Evaluating Expressions and Combining Like Terms

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					Evaluating Expressions
  and Combining Like
        Terms



                    R. Portteus
  Evaluating Expressions
• Vocabulary:
  – Variable – A symbol, usually a letter of the
    alphabet, such as the letter n, that is used to
    represent a number.
  – Variable expression (A.K.A. - Algebraic
    Expression) – An expression, such as n – 5, that
    consists of one or more numbers and variables
    along with one or more arithmetic operations.
    (Note: No equal sign)
  – Evaluate a Variable Expression – write the
    expression, substitute a number for each
    variable, and simplify the result.
  How do you describe a
   variable expression?
Variable             Meaning      Operation
Expression
5x, 5·x, (5)(x)      5 times x    Multiplication
(same as x·5)
   5                 5 divided by Division
     ,5  x
   x                 x
5 + x (same as x +   5 plus x     Addition
5)
5–x                  5 minus x    subtraction
            Evaluate a Variable
                Expression
     • Example 1: Evaluate each expression
         when n = 4.     Simplify (means to solve the problem or perform as
                         many of the indicated operations as possible.)
         a. n + 3
Solution:
            n + 3 = 4 + 3 Substitute 4 for n. Simplify
            =7
         b. n – 3
Solution:   n – 3 = 4 – 3 Substitute 4 for n. Simplify
            =1
          Evaluate an Algebraic
               Expression
    • Example 2: Evaluate each expression if x =
       8.
       a. 5x                Substitute 8 for x. Simplify
Solution: 5x = 5(8)          Using parenthesis is the preferred method to show
                             multiplication. Additional ways to show multiplication are

          = 40               5 · 8 and 5 x 8.


       b. x ÷ 4              Substitute 8 for x. Simplify
Solution: x÷4=8÷4
                                                                     x    8
                                                                       
          = 2 Recall that division problems are also
                fractions – this problem could be
                                                                     4    4
                                                                           2;
                      written as:
                                                                     because
                                                                              x
                                                                      x4 
                                                                              4
                Evaluating More
                  Expressions
       • Example 3: Evaluate each expression if
          x = 4, y = 6, and z = 24.
          a. 5xy         Substitute 4 for x; 6 for y. simplify
Solution:
             5xy = 5(4)(6)
             = 120
          b. z           Substitute 24 for z; 6 for y. Simplify.
            y
            z   24
Solution:
              
            y    6
            =4
        Now You Try…
Evaluate each expression given that a =
         6, b = 12, and c = 3.
1.   4ac      A

2.   a÷c      A

3.   a+b+c    A

4.   ba       A

5.   b–c      A
6.   c÷b      A
             You Try #1
Evaluate each expression given that a =
   6, b = 12, and c = 3.
1. 4ac         Substitute the value for a = 6 and c = 3
               into the problem and multiply

   4ac = 4(6)(3)
   = (24)(3)
   = 72
                                                Click to return to
                                                “You try it” slide
             You Try #2
Evaluate each expression given that a =
  6, b = 12, and c = 3.
2. a ÷ c        Substitute the value for a = 6 and c = 3
                into the problem and divide

     a÷c=6÷3
     =2


                                                 Click to return to
                                                 “You try it” slide
              You Try #3
Evaluate each expression given that a =
   6, b = 12, and c = 3.
3. a + b + c          Substitute the value for a = 6, b=12,
                      and c = 3 into the problem, then add.

   a + b + c = 6 + 12 + 3
   = 18 + 3
   = 21
                                                    Click to return to
                                                    “You try it” slide
             You Try #4
Evaluate each expression given that a =
  6, b = 12, and c = 3.
4. ba           Substitute the value for b=12 and a = 6
                into the problem, then multiply.

     ba = (12)(6)
     = 72


                                                Click to return to
                                                “You try it” slide
              You Try #5
Evaluate each expression given that a =
  6, b = 12, and c = 3.
5. b - c           Substitute the value for b=12 and a = 3
                   into the problem, then subtract.

