I'm a sucker for those math problems that go around Facebook.

x = 6 \div 2(1 + 2) \\ x = \frac{6}{2(1 + 2)} \\ x = \frac{6}{2 + 4} \\ x = \frac{6}{6} \\ x = 1 \\ y = 6 \div 2(1 + 2) \\ y = \frac{6}{2(1 + 2)} \\ y = \frac{2 \cdot 3}{2(1 + 2)} \\ y = \frac{2 (1 + 2)}{2(1 + 2)} \\ y = 1

Added what appear to be the original form of the problem.

x = 6 \div 2(1 + 2) \\x = \frac{6}{2(1 + 2)} \\x = \frac{6}{2 + 4} \\x = \frac{6}{6} \\x = 1 \\y = 6 \div 2(1 + 2) \\y = \frac{6}{2(1 + 2)} \\y = \frac{2 \cdot 3}{2(1 + 2)} \\y = \frac{2 (1 + 2)}{2(1 + 2)} \\y = 1 \\z = 6/2 \space \space (1 + 2) \\z = \frac{6}{2}(1 + 2) \\z = \frac{\tfrac{6}{2}}{\tfrac{12}{4}} \\z = \frac{3}{3} \\z = 1

The internet claims that the correct answer is actually 9. In this situation it's one of the reasons I hate the "division" operator when writing things out mathematically. Algebra uses the fractional notation for a reason: It's unambiguous.

Interestingly the form it was presented in best translates to way a line in a program might write it. It's a bit funny to me that I see the algebraic translation first before I see the pure programmatical version.

x = 6 \div 2(1 + 2) \\x = 6 \div 2 \cdot (1 + 2) \\x = \frac{6}{2} \cdot (1 + 2) \\x = 3 \cdot (1 + 2) \\x = 3 \cdot 3 \\x = 9
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youtube.com/watch?v=URcUvFIUIh

This video claims that this is a "historical usage" that was deprecated in 1917. As a matter of historical fact I have no clue if this is true. I wasn't alive in 1917 though so I suspect this notation was alive and well up until at least 2001.

The example they give is pretty good and exactly explains how I think about it.

6 \div 2(1 + 2) \\x \div y(j + k) \\\frac{x}{y(j + k)} \Leftrightarrow x/(y(j+k))

@gnu_lorien Without watching the video, I suspect that what happened is some guy in 1917 pointed out the problem, but he wasn't the King of Math so people kept doing it. We come here in search of a place to express our thoughts outside of the direct control and surveillance of unaccountable, mega-corporations. There is no common theme that binds us other than these being the bonds we've chosen rather than those that have been chosen for us.