# The Mediant

The mediant is the name for the answer you get by adding fractions incorrectly (‘the freshman dream’).

@berryprof wrote a great article on this in the Math Teacher.

http://www.nctm.org/Publications/Mathematics-Teacher/2016/Vol110/Issue1/Mediants-Make-(Number)-Sense-of-Fraction-Foibles/

You can also google for it. I encourage you to look at the MT article or google.

The mediant () can be thought of as the new batting average at the end of the day (in baseball). The mediant is always in between the original fractions.

For example,

• You start the day with a batting average of .375, because you are 15 for 40 (15 hits in 40 at-bats).
• You play a game. In the game you are 3 for 5 (3 hits in 5 AB’s). For the day your batting average is .600.
• At the end of the day your batting average is .400 (18 for 45).
• Notice that .400 is between .375 and .600.

One more example,

• You start the day with a batting average of .240.
• You play a game and go 1 for 3.
• Since 1/3 is .333 which is higher than .240, you know that your batting average will go up.

(This is all rather obvious for those with good number sense. It’s the way numbers work!)

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