Solution 1.1:2d

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Om vi försöker analysera hur uttrycket är uppbyggt så består det i sin mest övergripande form av en differens mellan två deluttryck
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If we try and analyse the way the expression is constructed we see it is essentially a difference of two sub-expressions,
<center><math>\bbox[#FFEEAA;,1.5pt]{\,3\cdot(-7)\,}-\bbox[#FFEEAA;,1.5pt]{\,(4+6)/(-5)\,}</math></center>
<center><math>\bbox[#FFEEAA;,1.5pt]{\,3\cdot(-7)\,}-\bbox[#FFEEAA;,1.5pt]{\,(4+6)/(-5)\,}</math></center>
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som kan räknas ut oberoende av varandra och sedan subtraheras.
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which can be calculated independently and then subtracted.
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Går vi in på deluttrycken så består den första termen av en produkt och den andra av en division
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Examining the sub-expressions,the first is a product and the second a division
<center><math>\bbox[#FFEEAA;,1.5pt]{\,3\vphantom{)}\,}\cdot\bbox[#FFEEAA;,1.5pt]{\,(-7)\,} - \bbox[#FFEEAA;,1.5pt]{\,(4+6)\,}/\bbox[#FFEEAA;,1.5pt]{\,(-5)\,}</math>.</center>
<center><math>\bbox[#FFEEAA;,1.5pt]{\,3\vphantom{)}\,}\cdot\bbox[#FFEEAA;,1.5pt]{\,(-7)\,} - \bbox[#FFEEAA;,1.5pt]{\,(4+6)\,}/\bbox[#FFEEAA;,1.5pt]{\,(-5)\,}</math>.</center>
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Vi kan därför exempelvis börja med att räkna ut täljaren <math>(4+6)</math> i det andra deluttrycket
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We thus can begin by calculating the numerator <math>(4+6)</math> in the second sub-expression
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::<math>3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{(4+6)}/(-5) = 3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{\,10\,}/(-5)</math>.
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::<math>3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{(4+6)}/(-5) = 3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{\,10\,}/(-5)</math>
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Sedan kan vi hoppa över till det första deluttrycket och räkna ut multiplikationen
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and then move over to the first sub-expression and do the multiplication
::<math>\phantom{3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{(4+6)}/(-5)}{} = \firstcbox{#FFEEAA;}{\,3\cdot(-7)\,}{-21}-10/(-5)</math>
::<math>\phantom{3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{(4+6)}/(-5)}{} = \firstcbox{#FFEEAA;}{\,3\cdot(-7)\,}{-21}-10/(-5)</math>
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::<math>\phantom{3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{(4+6)}/(-5)}{} = \secondcbox{#FFEEAA;}{\,3\cdot(-7)\,}{-21}-10/(-5)</math>
::<math>\phantom{3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{(4+6)}/(-5)}{} = \secondcbox{#FFEEAA;}{\,3\cdot(-7)\,}{-21}-10/(-5)</math>
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och därefter återgå till divisionen i den andra termen
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and return to the division in the second sub-expression
::<math>\phantom{3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{(4+6)}/(-5)}{} = -21-\firstcbox{#FFEEAA;}{\,10/(-5)\,}{(-2)}</math>
::<math>\phantom{3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{(4+6)}/(-5)}{} = -21-\firstcbox{#FFEEAA;}{\,10/(-5)\,}{(-2)}</math>
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::<math>\phantom{3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{(4+6)}/(-5)}{} = -21-\secondcbox{#FFEEAA;}{\,10/(-5)\,}{(-2)}</math>.
::<math>\phantom{3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{(4+6)}/(-5)}{} = -21-\secondcbox{#FFEEAA;}{\,10/(-5)\,}{(-2)}</math>.
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Till slut har vi fått ett uttryck som kan beräknas direkt
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Finally we have an expression that can be calculated directly
::<math>\phantom{3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{(4+6)}/(-5)}{} = -21-(-2)</math>
::<math>\phantom{3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{(4+6)}/(-5)}{} = -21-(-2)</math>
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Current revision

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

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

which can be calculated independently and then subtracted.

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

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

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.
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