evaluating expressions r. portteus. order of operations review how do you follow the order of...
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Evaluating Evaluating ExpressionsExpressionsEvaluating Evaluating
ExpressionsExpressions
R. PortteusR. Portteus
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Order of Operations Review
How do you follow the order of operations?
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Order of Operations1. ( )2. Exponents Ex. 3² = 3 x 3 = 93. x or ÷, from Left to Right4. + or ─, from Left to Right
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Order of Operations ReviewOrder of Operations ReviewOrder of Operations ReviewOrder of Operations Review
20 ÷ 4 x 220 ÷ 4 x 233 + (5 - 8) + (5 - 8) = =
A.A.4343 B. 27B. 27
C. 1C. 1 D. 37D. 37
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20 ÷ 4 x 220 ÷ 4 x 233 + (5 - 8) + (5 - 8) = =
A.A.4343
B.B.2727
C.C.11
D.D.3737
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, 5·x, (5)(x) (same as x·5)
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
xx
5,5
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Journal Reflection
• Evaluate Expressions Video
• Write your reflection from the video.
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Journal Reflection
• Let’s 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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Substitute 4 for n. Simplify
Simplify (means to solve the problem or perform as many of the indicated operations as possible.)
Simplify (means to solve the problem or perform as many of the indicated operations as possible.)
Solution:Solution: Substitute 4 for n. Simplify
Solution:Solution:
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 – 3n – 3 = 4 – 3 = 1
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Substitute 8 for x. Simplify
Solution:Solution:
Solution:Solution:
Using parenthesis is the preferred method to show multiplication. Additional ways to show multiplication are 5 · 8 and 5 x 8.
Using parenthesis is the preferred method to show multiplication. Additional ways to show multiplication are 5 · 8 and 5 x 8.
Substitute 8 for x. Simplify
Recall that division problems are also fractions – this problem could be written as:
Recall that division problems are also fractions – this problem could be written as:
44
2; 4
8
4
xx
because
x
Evaluate an Algebraic Expression
• Example 2: Evaluate each expression if x = 8.a. 5x
5x = 5(8)= 40
b. x ÷ 4x ÷ 4 = 8 ÷ 4= 2
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Let’s 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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Substitute 4 for x; 6 for y. simplify
Solution:Solution:
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
Solution:Solution:
y
z
6
24
y
z
Substitute 24 for z; 6 for y. Simplify.
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A
A
A
A
A
A
Now You Try… Evaluate each expression given that
a = 6, b = 12, and c = 3.
1. 4ac2. a ÷ c3. a + b + c4. ba5. b – c6. c ÷ b
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Substitute the value for a = 6 and c = 3 into the problem and multiply
Substitute the value for a = 6 and c = 3 into the problem and multiply
Click to return to “You try it” slide
Click to return to “You try it” slide
You Try #1Evaluate each expression given that a = 6, b = 12, and c = 3.1. 4ac
4ac = 4(6)(3)= (24)(3)= 72
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Substitute the value for a = 6 and c = 3 into the problem and divide
Substitute the value for a = 6 and c = 3 into the problem and divide
Click to return to “You try it” slide
Click to return to “You try it” slide
You Try #2Evaluate each expression given that a = 6, b = 12, and c = 3.2. a ÷ c
a ÷ c = 6 ÷ 3= 2
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Substitute the value for a = 6, b=12, and c = 3 into the problem, then add.
Substitute the value for a = 6, b=12, and c = 3 into the problem, then add.
Click to return to “You try it” slide
Click to return to “You try it” slide
You Try #3Evaluate each expression given that a = 6, b = 12, and c = 3.3. a + b + c
a + b + c = 6 + 12 + 3= 18 + 3= 21
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Substitute the value for b=12 and a = 6 into the problem, then multiply.
Substitute the value for b=12 and a = 6 into the problem, then multiply.
Click to return to “You try it” slide
Click to return to “You try it” slide
You Try #4Evaluate each expression given that a = 6, b = 12, and c = 3.4. ba
ba = (12)(6)= 72
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Substitute the value for b=12 and a = 3 into the problem, then subtract.
Substitute the value for b=12 and a = 3 into the problem, then subtract.
Click to return to “You try it” slide
Click to return to “You try it” slide
You Try #5Evaluate each expression given that a = 6, b = 12, and c = 3.5. b - c
b – c = 12 – 3= 9
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Substitute the value for c=3 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.
Substitute the value for c=3 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.
Divide both numerator and denominator by the GCF = (3) to reduce this fraction.
It is OK to have a fraction as an answer.
It is OK to have a fraction as an answer.
Click to return to “You try it” slide
Click to return to “You try it” slide
You Try #6Evaluate each expression given that a = 6, b = 12, and c = 3.6. c ÷ b
12
3
b
cbc
4
1
3
3
12
3
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SummaryTo evaluate expressions:1.Replace a variable with a number2.Follow order of operations to find the solution.3.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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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