chapter 1 section 2 part 2. in algebra, certain statements or properties are true for any number
DESCRIPTION
Four properties for equality are listed. Property of EqualitySymbolsNumbers SubstitutionIf a = b, then a may be replaced by b. If = 11, the may be replaced by 11 Reflectivea = a21 = 21 SymmetricIf a = b, then b = aIf 10 = 4 + 6, then = 10 TransitiveIf a = b and b = c, the a = cIf = 8 and 8 = 2(4), then = 2(4)TRANSCRIPT
![Page 1: Chapter 1 Section 2 Part 2. In Algebra, certain statements or properties are true for any number](https://reader036.vdocuments.net/reader036/viewer/2022081809/5a4d1b767f8b9ab0599b727c/html5/thumbnails/1.jpg)
Chapter 1 Section 2
Part 2
![Page 2: Chapter 1 Section 2 Part 2. In Algebra, certain statements or properties are true for any number](https://reader036.vdocuments.net/reader036/viewer/2022081809/5a4d1b767f8b9ab0599b727c/html5/thumbnails/2.jpg)
In Algebra, certain statements or properties are true for any number.
![Page 3: Chapter 1 Section 2 Part 2. In Algebra, certain statements or properties are true for any number](https://reader036.vdocuments.net/reader036/viewer/2022081809/5a4d1b767f8b9ab0599b727c/html5/thumbnails/3.jpg)
Four properties for equality are listed.
Property of Equality Symbols NumbersSubstitution If a = b, then a may be
replaced by b.If 9 + 2 = 11, the 9 + 2 may
be replaced by 11
Reflective a = a 21 = 21
Symmetric If a = b, then b = a If 10 = 4 + 6, then 4 + 6 = 10
Transitive If a = b and b = c, the a = c If 3 + 5 = 8 and 8 = 2(4), then 3 + 5 = 2(4)
![Page 4: Chapter 1 Section 2 Part 2. In Algebra, certain statements or properties are true for any number](https://reader036.vdocuments.net/reader036/viewer/2022081809/5a4d1b767f8b9ab0599b727c/html5/thumbnails/4.jpg)
Example 1
Name the property of equality shown by each statement.
If 9 + 3 = 12, then 12 = 9 + 3.Symmetric Property of Equality
![Page 5: Chapter 1 Section 2 Part 2. In Algebra, certain statements or properties are true for any number](https://reader036.vdocuments.net/reader036/viewer/2022081809/5a4d1b767f8b9ab0599b727c/html5/thumbnails/5.jpg)
Example 2
Name the property of equality shown by each statement.
If z = 8, then z ÷ 4 = 8 ÷ 4.Substitution Property of Equality
![Page 6: Chapter 1 Section 2 Part 2. In Algebra, certain statements or properties are true for any number](https://reader036.vdocuments.net/reader036/viewer/2022081809/5a4d1b767f8b9ab0599b727c/html5/thumbnails/6.jpg)
Your Turn
Name the property of equality shown by each statement.
7 – c = 7 – cReflective
![Page 7: Chapter 1 Section 2 Part 2. In Algebra, certain statements or properties are true for any number](https://reader036.vdocuments.net/reader036/viewer/2022081809/5a4d1b767f8b9ab0599b727c/html5/thumbnails/7.jpg)
Your Turn
Name the property of equality shown by each statement.
If 10 – 3 = 4 + 3 and 4 + 3 = 7, then 10 – 3 = 7Transitive
![Page 8: Chapter 1 Section 2 Part 2. In Algebra, certain statements or properties are true for any number](https://reader036.vdocuments.net/reader036/viewer/2022081809/5a4d1b767f8b9ab0599b727c/html5/thumbnails/8.jpg)
These properties of numbers help to find value of expressions.
Property Words Symbols NumbersAdditive Identity When 0 is added to
any number a, the sum is a.
For any number a, a + 0 = 0 + a = a
45 + 0 = 450 + 6 = 60 is the identity
Multiplicative Identity
When a number a is multiplied by 1, the product is a.
For any number a, a 1 = 1 a = a∙ ∙
12 1 = 12 ∙1 5 = 5 ∙
Multiplicative Property of Zero
If 0 is a factor, the product is 0.
