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

2. 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!
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3. 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
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4. Okay, are you ready? How can I tell?
You’re quiet.
You’re attentive.
Pencil
Smile
Pen
Notebook
Paper
Good attitude
Respect
Flash Cards
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5. 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
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6. 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
Everything equals 6! Easy, right?
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7. 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!
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8. 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
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9. 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!
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10. 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)
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11. 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
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12. 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
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13. 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
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14. 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
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15. Multiplicative Inverse Property
For every nonzero number
Where
There is exactly one number
Such that
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16. Okay, this one is a little confusing, I admit it!
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17. 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
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18. 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 = = =3 + 2
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19. 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, ,000=2,360+3,000
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20. 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
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21. 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 = then = 5
If = then = 3 + 4
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22. Time to try one more
Remember, the Symmetric Property of Equality says, if a = b then b = a
If 4 = 3 + 1, then = _______________
Right! 4
If 528= , then = what?
Of course, it’s still 528!
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23. 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
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24. 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
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25. 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 
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26. 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
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27. 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!
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28. 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
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29. 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
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30. 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.
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31. 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
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32. Great job everybody!
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