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Alg 1.3 Packet Condensed

This document covers algebraic properties including the commutative, associative, and distributive properties. It provides examples of using these properties to determine if expressions are equivalent. It also includes practice problems for students to simplify expressions and prove algebraic identities using the correct properties. Exercises are provided to have students analyze mistakes made in using the distributive property and to wrap up the lesson by stating properties and simplifying expressions. An exit ticket problem asks students to write expressions for the area and perimeter of a rectangular tomato garden based on the number of tomato plants.

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Melinda R. Francisco
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63 views5 pages

Alg 1.3 Packet Condensed

This document covers algebraic properties including the commutative, associative, and distributive properties. It provides examples of using these properties to determine if expressions are equivalent. It also includes practice problems for students to simplify expressions and prove algebraic identities using the correct properties. Exercises are provided to have students analyze mistakes made in using the distributive property and to wrap up the lesson by stating properties and simplifying expressions. An exit ticket problem asks students to write expressions for the area and perimeter of a rectangular tomato garden based on the number of tomato plants.

Uploaded by

Melinda R. Francisco
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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1.

3 Algebraic Properties NOTES


EXPRESSIONS
Numeric Expression Algebraic Expression
Write your
questions here!

COMMUTATIVE PROPERTY
ADDITION MULTIPLICATION

ASSOCIATIVE PROPERTY
ADDITION MULTIPLICATION

Determine if the expressions are equivalent. If so, state the property used to show equivalence.
8−6= 6−8 8 − 6 = −6 + 8

4 ∙ (𝑥 ∙ 𝑦) = (4 ∙ 𝑥) ∙ 𝑦 5 + (𝑥 + 2) = (5 + 𝑥) + 2 𝑎 + (𝑏 ∙ 𝑐) = (𝑏 ∙ 𝑐) + 𝑎

PROVE (𝑥𝑦)𝑧 = (𝑧𝑦)𝑥


(𝑥𝑦)𝑧 Given
𝑧(𝑥𝑦)
𝑧(𝑦𝑥)
(𝑧𝑦)𝑥

PROVE 𝑥 + (𝑦 + 𝑧) = 𝑧 + (𝑥 + 𝑦)
𝑥 + (𝑦 + 𝑧) Given
(𝑥 + 𝑦) + 𝑧
𝑧 + (𝑥 + 𝑦)

DISTRIBUTIVE PROPERTY

−4(2𝑥 + 3𝑦)
Distribute and combine like terms.
2ℎ − 4(3ℎ − 7) −4(2𝑥 + 3) − 6

7𝑑 + 2(5 + 3𝑑) 8 − 3(2𝑡 − 5) 2


(3𝑥 + 6) + 12
3

PROVE (3 + 𝑥)(2) = 6 + 2𝑥
(3 + 𝑥)(2) Given
(2)(3 + 𝑥)
6 + 2𝑥
SUMMARY:

Now,
summarize
your notes
here!

1.3 Algebraic Properties PRACTICE


TRUE/FALSE Circle true or false. If true, circle the property used to determine the expressions equivalent.
1. 7 + 9 = 9 + 7 2. (8 ∙ 3)4 = 8(3 ∙ 4) 3. 𝑎 + (9 + 𝑏) = (𝑎 + 9) + 𝑏
TRUE or FALSE TRUE or FALSE TRUE or FALSE
If true, equivalent by… If true, equivalent by… If true, equivalent by…
Commutative Property Commutative Property Commutative Property
Associative Property Associative Property Associative Property
Distributive Property Distributive Property Distributive Property

4. 𝑥 − 8 = 8 − 𝑥 5. 𝑎𝑐 + 𝑑𝑐 = 𝑑𝑐 + 𝑎𝑐 6. (𝑎 + 𝑏)2 = 𝑎2 + 𝑏 2
TRUE or FALSE TRUE or FALSE TRUE or FALSE
If true, equivalent by… If true, equivalent by… If true, equivalent by…
Commutative Property Commutative Property Commutative Property
Associative Property Associative Property Associative Property
Distributive Property Distributive Property Distributive Property
Fill in the reasons for each proof with the correct property used.
7. Prove: 𝑥 2 (2𝑦) = (2𝑥 2 )𝑦 8. Prove: 3(5 − 𝑥) = −3𝑥 + 15
𝑥 2 (2𝑦) Given 3(5 − 𝑥) Given
(𝑥 2 2)𝑦 ____________________________ 15 − 3𝑥 ____________________________
(2𝑥 2 )𝑦 −3𝑥 + 15
____________________________ ____________________________

9. Prove: 𝑡 + (2 + 𝑡) = 2𝑡 + 2 10. Prove: 2(ℎ + 5) + 4ℎ = 6ℎ + 10


𝑡 + (2 + 𝑡) Given 2(ℎ + 5) + 4ℎ Given
𝑡 + (𝑡 + 2) ____________________________ 2ℎ + 10 + 4ℎ ____________________________
(𝑡 + 𝑡) + 2 2ℎ + 4ℎ + 10
____________________________ ____________________________
2𝑡 + 2 Combine Like Terms 6ℎ + 10 Combine Like Terms

Simplify the expression by using the distributive property.


12. 4(𝑥 + 3) 13. 5(𝑚 + 5) 14. −8(𝑝 − 3)

15. (2𝑟 − 3)(2) 16. 6.5(𝑣 + 1) 17. −(3 + 𝑥)

3 19. −(6𝑛 − 9) 2
18. (8𝑚 − 4) 20. − 3 (6𝑛 − 9)
2

Simplify the expression using distributive property and combine like terms.
21. 6 + 2(𝑦 + 1) 22. 2(4𝑎 − 1) + 𝑎 23. 6𝑟 − 2(𝑟 + 4)

24. −3(𝑚 + 5) − 10 25. 3 − 8(𝑤 − 5) 1


26. (2𝑚 + 6) − 10
2
Analyze student work.
27. Mr. Bean and Mr. Brust are really, really bad at the distributive property. They both make huge mistakes using
the distributive property. Identify their mistakes and show them how to distribute correctly.

1.3 Algebraic Properties WRAP UP


State the property used below. Simplify
1. 𝑎(5 ∙ 𝑏) = (𝑎 ∙ 5)𝑏 2. 3 + 2(𝑏 − 4)

3. The expression 2𝑚 − (8 − 4𝑚) + 5 is equivalent to which of the following expressions?

A) 6𝑚 + 13
B) −2𝑚 − 3
C) 6𝑚 − 3
D) −2𝑚 + 13
E) none of the above
EXIT TICKET

Tommy is planning to make a tomato garden. The rectangular garden must be 4 foot wide. Tommy
doesn’t how long the garden will be, but would like 3 feet per tomato plant plus 1 foot extra at each end of
the garden. Tommy doesn’t know how many tomato plants he will buy. The diagram below shows the
dimensions of the garden for x amount of tomato plants. Create a simplified expression to represent both
the area and perimeter of the garden.

Area: Perimeter:
3x + 2

Now, use your expression to determine both the area and perimeter of the garden if Tommy plants 8
tomato plants.

SMP #4

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