Evaluating Expressions and Combining Like Terms

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Evaluating Expressions and Combining Like Terms

• R. Portteus

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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.

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How do you describe a variable expression?
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Evaluate a Variable Expression

• Example 1 Evaluate each expression when n 4.
• a. n 3
• n 3 4 3
• 7
• b. n 3
• n 3 4 3
• 1

Simplify (means to solve the problem or perform
as many of the indicated operations as possible.)

Solution
Substitute 4 for n. Simplify
Substitute 4 for n. Simplify
Solution
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Evaluate an Algebraic Expression

• Example 2 Evaluate each expression if x 8.
• a. 5x
• 5x 5(8)
• 40
• b. x 4
• x 4 8 4
• 2

Substitute 8 for x. Simplify
Using parenthesis is the preferred method to show
multiplication. Additional ways to show
multiplication are 5 8 and 5 x 8.
Solution
Substitute 8 for x. Simplify
Solution
Recall that division problems are also fractions
this problem could be written as
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Evaluating More Expressions

• Example 3 Evaluate each expression if x 4, y
  6, and z 24.
• a. 5xy
• 5xy 5(4)(6)
• 120
• b.
• 4

Substitute 4 for x 6 for y. simplify
Solution
Substitute 24 for z 6 for y. Simplify.
Solution
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Now You Try Evaluate each expression given that
a 6, b 12, and c 3.
A

• 4ac
• a c
• a b c
• ba
• b c
• c b

A
A
A
A
A
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You Try 1

• Evaluate each expression given that a 6, b
  12, and c 3.
• 4ac
• 4ac 4(6)(3)
• (24)(3)
• 72

Substitute the value for a 6 and c 3 into the
problem and multiply
Click to return to You try it slide
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You Try 2

• Evaluate each expression given that a 6, b
  12, and c 3.
• 2. a c
• a c 6 3
• 2

Substitute the value for a 6 and c 3 into the
problem and divide
Click to return to You try it slide
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You Try 3

• Evaluate each expression given that a 6, b
  12, and c 3.
• a b c
• a b c 6 12 3
• 18 3
• 21

Substitute the value for a 6, b12, and c 3
into the problem, then add.
Click to return to You try it slide
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You Try 4

• Evaluate each expression given that a 6, b
  12, and c 3.
• 4. ba
• ba (12)(6)
• 72

Substitute the value for b12 and a 6 into the
problem, then multiply.
Click to return to You try it slide
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You Try 5

• Evaluate each expression given that a 6, b
  12, and c 3.
• 5. b - c
• b c 12 3
• 9

Substitute the value for b12 and a 3 into the
problem, then subtract.
Click to return to You try it slide
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You Try 6

• Evaluate each expression given that a 6, b
  12, and c 3.
• 6. c b

Substitute the value for c3 and b 12 into the
problem, then Divide Note It is better to
rewrite this division problem as a fraction.
This fraction can now be reduced to its simplest
form.
Divide both numerator and denominator by the GCF
(3) to reduce this fraction.
It is OK to have a fraction as an answer.
Click to return to You try it slide
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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

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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.

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Lets 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.
• 4x5x-2x 9x-2x 7x
• Simplify the constant (number) terms.
• -27 5
• You have a simplified expression by writing all
  of the results from simplifying.
• 7x 5

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Another example

• 10x 4y 3x2 2x 2y
• 3x2
• 10x, 2x
• -4y 2y
• 3x2 12x 6y

Remember you cannot combine terms with the same
variable but different exponents.
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Now you try

• Simplify the following
• 5x 3y - 6x 4y 3z
• 3b - 3a - 5c 4b
• 4ab 2a2b 5 ab ab2 2a2b 4
• 5xy 2yx 7y 3x 4xy 2x

A
A
A
A
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You Try 1

• Simplify the following
• 5x 3y - 6x 4y 3z
• 5x, -6x
• 3y, 4y
• 3z
• -x 7y 3z

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You Try 2

• Simplify the following
• 3b - 3a - 5c 4b
• 3b, 4b
• -3a
• -5c
• -3a 7b 5c

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You Try 3

• Simplify the following
• 4ab 2a2b 5 ab ab2 2a2b 4
• 4ab, -ab
• -2a2b, 2a2b
• 5, 4
• ab2
• 3ab ab2 9

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You Try 4

• Simplify the following
• 5xy 2yx 7y 3x 4xy 2x
• 5xy, -2yx, -4xy
• 7y
• 3x, 2x
• -xy 7y 5x

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Conclusion

• A variable or algebraic expression is an
  expression that consists of one or more ________
  and _________ along with one or more ________
  _________. (Note No _______ sign)
• To evaluate an expression write the _________,
  substitute a _______ for each variable, and
  _________ the result.

numbers
variables
arithmetic
operations
equal
expression
number
simplify
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Conclusion Continued

• In an expression, __________ are the terms that
  have the same ________, raised to the same
  ________ (same exponents).
• A coefficient is a number that ________ a
  variable.

like terms
variables
power
multiplies