Future Design MCTB 4.3, User Manual

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MCTB
69
Parentheses First
4 x (5 + 3)
– (4 / 2)
(5 + 3) = 8 and (4 / 2) = 2 are evaluated first
4 x 8
– 2
4 x 8 = 32 is evaluated first since multiplication before addition
32
– 2
subtraction performed last to get result of 30
Else Multiply or Divide before Add or Subtract
4 x 5 + 3
– 4 / 2
4 x 5 = 20 and 4 / 2 = 2 are evaluated first
20 + 3
– 2
addition and subtraction performed last to get result of 21
With the introduction of exponents in the 16th and 17th centuries, they were given precedence over both
addition and multiplication and could be placed only as a superscript to the right of their base. For example, 3
+ 5
2
= 28 and 3 × 5
2
= 75. The MCTB does not provide the exponent operator; however, it can be accomplished
by multiplying the number by itself the same number of times as the value of the exponent, i.e., 5
2
= 5 x 5 = 25.
If you require a value raised to a power, you must multiply the value by itself in the equation remembering to
ensure proper order of operation using parenthesis. If you do not use parenthesis to prioritize the operation,
you will not get the desired result.
Exponent
Example: 75 / 5
2
Correct:
75 / (5 * 5) (5 * 5) = 25 evaluated first since it is in parenthesis
75 / 25 division performed last to get proper result of 3
Incorrect: 75 / 5 * 5 75 / 5 = 15 evaluated first since multiply/divide performed from left to right
15 * 5
multiplication performed last results in incorrect value of 75
In order to calculate the average of several values, you simply add each of the variables together, and then
divide by the number of variables. Again, the parenthesis are required in order for the calculation to be proper
evaluated.
Averaging Example:
Average monitor points 1 to 4 where Mon1=72, Mon2=74, Mon3=78 and Mon4=77.
Correct entry: (Mon1 + Mon2 + Mon3 + Mon4) / 4
(72 + 74 + 78 + 77) / 4 = 75.25
Incorrect entry: Mon1 + Mon2 + Mon3 + Mon4 / 4
72 + 74 + 78 + (77 / 4) = 243.25
Without the parenthesis, the equation would incorrectly divide the process value of monitor point 4 by 4 and
then add that to the sum total of monitor points 1, 2 and 3. By utilizing the parenthesis, the sum total of all
monitor points will be determined first, and that value will then be divided by 4 to get the proper average of all
four points.