Identity and Equality Properties

Identity and Equality Properties Algebra 1A Coventry High School Ms. Della Porta and Ms. Becker

What you’ll learn • To recognize and use the properties of identity and equality • To determine the multiplicative inverse of a number Sounds pretty hard, doesn’t it? It’s not!

Things You’ll Need • Notebook or piece of paper • Pencil or pen • A good attitude • Flash cards • A smile  • RESPECT

Okay, are you ready? How can I tell? • You’re quiet. • You’re attentive. Pencil Smile Pen Paper Notebook Good attitude Respect Flash Cards

Vocabulary • Additive Identity Property • Multiplicative Identity Property • Multiplicative Property of Zero • Multiplicative Inverse Property • Reflexive Property of Equality • Symmetric Property of Equality • Transitive Property of Equality • Substitution Property of Equality

Additive Identity Property For any number a, a + 0 = 0 + a = a Let’s try one if a=6 6+0=0+6=6 6+0=6 0+6=6 Therefore, 6 + 0 = 0 + 6 = 6 Everything equals 6! Easy, right?

Want to try one more? Remember that the Additive Identity Property says that for any number x, x + 0 = 0 + x = x Let’s make x=72 72+0=0+72=72 72+0=72 0+72=72 So, 72+0=0+72=72 It works every time!

Flash Card Time • Write on the front of the flash card: Additive Identity Property • Okay, now turn the card over and write: For any number a, a+0=0+a=a

Multiplicative Identity Property For any number a, a X 1 = 1 X a = a Let’s try one if a = 8 8 X 1=1 X 8= 8 8 X 1=8 1 X 8=8 See what I mean? 8 X 1=1 X 8= 8 Everything equals 8! I told you this was easy!

It’s One More Time Time! • The multiplicative identity property says the product if any number and 1 is equal to the number. The formula is a * 1=1 * a = a. • If a=2 2 * 1= 2 and 1 * 2 =2, so 2*1=1*2=2  (when you see the word product it’s a hint that they want you to multiply!)  Some signs that can be used to say multiply or times are: X or * or • or 3(1)

Flash Card Time • Write on the front of the flash card: Multiplicative Identity Property • Okay, now turn the card over and write: For any number a, a*1=1*a=a

Multiplicative Property of Zero • For any number a, a * 0 = 0 * a = 0 Time to try one, right? Let’s let a = 52 52 * 0 = 0 * 52 = 0 52 * 0 = 0 0 * 52 = 0 So, 52 * 0 = 0 * 52 = 0

What do you think? • ANY number times zero is zero! That means no matter what number we make a, the answer will still be zero. 1,000,000 * 0 = 0 * 1, 000,000= 0 1,000,000 * 0 = 0 0 * 1, 000,000= 0

Flash Card Time • Write on the front of the flash card: Multiplicative Property of Zero • Okay, now turn the card over and write: For any number a, a*0=0*a=0

Multiplicative Inverse Property • For every nonzero number Where There is exactly one number Such that

Okay, this one is a little confusing, I admit it!

Flash Card Time • Write on the front of the flash card: Multiplicative Inverse Property • Okay, now turn the card over and write: For every nonzero number a/b Where a, b There is exactly one number b/a Such that a/b * b/a = 1

Reflexive Property of Equality Why do they use such BIG words? Is it just to confuse us? •For any number a, a = a Isn’t that a big name for such a simple rule? Any quantity is equal to itself. 8 = 8 6 + 2 = 6 + 2 3 + 2=3 + 2

Some Practice examples • Remember the rule: for any number a, a = a Reflexive Property of Equality says that any number is equal to itself 1,000,001 = 1,000,001 3.67=3.67 2,360 + 3,000=2,360+3,000

Flash Card Time • Write on the front of the flash card: Reflexive Property of Equality • Okay, now turn the card over and write: For any number a, a = a

Symmetric Property of Equality • For any numbers a and b, if a = b, then b = a Are you asking yourself, what does that mean? If 5 = 3 + 2 then 3 + 2 = 5 If 3 + 4 = 5 + 2 then 5 + 2 = 3 + 4

Time to try one more • Remember, the Symmetric Property of Equality says, if a = b then b = a If 4 = 3 + 1, then 3 + 1 = _______________ Right! 4 If 528=500 + 28, then 500 + 28 = what? Of course, it’s still 528!

Flash Card Time • Write on the front of the flash card: Symmetric Property of Equality • Okay, now turn the card over and write: For any numbers a and b, if a = b, then b=a

Transitive Property of Equality • For any numbers a, b and c, if a = b and b = c, then a = c If one quantity equals a second quantity and that second quantity is equal to a third quantity, then the first quantity equals the third quantity too. If 6= 3+3 and 3+3=5+1 then 6=5+1

So many examples, so little time! • Remember a, b and c, if a=b and b=c, then a=c If 15=9+6 and 9+6=10+5, then 15= _______ If 3+7=10 and 10=8+2, then 3+7=8+ ______ If Ms. Della Porta’s age = Matthew Brennan’s age and Matt Brennan’s age equals Jason Phillip’s age, then Ms. Della Porta’s age = Jason Phillip’s age 

Flash Card Time • Write on the front of the flash card: Transitive Property of Equality • Okay, now turn the card over and write: For any numbers a, b, and c if a = b, and b=c, then a=c

Substitution Property of Equality • If a = b, then a can be replaced by b in any expression. A quantity can be substituted for its equal in any expression. X + 3 = 5 (X=2), go ahead, substitute 2 + 3 = 5 Just a BIG name for a simple thing!

Practice • 6+1=7+0 We know that 6+1 = 7, therefore we can replace 6 +1 for 7 7=7+0 Y=52 Therefore in the problem, y + 3= 55 We can replace the y with 52 and say 52+3=55

Flash Card Time • Write on the front of the flash card: Substitution Property of Equality • Okay, now turn the card over and write: If a = b, then a may be replaced by b in any expression

Congratulations! Now, at your seat and on your own, you are to make up one example of each of these properties. Go back to your flash cards for help. Your teachers will help you if you get stuck. RAISE your hand and we will come to you.

Properties • Additive Identity Property • Multiplicative Identity Property • Multiplicative Property of Zero • Multiplicative Inverse Property • Symmetric Property of Equality • Transitive Property of Equality • Substitution Property of Equality

Great job everybody!

Identity and Equality Properties