Efficiency of Different Representations
Lesson
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The simplest or easiest way to solve a problem

 

There are many ways to come up with the correct solution to a problem, however coming up with the solution in the most efficient (most effective, fewest steps) way  will cut down on careless mistakes.

 It is important to solve a problem in a way you're most comfortable with. If you prefer adding to multiplying then add, or subtracting to dividing, then subtract however, some operations are not interchangeable so let's be careful of that.

Examples: Find the perimeter of a square that has a side measuring 6 inches.
1st way: Add all 4 sides 6+6+6+6= 24inches
2nd way: Take the length of the side and multiply it by 4. 6x4=24inches
 
3rd way: Take the length x2 and add it to the width x2. (2xl)+(2xw).  (6x2)+(6x2)=24inches
 

The 2nd way is probably the most efficient way of solving this problem. However the important thing is getting the correct solution to the problem.

 

Examples: Solve 3/4 + 5/12 =
1st way: Change 3/4 to 9/12, Then solve 9/12 + 5/12 = 14/12. Next reduce fraction 14/12 to 7/6. Finally change the improper fraction to the mixed number 1 1/6.
2nd way: Change 3/4 to 36/48 and 5/12 to 20/48. Then solve 36/48 + 20/48 = 56/48. Next change the improper fraction to mixed number 1 8/48. Finally reduce the fraction to  1 1/6.
 
3rd way: Change 3/4 to 18/24 and 5/12 to 10/24. Then solve 18/24 + 10/24 = 28/24. Next change the improper fraction to mixed number 1 4/24.  Reduce the fraction 1 4/24 to 1 2/12. Finally reduce 1 2/12 to 1 1/6.
 

The 1st way is probably the most efficient way of solving this problem. However the important thing is getting the correct solution to the problem.

 

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Created by John Rice
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