Order of Operation Example TI84

JoeStat’s want you to calculate the following equation.

This is a complex standard deviation problem: s= frac{^{-}9sqrt{4+3^{2} cdot 10+6}}{15-(3+2) cdot 5}

Priority

Order of Operations

Highest Parenthesis Brackets
High Exponents Roots
Low Multiplication Division
Lowest Addition Subtraction

Hint:
Hint for dealing with fractions in order of operations s= frac{1+1+1}{9-3} = (1+1+1)/(9-3)

Hint for dealing with roots in order of operation problems: s= sqrt[4]{625} = 625^{(frac{1}{4})} = 625^{(4^{-1})}

Solving the equation using a (TI83, TI84, TI89) calculator:  First convert the equation into something easy to enter into the calculator.
Original:
This is a complex standard deviation problem: s= frac{^{-}9sqrt{4+3^{2} cdot 10+6}}{15-(3+2) cdot 5}

Step 1: Reformat fractions to one line
Order of Operations, first make everyhting on one line: s= (^{-}9sqrt{4+3^{2}cdot 10+6}) / (15-(3+2)cdot5)
Step 2: Reformat Radicals with parenthesis and brackets
Step 2 order of operatiosn s= (^{-}9sqrt{(}4+3^{2}cdot 10+6)) / (15-(3+2)cdot5)
Step 3: Entering the equation into the calculator

  • Entdering the first part into your calculator s(^{-}9
    | [ ( ] | [ (-) ] | [ 9 ] |
  • Using the TI-84 to assist in Order of Operation sqrt{(}4+3^{2})
    | [2nd] | [X^2] | [ 4 ] | [ + ] | [ 3 ] | [ ^ ] | [ 2 ] | [ ) ] |
  • /(15-(3+2) cdot5)
    | [  / ] | [ ( ] | [ 1 ] | [ 5 ] | [ - ] | [ ( ] | [ 3 ] | [ + ] | [ 2] | [ ) ] | [ * ] | [ 5 ] | [ ) ] |

Solution:
Order of Operation problem solved in the TI-84 or TI-83 calculator.

Solving the equation by hand:
This is a complex standard deviation problem: s= frac{^{-}9sqrt{4+3^{2} cdot 10+6}}{15-(3+2) cdot 5}

Step 1: If you have problems dealing with fractions, or have already input the solution to into a calculator reformat it to:
standard-deviation-help-1

Step 2:

  1. An alternative to dealing with the standard deviation is removing fractions s= (^{-}9sqrt{(}4+9cdot 10+6)) / (15-(3+2)cdot5)
  2. s= (^{-}9sqrt{(}4+90+6)) / (15-(3+2)cdot5)
  3. s= (^{-}9sqrt{100}) / (15-(3+2)cdot5)
  1.  If you have problems dealing with fractions, or have already input the solution to into a calculator reformat it to:
    s= (^{-}9sqrt{(}4+90+6)) / (15-(3+2)cdot5)
  2. Calculate the inner-most nested parenthesis
    s= (^{-}9sqrt{(}4+3^{2}cdot 10+6) / (15-(3+2)cdot5)
    s= (^{-}9sqrt{(}4+90+6) / (15-(3+2)cdot5)
    s= (^{-}9sqrt{100}) / (15-(3+2)cdot5)
  3. Calculate net inner-most nested parenthesis
    s= (^{-}9sqrt{100}) / (15-(3+2)cdot5)
    s= (^{-}9sqrt{100}) / (15-5cdot5)
  4. Calculate next inner-most nested parenthesis
    s= (^{-}9sqrt{100}) / (15-5cdot5)
    s= (^{-}9sqrt{100}) / (15-5cdot5)
    s= (^{-}90) / (15-5cdot5)
  5. Calculate next inner-most nexted parenthesis
    s= (^{-}90) / (15-25)
    s= (^{-}90) / (^-10)
  6. Finish the problem
    s= (^{-}90) / (^-10)
    s= frac{^{-}90}{^-10}
    Sample Standard Deviation Solution by hand
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Last Modified on September 7, 2013 by JoeStat

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