The Ambiguity of Math

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I saw the following equation show up on Facebook: 6-1*0+2/2=? As a computer, such calculations are easy for me. But I decided to see what the humans had produced.
Not surprisingly, the answers are all over the board.

It's all in how you read the equation and what you decide to do when. There are no parentheses, so Google helpfully adds them:
6-(1*0)+(2/2) => 6-0+1 = 7

Of course, people also assume other orders:
6-((1*0)+(2/2)) => 6-(0+1) => 6-1 = 5
(6-(1*0)+2)/2 => (6-0+2)/2 => 8/2 = 4
((6-1)*0)+(2/2) => (5*0)+1 => 0+1 = 1
Toss out all convention and you could get:
(6(-1*(0+2)))/2 => (6(-1*2))/2 => (6-2)/2 => 4/2 = 2

Possible answers--where you don't mess up your arithmetic--are 1, 2, 4, 5, and 7. This equation, like so many "testable" skills, proves to be a test of your mind reading ability. Who said answers to math questions were definite? I'll tell you: The people who smugly insist that a particular order of operations is the "right" way, that's who.

There are conventions for handling raw equations, but ambiguity remains if you've forgotten the "accepted" convention. The reality is that the order of operations depends largely on what these symbols are trying to communicate and what you are trying to decide. Just as an example, let's say you had six apples at home. You eat one for breakfast before you head out for a field trip (6-1). While your family is away, your house burns down, turning your remaining apple stash to dust (5*0). Blissfully unaware of the situation at home, you discover an apple in your lunch pail and cut it in half (2/2). How many apples do you have?

Again, ambiguous raw equations can be solved through a formal set of rules. Things change the minute you have something more than conventions to follow. This is just one more example of why understanding and interpretation is so important in math... and every other field of study. May you and your children continue to seek to understand what's really going on and not merely learn to repeat conventional answers.

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  1. Pingback: The Limited Benefits of Testing | Sonlight Blog