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1.02 Order of Operations Basic Algebra: One Step at a Time. Page 7 - 12: #36, 37, 42, 44 , 48. Bittinger: p.71: 49, 51, 53, 55, 63, 67, 69, 70 Dr. Robert J. Rapalje Seminole State College of Florida Sanford, FL 32773 To see Section 1.02, with detailed explanations, examples, exercises, and answers, click here!
p. 11:
36. According to the order of operations, since there are NO parentheses here, the next step is to Raise to the Power.
The next step is to Multiply or Divide from Left to Right. This means to divide by 3 first, and then multiply by 2. [NOTE: DO NOT multiply 3•2!!]
The last step is to add, so the final answer is 30.
37.
Since there
ARE parentheses, do what is within Parentheses first! This would be the
The next step is to Multiply or Divide from Left to Right. This means to divide by 2 first, and then multiply by 2.
Final Answer: 20
42.
According to the order of operations, since there are NO parentheses here, the next step is to Raise to the Power.
The next step is to Multiply or Divide from Left to Right. Be sure to do the operations from Left to Right. First divide by 2, and then multiply by 3. [NOTE: DO NOT multiply 2•3!!]
Multiply 6•8=48:
Finally subtract, and then add from left to right:
Final Answer: 54
44.
Again, since there are NO parentheses here, the next step is to Raise to the Power.
The next step is to Multiply or Divide from Left to Right. Be sure to do the operations from Left to Right.
Finally, do the Addition and Subtraction, of course from left to right:
Final Answer: 125
48.
The first step is Parentheses. Since there are sometimes two operations within a set of parentheses, it will take two steps to do this.
The next step is to Raise to the Power.
The next step is to Multiply or Divide from Left to Right. Be sure to do the operations from Left to Right.
Finally, do the Addition and Subtraction, of course from left to right:
Final Answer: 4
[By the way, you should show as many steps as you need to be comfortable with your work. You would not be expected to show ALL of these steps!!]
Bittinger Problems Page 71: #49, 51, 53, 55, 63, 67, 69, 70
49.
First, do what is above and below the fraction bar:
Now, below the fraction bar, you must do the exponents first!
1
51.
Multiply the numbers first.
You know
that
26
53.
Above and below the fraction bar, do the exponents first!
Next, do the multiplication in the denominator.
Now, do the numerator and denominator from left to right.
2
55.
Above and below the fraction bar, do the exponents first!
Next, do the multiplication in the numerator and division in denominator.
Now, do the subtractions.
63.
Note: While there are probably easier ways to do this, this method uses only the use of order of operations explained in this section, beginning with “Plug it in, plug it in!” Of course, other methods are also entirely acceptable here!
Do the exponent first.
Divide out the 15 (or you can multiply the numbers out, and reduce the fraction that results).
67.
NOTE: I have always used the tradition of placing parentheses around a negative number! This tradition will never let you down, and it saves a lot of errors! So let’s get started with the other tradition: “PLUG IT IN!!”
Do the exponents first.
Next, multiply! Remember, a negative times a negative is a positive!
6
69.
Above and below the fraction bar, do the exponents first.
Multiply!
Subtract!
70.
Do inside the gold parentheses first.
Do the exponent next.
Multiply! Again, remember that a negative times a negative is a positive!
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