Name: chuck kennedy
Who is asking: Teacher
Level: Secondary

  1. Assume a=b
  2. Multiply both sides by a, a2=ab
  3. Subtract b2, a2-b2=ab-b2
  4. Factor (a-b)(a+b)=b(a-b)
  5. Cancel like factors a+b=b
  6. Substitue b for a b+b=b
  7. Then 2b=b
  8. Therefore 2=1
Question; Were is the mistake?

Please help!!A happy meal is riding on this one!!

Hi Chuck,

The error is in step 5. Cancel like factors.

You can only cancel like nonzero factors. You cannot cancel 0 * 2 = 1 * 0 to get 2 = 1.

One way to understand this type of fallacy is to try the procedure with numbers. Suppose a = b = 5 and proceed through the steps.

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