Algebra Properties Notes 1 - 4

Rules, Rules, Rules…… Identity and Equality Properties

Identity

and

Equality Properties

Addition The additive identity property a + 0 = 0 + a = a (adding 0 to anything doesn’t change what it is!)

The additive identity property

a + 0 = 0 + a = a

(adding 0 to anything

doesn’t change what it is!)

Multiplication Multiplication identity property a(1) = 1(a) = a (multiplying something by 1 doesn’t change what it is!)

Multiplication identity property

a(1) = 1(a) = a

(multiplying something by 1 doesn’t change what it is!)

BIG FAT ZERO! Multiplicative Property of Zero a • 0 = 0 • a = 0 (0 times any number equals 0!) “ Duh” property

Multiplicative Property

of Zero

a • 0 = 0 • a = 0

(0 times any number equals 0!)

“ Duh” property

INVERSE Multiplicative Inverse Property: Two numbers whose product is 1 are called multiplicative inverses or reciprocals (like 1/5 and 5, or 2/3 and 3/2: you just flip the fraction!)

Multiplicative Inverse Property:

Two numbers whose product is 1 are called multiplicative inverses or reciprocals

(like 1/5 and 5, or 2/3 and 3/2: you just flip the fraction!)

Properties of Equality (=) Reflexive Property The reflexive property of equality says that any number equals itself. For any number a , a = a . Symmetric Property The symmetric property of equality says that if one quantity equals a second quantity, then the second quantity also equals the first. For any numbers a and b , if a = b , then b = a .

Reflexive Property The reflexive property of equality says that any number equals itself. For any number a , a = a .

Symmetric Property The symmetric property of equality says that if one quantity equals a second quantity, then the second quantity also equals the first. For any numbers a and b , if

a = b , then b = a .

MORE Properties of Equality…. Transitive Property For any numbers a , b , and c , if a = b and b = c , then a = c . Substitution If a = b , then a may be replaced by b in any expression.

Transitive Property

For any numbers a , b , and c , if a = b and

b = c , then a = c .

Substitution

If a = b , then a may be replaced by b in any expression.

Your Turn….. Name the multiplicative inverse of each number or variable: 3 2/7 4/x 2 ½ m

Name the multiplicative inverse of each number or variable:

3

2/7

4/x

2 ½

m

Pretty good….now try these: Name the property or properties illustrated: x • 1 = x 15/3 + 4 = 5 + 4 2/3 • 3/2 = 1 11 • 0 = 0 2 + 3 = 2 + 3 If 12 + 3 = 15 then 15 = 12 + 3 0 + m = m

Name the property or properties illustrated:

x • 1 = x

15/3 + 4 = 5 + 4

2/3 • 3/2 = 1

11 • 0 = 0

2 + 3 = 2 + 3

If 12 + 3 = 15 then 15 = 12 + 3

0 + m = m

Bet you can’t get this one! Which property is illustrated? If x + 5 = 9 and 9 = y, then x + 5 = y

Which property is illustrated?

If x + 5 = 9 and 9 = y, then x + 5 = y

Hmmmm….. What would the multiplicative inverse of __ 5 __ r – 7 look like?

What would the multiplicative inverse of

__ 5 __

r – 7 look like?

Coming Soon…. To a classroom near you…… More Properties!! (It will be a real scream!)

To a classroom near you……

More Properties!!

(It will be a real scream!)