Identity and Equality Properties Algebra 1A Coventry High School Ms. Della Porta and Ms. Becker 12/6/2018

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! 12/6/2018

Notebook or piece of paper Pencil or pen A good attitude Flash cards Things You’ll Need Notebook or piece of paper Pencil or pen A good attitude Flash cards A smile  RESPECT 12/6/2018

Okay, are you ready? How can I tell? You’re quiet. You’re attentive. Pencil Smile Pen Notebook Paper Good attitude Respect Flash Cards 12/6/2018

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 12/6/2018

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? 12/6/2018

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! 12/6/2018

Flash Card Time Additive Identity Property For any number a, a+0=0+a=a 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 12/6/2018

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! 12/6/2018

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) 12/6/2018

Flash Card Time Multiplicative Identity Property 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 12/6/2018

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 12/6/2018

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 12/6/2018

Flash Card Time Multiplicative Property of Zero 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 12/6/2018

Multiplicative Inverse Property For every nonzero number Where There is exactly one number Such that 12/6/2018

Okay, this one is a little confusing, I admit it! 12/6/2018

Flash Card Time Multiplicative Inverse Property 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 12/6/2018

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 12/6/2018

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 12/6/2018

Flash Card Time Reflexive Property of Equality For any number a, a = a 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 12/6/2018

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 12/6/2018

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! 12/6/2018

Flash Card Time Symmetric Property of Equality 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 12/6/2018

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 12/6/2018

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  12/6/2018

Flash Card Time Transitive Property of Equality 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 12/6/2018

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! 12/6/2018

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 12/6/2018

Flash Card Time Substitution Property of Equality 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 12/6/2018

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. 12/6/2018

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 12/6/2018

Great job everybody! 12/6/2018