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Mathematical Mistakes

Though I am currently doing some history research, I thought it would be a nice idea to throw some mathematical myths out there for some people. There are plenty of myths or mistakes to go around, but a few of these should suffice. These reside in the algebra zone but apply elsewhere.

1. ax + b = a(x + b). An easy way to check this is to apply some values. a =2, x = 3 and b = 4. {2*3 +4 = 10} does not equal {2(3 + 4) = 14}.

2. a – (b + c) = a – b + c. Again, using a = 2, b = 3 and c = 4 you clearly see the mistake. {2-(3+4) = -10} does not equal {2 – 3 + 4 = 3}.

3.(a + b)^2 = a^2 + b^2. Apply the numbers and you see these do not equal.

4. (a – b)^2 = a^2 – b^2.

5. (a – b)/(c + b) = a/c

6. a(b + c)/(b + a) = (ac)/a = c

7. a/(b+c) = a/b + a/c I’ve seen my oldest make this mistake many times.

8. (ax + b)/(ac) = (x + b)/c

9. (a^x)(a^y) = a^(xy) Keep in mind ‘^’ means raised to the power.

10. a^(x+y) = a^x = a^y

These are but ten of the common mistakes students make. The easiest to double check yourself is to apply values to the variables and do the calculation.

  1. October 17, 2014 at 7:21 am

    It’s good using a couple quick tests to verify that some algebraic relationship is a mistake. There is the potential danger of happening to try a couple numbers which work, which would be a fluke but likely if you go looking in nice easy numbers.

    I wonder if there’s a simple-to-remember, simple-to-calculate set of choices for a, b, c, x, and y that would break every one of these errors.

    • October 17, 2014 at 11:05 am

      I don’t know. Seldom do I need to do these checks myself, so I never investigated it further than a test or two.

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