers a and b, a + b = b + a and a(b) = b(a) ·Associative Property The way you group three or more numbers when adding or multiplying does not change their sum or product For any numbers a, b, and c, (a + b) + c = a + (b + c) and a(bc) = (ab)c

  6. Evaluate each expression using propertie of numbers. Name the property used in each step. 14 + 18 + 26 3½ + 4 + 2½ 5(3)(6)(4) (5/6)(16)(3/4) Simplify each expression 4x + 5y + 6x 5a + 3b + 2a + 7b 3(4x + 2) + 2x 7(ac + 2b) + 2ac Find the perimeter of the triangle with the given legs xy, 5 + x, 5 + x

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