Understanding Simplifying Algebraic Expressions in Pre-Algebra

 
Agenda
 
Do Now
Introduction
Video
Cornell Notes
Guided Practice
Independent
Practice
 
Do Now
 
Turn in Avid one pager
Format your paper for Cornell
Notes
Topic: Simplifying Algebraic
Expressions
E.Q.- How do I simplify
Algebraic Expressions
D.E.A.R.!!!
 
 
An expression is a math sentence that
does not have an equal sign.
 
 
For example:  3x + 7 – 4x -2
 
Remember:
We evaluate expressions.
We solve equations.
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Simplifying Expressions
Simplifying Expressions
 
 
 
 
 
 
 
 
 
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Simplifying Expressions
Simplifying Expressions
Positively Pre-Algebra Plus 2017
Simplifying Expressions
Simplifying Expressions
 
Terms that have identical variable parts
are 
like terms
.
  In the expression 
3x + 7 – 4x -2
 
 
3x and -4x are like terms
   7 and -2 are like terms
 
We can combine like terms.
Positively Pre-Algebra Plus 2017
Simplifying Expressions
Simplifying Expressions
 
The 
coefficient 
of a term is the number
part of the term.
 
In the expression 
3x + 7 – 4x -2
 the coefficients are 3 (from 3x) and -4
(from -4x).
 
If a variable has no number in front of it,
the coefficient is 1.
Positively Pre-Algebra Plus 2017
Simplifying Expressions
Simplifying Expressions
 
A term that has a number, but no
variable, is a 
constant term.
 
       In the expression 
3x + 7 - 4x -2
       the constants are:
   
 
7 and -2.
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Your Turn - Identify the coefficients,
Your Turn - Identify the coefficients,
constant term(s), and like terms
constant term(s), and like terms
 
1.
a – 5 + 4a
 
2.
7 – 2b + b -8
 
3.
-3c + 2 + 6c + 5
 
1.
4, 1; -5; a and 4a
 
2.
-2, 1; 7, -8; 7 and
-8, -2b and b
 
3.
-3 and 6; 2 and 5;
-3c and 6c, 2 and
5
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Combining Like Terms
Combining Like Terms
 
We can only add or subtract terms that
are alike.  2x + 2 cannot be added
because 2x and 2 are not like terms.
 
Like terms have identical variable parts
and identical exponents!
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Combining Like Terms
Combining Like Terms
 
Example:  11x + 1 – 4x
 
11x and -4x are like terms
, so we can
combine them:
  
11x – 4x = 7x
 
Rewrite the simplified expression:
 
= 7x + 1
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Combining Like Terms
Combining Like Terms
 
Example:  12m + 9 -2m -16
 
  
12m and -2m are like terms.
  
9 and -16 are like terms.
 
 
12m – 2m = 10m
 
9 – 16 = -7
 
So, we can rewrite the expression to be:
                          
10m - 7
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Your Turn - Simplify Each Expression
Your Turn - Simplify Each Expression
 
1.
10k + 6km + 5k
 
2.
8g – 9g + 2
 
3.
y + y + y
 
4.
4a + 7b + 4b + 5a
 
5.
8 – 6a + 2b - 8
 
1.
15k + 6km
 
2.
-g + 2
 
3.
3y
 
4.
9a + 11b
 
5.
-6a + 2b
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Distributive Property
Distributive Property
 
Sometimes you need to use distributive
property to simplify the expression
before you combine like terms.
 
  
2(y - 4) + 5y
 =
  
(2 • y) - (2 • 4) + 5y
 =     2y – 8 + 5y
 =      
7y - 8
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Distributive Property
Distributive Property
 
    5(n + 2r) + 3n
 
=
 
(5 • n) + (5 • 2r) + 3n
 
=
 
5n + 10r + 3n
 
=
 
(5n + 3n) + 10r
 
=   
8n + 10r
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Your Turn - Simplify the expressions
Your Turn - Simplify the expressions
 
1.
4(2n + 10)
 
2.
2(15xy + 8x)
 
3.
-2(c + 10) + 4c +22
 
4.
3(2v + 5m) - 2(3v –2m)
 
1.
8n + 40
 
2.
30xy + 16x
 
3.
2c + 2
 
4.
19m
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Simplifying algebraic expressions involves identifying terms, like terms, coefficients, and constant terms. By combining like terms and following basic rules, expressions can be simplified to make solving equations easier for pre-algebra students.


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  1. 09.24.2018 Agenda Do Now Introduction Video Cornell Notes Guided Practice Independent Practice Do Now Turn in Avid one pager Format your paper for Cornell Notes Topic: Simplifying Algebraic Expressions E.Q.- How do I simplify Algebraic Expressions D.E.A.R.!!!

