Multiply Sum by Difference then Divide

Keywords: Starter | Mental Methods

• 7 Mandelbrot, Admiral Lord Nelson School
• Friday, October 26, 2007
• "When calculating difference the order is usually taken as important so some of the answers should be negative. Or are we mistaken?"
• Laura, Minnesota
• Saturday, October 27, 2007
• "I think this is a good way to get your students to do mental math, however if I were to use this with students who knew about negative numbers it wouldn't work. With the order the numbers are set up in 4 of the answers should have actually been the negatives of what the 'correct' answer on the site gives."
• Transum,
• Saturday, October 27, 2007
• "Thanks so much for your comments. I think we have an ambiguous situation here. Should the difference between two numbers always be positive? This topic was discussed on the Math Forum - Ask Dr. Math. In support of this idea is the following:
  

  In any real situation I can think of, if you were to ask someone for the difference between, say, 3 and 5, the answer would be 2 not -2! We tend to think of differences as positive numbers, and thus the proper rendition of that expression algebraically would be |3-5| (or |5-3|). This is the same idea as the "distance" between two numbers on the number line, which is always positive.
  In textbooks, as you've observed, it seems common in 'word problems' to make a different convention, that 'the difference between a and b' means a - b.
  
  The full discussion can be seen here.

  Perhaps we'll wait for a few more comments on this page and then adapt this starter to conform with the opinions of the majority. In the meantime you'll see that all the pairs of numbers above have the largest first to take out the ambiguity.

  Thanks once again for your feedback 7 Mandelbrot and Laura."
• Don, Loughborough
• Saturday, October 24, 2009
• "I disagree with Mandlebrot and Laura. I think difference means the positive difference and not a rigid formula of the first number take away the second - in this regard it's disappointing that you've changed the starter (it looks as though you have). If you have students provide you with a negative answer then perhaps it will lead to an interesting discussion about word problems and the wording of questions, which they'll learn more from than just a correct answer."
• Y. Bonter, Cardinal Newman School
• Friday, March 11, 2011
• "Isnt the definition of the difference the highest number take away the lowest number."

 

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