2 different solutions on 2 calculators

Question

I used Photomath and Microsoft Math to compute an equation, but they gave me two different results (-411 and -411/38) Why did that happen and which is the correct answer?

https://i.stack.imgur.com/egt5A.jpg https://i.stack.imgur.com/RIHb0.png

Answer 1

Note the first step in the second solution. It starts by multiplying both sides by 38.

Anyway, this is not a good way to do arithmetic. You are trying to find a solution that makes $\frac{411}{38}$ equal to $0$, which cannot be done.

Maybe you could try to solve $x = \frac{16}{19} - \frac{5 \times 81}{38} - 1$, which should give you the solution $x = -\frac{411}{38}$.

Or, depending on the calculator, just type in $\frac{16}{19} - \frac{5 \times 81}{38} - 1$ (without the $=0$). That should work.

Answer 2

Both calculators gave you the correct answer: false.

Answer 3

Neither attempt are trying to tell you what $\frac {16}{19} -\frac {5\times 81}{38} -1$ is. There are both trying to tell you why it is not equal to $0$. And the both giving you correct reasons why it isn't $0$.

Consider I asked Amy and Bill "Is $\frac 73 = 2$" and Amy said "No, if $\frac 73 = 2$ that would mean $7 = 2\times 3$ which would mean $7 = 6$ and that isn't true". But Bill said "No, if $\frac 73 = 2$ then $\frac 7{2\times 3} = 1$ and so $\frac 76 = 1$ annd that isn't true."

Are those two different answers? Or are they the same answer giving different but both correct arguments? Note, neither of them actually evaluated that $\frac 73 = 2\frac 13$ and $2\frac 13 \ne 2$.

If you want to evaluate $\frac {16}{19} -\frac {5\times 81}{38} -1=\frac {16\times 2}{19\times 2} -\frac {5\times 81}{38} -\frac {38}{38}$
$\frac {16\times 2 - 5*81 -38}{38} = \frac {32-405-38}{38} = -\frac {411}{38}$.

But you don't have to evaluate it just to find out that it isn't $0$.

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If it were me I'd argue

$\frac {16}{19} -\frac {5\times 81}{38} -1= 0 \iff$

$\frac {16}{19} -\frac {5\times 81}{38} = 1\iff$

$32 - 5*81 = 38\iff$

$32-38 = 5*81\iff$

$-6 = 5*81=405$

And as $405\ne -6$ then $\frac {16}{19} -\frac {5\times 81}{38} -1\ne 0$.