Identity & Equality Properties

1-4

Warm-Ups

1.  10 - x > 6;  {3, 5, 6, 8}

2.  4x + 2< 58;  {11, 12, 13, 14, 15}

 Evaluate:

3.  (3 + 6) / 3^2  4.  20/4*8/10 5.  9(3) - 4^2 + 6^2 /2

Vocabulary:

additive identitymultiplicative identitymultiplicative inversesreciprocal

The sum of any number and 0 is equal to the number.  Thus, 0 is called the additive identity.

Additive Identity:

Words:  For any number a, the sum of a and 0 is a.

Symbols:  a + 0 = 0 + a = a

Examples:  5 + 0 = 0 + 5 = 5

Multiplicative Identity- the product of any number and 1 is equal to the number, 1 is called the multiplicative identity.

ex. 7 * n = 7

Words:  For any number a, the product of a and 1 is a.

Symbols:  a * 1 = 1 * a = a

Example:  12 * 1 = 12,   1 * 12 = 12

Multiplicative Property of Zero- the product of any number and 0 is equal to 0.

ex. 9 * m = 0

Words:  For any number a, the product of a and 0 is 0.

Symbols:  a * 0 = 0 * a = 0

Example:  8 * 0 = 0 * 8 = 0

Two numbers whose product is 1 are called multiplicative inverses or reciprocals.  Zero has no reciprocal because any number times 0 is 0.

ex.  1/3 * 3 = 1

Symbols:  a/b * b/a = b/a * a/b = 1

Example:  2/3 * 3/2 = 6/6 = 1

Identify Properties

Name the property used in each equation.  Then find the value of n.

a.  n * 12 = 0

b.  n * 1/5 = 1

c.  0 + n = 8

Properties of Equality

Reflexive:  any quantity is equal to itself            ex.  7 = 7 or 2 + 3 = 2 + 3Symmetric:  If one quantity equals a second quantity, then the second quantity equals the first quantity.            ex.  9 = 6 + 3Transitive:  If one quantity equals a second quantity and the second quantity equals a third quantity , then the first quantity equals the third quantity.            ex.  5 + 7 = 8 + 4 = 12Substitution:A quantity may be substituted for its equal in any expression              ex.  n = 15, 3n = 3*15

Evaluate Using Properties

Evaluate and name the property used in each step:

1/4(12 - 8) + 3(15/5 - 2)

Glencoe/McGraw-Hill 2003