Find out the mistake in this :
Division by Zero
zero so don’t do it!
Here is a very good example of the kinds of havoc that can arise when you divide by zero. See if you can find the mistake that I made in the work below.
1. a = b We’ll start assuming this to be true.
2. ab = a ^2 Multiply both sides by a.
3. ab - b^2 = a^ 2 - b^2 Subtract b^2 from both sides.
4. b ( a - b) = ( a + b ) ( a - b )Factor both sides.
5. b = a + b Divide both sides by a - b .
6. b = 2b Recall we started off assuming a = b .
7. 1 = 2 Divide both sides by b.
So, we’ve managed to prove that 1 = 2! Now, we know that’s not true so clearly we
made a mistake somewhere. Can you see where the mistake was made?
The mistake was in step 5. Recall that we started out with the assumption a = b .
However, if this is true then we have a - b = 0 ! So, in step 5 we are really dividing by zero!
That simple mistake led us to something that we knew wasn’t true, however, in most
cases your answer will not obviously be wrong. It will not always be clear that you are dividing by zero, as was the case in this example. You need to be on the lookout for this kind of thing.
Remember that you CAN’T divide by zero!