Evaluating Expressions

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Evaluating Expressions

• R. Portteus

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Order of Operations Review

• How do you follow the order of operations?

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Order of Operations

1. ( )
2. Exponents Ex. 3² 3 x 3 9
3. x or , from Left to Right
4. or -, from Left to Right

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Order of Operations Review

• 20 4 x 23 (5 - 8)
• 43 B. 27
• C. 1 D. 37

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• 20 4 x 23 (5 - 8)
• 43
• 27
• 1
• 37

20 4 x 23 (5 - 8)
20 4 x 23 (-3) 20
4 x 8 (-3) 5 x 8
(-3) 40 -3
37
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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?
Variable Expression Meaning Operation
5x, 5x, (5)(x) (same as x5) 5 times x Multiplication
5 divided by x Division
5 x (same as x 5) 5 plus x Addition
5 x 5 minus x subtraction
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Journal Reflection

• Evaluate Expressions Video
• Write your reflection from the video.

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Journal Reflection

• Lets watch a short video
• Write your reflection from the video.

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• How do we evaluate expressions for each math
  operation, - x ?

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Evaluate a Variable Expression with each
operation

• 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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Lets go to the next level!

• What if an expression has more than one variable?
• How do I evaluate expressions with more than one
  variable?

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Evaluating Expressions with more than one variable

• 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.

1. 4ac
2. a c
3. a b c
4. ba
5. b c
6. c b

A
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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Summary

• To evaluate expressions
• Replace a variable with a number
• Follow order of operations to find the solution.
• Follow the algorithms for integers.

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Exit Ticket
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5 x 6 30
9 x 5 45 2(8) 4

18/3 18 16 4 12
6 18
24 3 x 4 12
10 2 10

5 10
15
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(No Transcript)
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9(4) 25 36 25 11 9 x 9 81 56/8
5 7 5 2 14 3(6) 14 18 32
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Homework

• Homework Evaluate Expressions 3 Terms
  Add/Subtract A and B here