For any number a,a 0 = 0 a = 0∙ ∙
7 0 = 0∙0 23 = 0∙
![Page 9: Chapter 1 Section 2 Part 2. In Algebra, certain statements or properties are true for any number](https://reader036.vdocuments.net/reader036/viewer/2022081809/5a4d1b767f8b9ab0599b727c/html5/thumbnails/9.jpg)
When two or more sets of grouping symbols are used, simplify within the innermost
grouping symbols first.
![Page 10: Chapter 1 Section 2 Part 2. In Algebra, certain statements or properties are true for any number](https://reader036.vdocuments.net/reader036/viewer/2022081809/5a4d1b767f8b9ab0599b727c/html5/thumbnails/10.jpg)
Example 3
Find the value of 5[3 – (6 ÷ 2)] + 14. Identify the properties used. 5[3 – (6 ÷ 2)] + 14
= 5[3 – 3] + 14= 5(0) + 14
= 0 + 14= 14
Substitution Property of
EqualitySubstitution Property of
Equality Multiplication Property of Zero
Additive Identity
![Page 11: Chapter 1 Section 2 Part 2. In Algebra, certain statements or properties are true for any number](https://reader036.vdocuments.net/reader036/viewer/2022081809/5a4d1b767f8b9ab0599b727c/html5/thumbnails/11.jpg)
Your Turn
(22 – 15) ÷ 7 9∙
9- Substitution Property of Equality
![Page 12: Chapter 1 Section 2 Part 2. In Algebra, certain statements or properties are true for any number](https://reader036.vdocuments.net/reader036/viewer/2022081809/5a4d1b767f8b9ab0599b727c/html5/thumbnails/12.jpg)
Your Turn
8 ÷ 4 6(5 – 4)∙
12- Substitution Property of EqualityAnd Multiplicative Identity
![Page 13: Chapter 1 Section 2 Part 2. In Algebra, certain statements or properties are true for any number](https://reader036.vdocuments.net/reader036/viewer/2022081809/5a4d1b767f8b9ab0599b727c/html5/thumbnails/13.jpg)
You can apply the properties of numbers to find the value of an algebraic expression.
This is called evaluating an expression.
Replace the variables with the known values and then use the order of operations.
![Page 14: Chapter 1 Section 2 Part 2. In Algebra, certain statements or properties are true for any number](https://reader036.vdocuments.net/reader036/viewer/2022081809/5a4d1b767f8b9ab0599b727c/html5/thumbnails/14.jpg)
Example 4
Evaluate each expression if a = 9 and b = 1.7 + (a/b – 9)= 7 + (9/1 – 9) Replace a with 9 and b with 1= 7 + (9 – 9) Substitution Property of Equality= 7 + 0 Substitution Property of Equality= 7 Additive Inverse
![Page 15: Chapter 1 Section 2 Part 2. In Algebra, certain statements or properties are true for any number](https://reader036.vdocuments.net/reader036/viewer/2022081809/5a4d1b767f8b9ab0599b727c/html5/thumbnails/15.jpg)
Example 5
Evaluate each expression if a = 9 and b = 1.(a + 4) – 3 b∙= (9 + 4) – 3 ∙ 1 Replace a with 9 and b with 1= (13) – 3 1 Substitution Property of Equality∙= 13 – 3 Multiplicative Identity= 10 Substitution Property of Equality
![Page 16: Chapter 1 Section 2 Part 2. In Algebra, certain statements or properties are true for any number](https://reader036.vdocuments.net/reader036/viewer/2022081809/5a4d1b767f8b9ab0599b727c/html5/thumbnails/16.jpg)
Your Turn
Evaluate each expression if m = 8 and p = 2.
6 p – m ÷ p∙
8
![Page 17: Chapter 1 Section 2 Part 2. In Algebra, certain statements or properties are true for any number](https://reader036.vdocuments.net/reader036/viewer/2022081809/5a4d1b767f8b9ab0599b727c/html5/thumbnails/17.jpg)
Your Turn
Evaluate each expression if m = 8 and p = 2.
[m + 2(3 + p)] ÷ 2
9