Why doesnt 2=1? ; algebraic proof?

Question

statement: Reason:

a=b given

a+a=b+a additiona property of equality

2a=b+a like terms

2a-2b=a+b-2b addition property of eqaulity

2a-2b=a-b like terms

2(a-b)=a-b distributive property

2(a-b)/a-b=a-b/a-b multiplication property of equality

2=1

My teacher played this trick on us. what am i missing?

Answer 1

2(a-b)/a-b=a-b/a-b multiplication property of equality

if a=b then you are dividing by zero in the above statement,  which is an illegal math property

Answer 2

you can't divide by 0.

Notice a = b, therefore a-b is 0.

Answer 3

a-b/a-b cancels out = 0

2(a-b)/a-b cancels 1 a-b  so = a-b

there for a-b = 0

a=b

were back at the beginning.

cancel all common variables before you substitute and compute.

Answer 4

2(a-b)=a-b

until here every thing is perfect

but if a=b as you said then a-b =0

so you don't have the possibility to  divide by 0

good luck

Answer 5

This is an oldie.

Since a=b, then dividing by (a-b) is dividing my zero.  You can't divide by 0 in mathematics, because it leads to contradictions like this.

2(a-b) = (a-b) is only true because 2*0 = 1*0 is true.  But that doesn't mean you can divide both sides by 0 and get 2 = 1.

Answer 6

Nothing. Its looks good.

Answer 7

I remember this one! can't divide by 0 mate : )

Answer 8

The issue comes from the fact that a=b.  This means that a-b=0.  This means that we cannot do the division by (a-b) in the second last line, as the reciprocal of 0 is undefined.

Answer 9

You are dividing by 0 and that's verbotten!

a-b = 0 and at the end you divide by that.

Answer 10

You can not do the last equation.

If a is 2 and b is 2 you get 2(2-2)/2-2   -- the denominator is zero, question is void