  2. Simplifying Algebraic Expressions https://www.youtube.com/watch?v=T5DcqV wyrfk

  3. Simplifying Expressions An expression is a math sentence that does not have an equal sign. For example: 3x + 7 4x -2 Remember: We evaluate expressions. We solve equations. Positively Pre-Algebra Plus 2017

  4. Simplifying Expressions Each part of an expression is called a term. In the expression 3x + 7 - 4x -2 the terms are: 3x, 7, -4x, and -2 Notice that the sign in front of each term goes with that term. Positively Pre-Algebra Plus 2017

  5. Simplifying Expressions Terms that have identical variable parts are like terms. In the expression 3x + 7 4x -2 3x and -4x are like terms 7 and -2 are like terms We can combine like terms. Positively Pre-Algebra Plus 2017

  6. Simplifying Expressions The coefficient of a term is the number part of the term. In the expression 3x + 7 4x -2 the coefficients are 3 (from 3x) and -4 (from -4x). If a variable has no number in front of it, the coefficient is 1. Positively Pre-Algebra Plus 2017

  7. Simplifying Expressions A term that has a number, but no variable, is a constant term. In the expression 3x + 7 - 4x -2 the constants are: 7 and -2. Positively Pre-Algebra Plus 2017

  8. Your Turn - Identify the coefficients, constant term(s), and like terms 1. a 5 + 4a 1. 4, 1; -5; a and 4a 2. -2, 1; 7, -8; 7 and -8, -2b and b 2. 7 2b + b -8 3. -3c + 2 + 6c + 5 3. -3 and 6; 2 and 5; -3c and 6c, 2 and 5 Positively Pre-Algebra Plus 2017

  9. Combining Like Terms We can only add or subtract terms that are alike. 2x + 2 cannot be added because 2x and 2 are not like terms. Like terms have identical variable parts and identical exponents! Positively Pre-Algebra Plus 2017

  10. Combining Like Terms Example: 11x + 1 4x 11x and -4x are like terms, so we can combine them: 11x 4x = 7x Rewrite the simplified expression: = 7x + 1 Positively Pre-Algebra Plus 2017

  11. Combining Like Terms Example: 12m + 9 -2m -16 12m and -2m are like terms. 9 and -16 are like terms. 12m 2m = 10m 9 16 = -7 So, we can rewrite the expression to be: 10m - 7 Positively Pre-Algebra Plus 2017

  12. Your Turn - Simplify Each Expression 1. 10k + 6km + 5k 1. 15k + 6km 2. 8g 9g + 2 2. -g + 2 3. y + y + y 3. 3y 4. 4a + 7b + 4b + 5a 4. 9a + 11b 5. 8 6a + 2b - 8 5. -6a + 2b Positively Pre-Algebra Plus 2017

  13. Distributive Property Sometimes you need to use distributive property to simplify the expression before you combine like terms. = = 2y 8 + 5y = 7y - 8 2(y - 4) + 5y (2 y) - (2 4) + 5y Positively Pre-Algebra Plus 2017

  14. Distributive Property 5(n + 2r) + 3n = (5 n) + (5 2r) + 3n = 5n + 10r + 3n = (5n + 3n) + 10r = 8n + 10r Positively Pre-Algebra Plus 2017

  15. Your Turn - Simplify the expressions 1. 4(2n + 10) 1. 8n + 40 2. 2(15xy + 8x) 2. 30xy + 16x 3. -2(c + 10) + 4c +22 3. 2c + 2 4. 3(2v + 5m) - 2(3v 2m) 4. 19m Positively Pre-Algebra Plus 2017

  16. Thank you for downloading this product. Please let me know how it worked for you by visiting my store again and leaving some feedback (which also earns you future purchase credit). I welcome all comments and suggestions so I can create products that are truly useful to you in your classroom. I do not lock my PowerPoint lessons. We all have to differentiate and teach to the children in front of us each day. Locking the lesson seems counterproductive to helping you reach all students. I do ask that you honor the terms of use at TPT and not share these materials with others. Additional licenses are available to purchase at a discount if you want to share with other teachers at your school, or within the school district. Permission is given to modify the product to best suit your students needs, but the credit page should not be removed. Thank you. I d love to have you follow my TPT store! Just click on the green star next to my name at TPT. When you follow me you get: Notified whenever I have a sale Notified of new and free products 2017 Positively Pre-Algebra Plus

  17. QUESTIONS? Positively Pre-Algebra Plus 2017

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