Tuesday, March 11, 2008

Tricky Math?

Here's some weird math you'll see in Norway. A sale on vegetables, prices ÷ 40%. Another gigantic sale with prices ÷20 to ÷80. And some more sale items, prices ÷ 50%. Divided by 50 percent???


What would dividing by 50% do to a price? Dividing by 50% is the same as dividing by 1/2, which is not the same as dividing by 2! Dividing by 1/2 is the same as doubling, so for example $100 ÷ 50% = $200!* (For fun, find $100 ÷ 40%.)

I was surprised to see this 'mistake' in so many places. Then came the aha! moment. The answer is not a misunderstanding of fraction operations – although dividing by fractions is certainly tricky. There difference is that the symbol "÷" doesn't mean "divided by" in Norway, it means "minus." The vegetable prices are "minus 40%" not "divided by 40%." Norwegians use a colon or slash for division, so 12:3=4 and12/3=4, but 12÷3=9.

Mystery solved!




* Quick fraction lesson... why does dividing by 1/2 result in doubling a quantity?

Consider 12 divided by 2. This can mean two things:

  • 12 is 2 sets. How big is 1 set? (1 set is 6 items, so 12/2 = 6)
  • 12 is divided into sets of 2. How many sets? (There are six 2s in 12, so 12/2 = 6)
Now compare with 12 divided by 1/2:
  • 12 is 1/2 of a set. How big is 1 set? (1 set is 24 items. 12/ (1/2) = 24.)
  • 12 is divided into groups of 1/2. How many sets? (There are 24 halves in 12, so 12/ (1/2) = 24).
Fun, yes? Homework: Determine 100 divided by 40%. Do it two different ways.

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