Lösung 1.1:2d

If we try and analyse the way the expression is constructed we see it is essentially a difference of two sub-expressions,

which can be calculated independently and then subtracted.

Examining the sub-expressions,the first is a product and the second a division

We thus can begin by calculating the numerator \displaystyle (4+6) in the second sub-expression

\displaystyle 3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{(4+6)}/(-5) = 3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{\,10\,}/(-5)

and then move over to the first sub-expression and do the multiplication

\displaystyle \phantom{3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{(4+6)}/(-5)}{} = \firstcbox{#FFEEAA;}{\,3\cdot(-7)\,}{-21}-10/(-5)

\displaystyle \phantom{3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{(4+6)}/(-5)}{} = \secondcbox{#FFEEAA;}{\,3\cdot(-7)\,}{-21}-10/(-5)

and return to the division in the second sub-expression

\displaystyle \phantom{3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{(4+6)}/(-5)}{} = -21-\firstcbox{#FFEEAA;}{\,10/(-5)\,}{(-2)}

\displaystyle \phantom{3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{(4+6)}/(-5)}{} = -21-\secondcbox{#FFEEAA;}{\,10/(-5)\,}{(-2)}.

Finally we have an expression that can be calculated directly

\displaystyle \phantom{3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{(4+6)}/(-5)}{} = -21-(-2)

\displaystyle \phantom{3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{(4+6)}/(-5)}{} = -21+2

\displaystyle \phantom{3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{(4+6)}/(-5)}{} = -19.