Question

Prove (100-100)÷(100-100) = 2​

Answer 1

(100-100)÷(100-100) = 2 is false.

(100-100)÷(100-100) = 0 ÷ 0(undefined)

since any no. divided by 0 is not defined.

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Answer 2

Given Data:

$(100-100)/(100-100)$

Step 1:

We have  

$(100-100)/(100-100)$

We can write 100 as $10^{2}$

So, $(100-100)=\left(10^{2}-10^{2}\right)$ in the numerator.

Step 2:

In the denominator, we can write  

100-100=$10 \times(10-10)$

So, that will make  

$\frac{100-100}{100-100}=\frac{10^{2}-10^{2}}{[10 \times(10-10)]}$

Step 3:

We know that $a^{2}-b^{2}$ can be written as (a+b) \times(a-b)  and I’m applying this rule to $(10^{2}-10^{2})$, neglecting the fact that both a and b are 10 here.

So, we get $\frac{10^{2}-10^{2}}{[10 \times(10-10)]}$ $=\frac{[(10+10) \times(10-10)]}{[10 \times(10-10)]}$

Step 4:

Cancelling 10–10 in the numerator and denominator.  

This is not actually possible in mathematics, but here we are not simplifying it to $\frac{0}{0}$

Now, we have  

$\frac{[(10+10) \times(10-10)]}{[10 \times(10-10)]}=\frac{10+10}{10}$

$=\frac{20}{10}$

$\frac{100-100}{100-100}=2$

Hence Proved.