Upcoming SlideShare
×

# Section 1.4 identity and equality properties (algebra)

4,691 views

Published on

0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total views
4,691
On SlideShare
0
From Embeds
0
Number of Embeds
4
Actions
Shares
0
9
0
Likes
0
Embeds 0
No embeds

No notes for slide

### Section 1.4 identity and equality properties (algebra)

1. 1. Section 1.4Identity and Equality Properties<br />
2. 2. WITHOUT using any calculator or pencil/pen, evaluate the following expressions:<br />901 + 00 + 357 <br />439 + 0 4358 + 0<br />Subconsciously, you have applied the Additive Identity.<br />The sum of any number and 0 is equal to the number. <br />Thus, 0 is called the additive identity.<br />
3. 3. By understanding Additive Identity. What do you think is the Multiplicative Identity? Why?<br />1 is the multiplicative identity, since the product of any number and 1 is equal to the number itself.<br />
4. 4. Complete the following sentence:<br />The product of any number and zero is equal to ______.<br />This is known as the Multiplicative Property of Zero<br />i.e.<br />8*0 15x0 a(0) (-7)(0)<br />
5. 5. Two numbers whose produce is 1 is known as ________.<br />Reciprocals or Multiplicative inverses.<br />An example of reciprocals would be:<br />2 / 7 and ____ ¾ and _____ ½ and _____<br />5 and ____ 8 and _____ n and _____<br />
6. 6. Identity and Equality Properties<br />Identity Properties<br /><ul><li>Additive Identity Property
7. 7. Multiplicative Identity Property
8. 8. Multiplicative Identity Property of Zero
9. 9. Multiplicative Inverse Property</li></li></ul><li>Identity and Equality Properties<br />Identity Properties<br />Additive Identity Property<br />For any number a, a + 0 = 0 + a = a.<br />The sum of any number and zero is equal to that number.<br />The number zero is called the additive identity.<br />Example<br />If a = 5 then 5 + 0 = 0 + 5 = 5<br />
10. 10. Identity and Equality Properties<br />Identity Properties<br />Multiplicative identity Property<br />For any number a, a  1 = 1  a = a.<br />The product of any number and one is equal to that number.<br />The number one is called the multiplicative identity.<br />Example<br />If a = 6 then 6  1 = 1  6 = 6<br />
11. 11. Identity and Equality Properties<br />Identity Properties<br />Multiplicative Property of Zero<br />For any number a, a  0 = 0  a = 0.<br />The product of any number and zero is equal to zero.<br />Example<br />If a = 6 then 6  0 = 0  6 = 0<br />
12. 12. Identity and Equality Properties<br />Identity Properties<br />Multiplicative Inverse Property<br />Two numbers whose product is 1 are called multiplicative inverses or reciprocals.<br />Zero has no reciprocal because any number times 0 is 0.<br />Example<br />
13. 13. Identity and Equality Properties<br />Equality Properties<br /><ul><li>Equality Properties allow you to compute with expressions on both sides of an equation by performing identical operations on both sides of the equation. This creates a balance to the mathematical problem and allows you to keep the equation true and thus be referred to as a property. The basic rules to solving equations is based on these properties. Whatever you do to one side of an equation; You must perform the same operation(s) with the same number or expression on the other side of the equals sign.
14. 14. Reflexive Property of Equality
15. 15. Symmetric Property of Equality
16. 16. Transitive Property of Equality
17. 17. Substitution Property of Equality</li></li></ul><li>Identity and Equality Properties<br />Equality Properties<br />Reflexive Property of Equality<br />For any number a, a = a.<br />The reflexive property of equality says that any real number is equal to itself. <br />Many mathematical statements and algebraic properties are written in if-then form when describing the rule(s) or giving an example. <br />The hypothesis is the part following if, and the conclusion is the part following then.<br />Example<br />If a = a ; then 7 = 7; <br />then 5.2 = 5.2<br />
18. 18. Identity and Equality Properties<br />Equality Properties<br />Symmetric Property of Equality<br />For any numbers a and b, if a = b, then b = a.<br />The symmetric property of equality says that if one quantity equals a second quantity, then the second quantity also equals the first. <br />Many mathematical statements and algebraic properties are written in if-then form when describing the rule(s) or giving an example. <br />The hypothesis is the part following if, and the conclusion is the part following then.<br />Example<br />If 10 = 7 + 3; then 7 +3 = 10<br />If a = b then b = a<br />
19. 19. Identity and Equality Properties<br />Equality Properties<br />For any numbers a, b and c, if a = b and b = c, then a = c.<br />Transitive Property of Equality<br />The transitive property of equality says that if one quantity equals a second quantity, and the second quantity equals a third quantity, then the first and third quantities are equal. <br />Many mathematical statements and algebraic properties are written in if-then form when describing the rule(s) or giving an example. <br />The hypothesis is the part following if, and the conclusion is the part following then.<br />Example<br />If 8 + 4 = 12 and 12 = 7 + 5, then 8 + 4 = 7 + 5<br />If a = b and b = c , then a = c<br />
20. 20. Identity and Equality Properties<br />Equality Properties<br />Substitution Property of Equality<br />If a = b, then a may be replaced by b in any expression.<br />The substitution property of equality says that a quantity may be substituted by its equal in any expression. <br />Many mathematical statements and algebraic properties are written in if-then form when describing the rule(s) or giving an example. <br />The hypothesis is the part following if, and the conclusion is the part following then.<br />Example<br />If 8 + 4 = 7 + 5; since 8 + 4 = 12 or 7 + 5 = 12;<br />Then we can substitute either simplification into the original mathematical statement. <br />
21. 21. Classwork<br />PAGE 23 # 12 – 28 ALL<br />Homework<br />PAGE 25 # 44 – 62 EVEN <br />