My son was doing a math problem and getting the wrong result, so he asked me to help out. The problem was:
$4.5-8.2 = x$, solve for $x$
He was getting $-4.3$, where the correct answer is of course $-3.7$.
It turns out the reason he got the answer wrong is because he was doing the subtraction directly, and when he subtracted $.2$ from $.5$ he got $.3$. I showed him that he could multiply both sides by $-1$ and solve for $-x$, negate the answer and thus get the right result. Being the curious kid that he is, he asked why the two results weren't the same, and I couldn't give him an answer.
Why doesn't the direct subtraction work?
Best Answer
That's because the two results are the same, and he is implicitly using a slightly different and context-dependent notation to express his answer.
The arithmetic is correct, but $-4$ is not a decimal digit in the usual scheme of things.
A correct answer of $(-4).3$ was found, with an intended meaning of $-4 +0.3$. That notation is non-standard, and writing it as $-4.3$ gives the wrong answer when read as a standard decimal.
Although it's clear what an expression like $(-4).3$ should mean here, to represent that result in the standard system with digits 0-9, the minus sign can only apply to all digits in the number at once. The conversion to standard notation is $("-4").3 = -(3.7) = -3.7 $