Understanding Simplifying Algebraic Expressions in Pre-Algebra
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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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.!!!
Simplifying Algebraic Expressions https://www.youtube.com/watch?v=T5DcqV wyrfk
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
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
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 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 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
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
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
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
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
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
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
Distributive Property 5(n + 2r) + 3n = (5 n) + (5 2r) + 3n = 5n + 10r + 3n = (5n + 3n) + 10r = 8n + 10r Positively Pre-Algebra Plus 2017
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
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