     b – c = 12 – 3
     =9


                                                   Click to return to
                                                   “You try it” slide
                      You Try #6
        Evaluate each expression given that a =
           6, b = 12, and c = 3.
        6. c ÷ b                  Substitute the value for c=3 and b = 12 into
                                  the problem, then Divide
                       c 3 Note: It is better to rewrite this division
Divide both
numerator and    c b           problem as a fraction.
denominator by         b 12 This fraction can now be reduced to its
                  3 3 1
the GCF = (3) to                  simplest form.

                       
reduce this
fraction.
                 12  3 4 as an answer.
                            It is OK to have a fraction

                                                                  Click to return to
                                                                  “You try it” slide
  Combining Like Terms
• Now that we have seen some algebraic
  expressions, we need to know how to
  simplify them.
• Vocabulary
  – Like terms: In an expression, like terms are the
    terms that have the same variables, raised to
    the same powers (same exponents).
     • i.e. 4x and -3x or 2y2 and –y2
  – Coefficient: A constant that multiplies a
    variable.
     • i.e. the 3 in 3a or the -1 in –b
  Combining Like Terms
• In algebra we often get very long
  expressions, which we need to make
  simpler. Simpler expressions are
  easier to solve!
• To simplify an expression we collect
  like terms. Like terms include letters
  that are the same and numbers.
               Let’s try one…
•   Step One: Write the expression.
    4x + 5x -2 - 2x + 7
•   Collect all the terms together which are alike. Remember that
    each term comes with an operation (+,-) which goes before it.
    4x, 5x, and -2x
    -2 and 7
•   Simplify the variable terms.
    4x+5x-2x = 9x-2x = 7x
•   Simplify the constant (number) terms.
    -2+7 = 5
•   You have a simplified expression by writing all of the results from
    simplifying.
    7x + 5
      Another example…
• 10x – 4y + 3x2 + 2x – 2y
  3x2
                          Remember you cannot
  10x, 2x                  combine terms with
                          the same variable but
  -4y – 2y                different exponents.

• 3x2 + 12x – 6y
        Now you try…
Simplify the following:
• 5x + 3y - 6x + 4y + 3z                 A

• 3b - 3a - 5c + 4b                      A

• 4ab – 2a2b + 5 – ab + ab2 + 2a2b + 4   A

• 5xy – 2yx + 7y + 3x – 4xy + 2x         A
         You Try #1
• Simplify the following:
1. 5x + 3y - 6x + 4y + 3z
   5x, -6x
   3y, 4y
   3z
   -x + 7y + 3z
         You Try #2
• Simplify the following:
2. 3b - 3a - 5c + 4b
   3b, 4b
   -3a
   -5c
   -3a + 7b – 5c
           You Try #3
• Simplify the following:
3. 4ab – 2a2b + 5 – ab + ab2 + 2a2b + 4
   4ab, -ab
   -2a2b, 2a2b
   5, 4
   ab2
   3ab + ab2 + 9
         You Try #4
• Simplify the following:
4. 5xy – 2yx + 7y + 3x – 4xy + 2x
   5xy, -2yx, -4xy
   7y
   3x, 2x
   -xy + 7y + 5x
           Conclusion
• A variable or algebraic expression is an
  expression that consists of one or more
  ________ and _________ along with one
   numbers             variables
  or more ________ _________. (Note: No
             arithmetic     operations
  _______ sign)
   equal

• To evaluate an expression write the
  _________, substitute a _______ for
  expression                         number
  each variable, and _________ the result.
                         simplify
  Conclusion Continued…
• In an expression, __________ are
                      like terms
  the terms that have the same
  ________, raised to the same
    variables

  ________ (same exponents).
   power

• A coefficient is a number that
  ________ a variable.
   multiplies

				
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posted:3/15/2013
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