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\n" ); document.write( "A phrase like \"6 times less than\" is commonly used in everyday language; but in fact is is ALWAYS used incorrectly.
\n" ); document.write( "\"Product A is 3 times less expensive than product B.\"
\n" ); document.write( "\"My new laptop takes 5 times less time to do a job than my old one.\"
\n" ); document.write( "etc., etc. You hear it all the time.
\n" ); document.write( "But it makes no logical sense.
\n" ); document.write( "\"less than\" in a mathematical statement implies subtraction.
\n" ); document.write( "So, given a number, for example 10, \"6 times less than 10\" means 10, minus 6 times 10, which is 10-60 = -50.
\n" ); document.write( "In general, \"6 times less than\" a number n means n-6n = -5n.
\n" ); document.write( "Clearly in this problem we are talking about positive numbers, in fact positive integers. 6 times less than a positive integer is a negative integer; and a negative integer is not valid for the number of hockey cards Kristie has.
\n" ); document.write( "The only interpretation of the words \"Kristie has six times less hockey cards than her brother Mark\" that makes ANY sense is that she has one-sixth as many.
\n" ); document.write( "But grammatically, that is not what the words say.
\n" ); document.write( "The phrase \"n times less than' should NEVER be used.
\n" ); document.write( "Whenever you hear an advertisement for a product that uses the phrase, you can bet you are not hearing the true data.
\n" ); document.write( "And whenever you see a math problem that uses the phrase, you can throw it in the trash bin.
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