Solution 1.1:2d
From Förberedande kurs i matematik 1
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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> [[ | + | which can be calculated independently and then subtracted. |
- | + | {{NAVCONTENT_STEP}} | |
+ | 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> | ||
+ | {{NAVCONTENT_STEP}} | ||
+ | We thus can begin by calculating the numerator <math>(4+6)</math> in the second sub-expression | ||
+ | ::<math>3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{(4+6)}/(-5) = 3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{\,10\,}/(-5)</math> | ||
+ | {{NAVCONTENT_STEP}} | ||
+ | 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> | ||
+ | {{NAVCONTENT_STEP}} | ||
+ | ::<math>\phantom{3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{(4+6)}/(-5)}{} = \secondcbox{#FFEEAA;}{\,3\cdot(-7)\,}{-21}-10/(-5)</math> | ||
+ | {{NAVCONTENT_STEP}} | ||
+ | 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> | ||
+ | {{NAVCONTENT_STEP}} | ||
+ | ::<math>\phantom{3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{(4+6)}/(-5)}{} = -21-\secondcbox{#FFEEAA;}{\,10/(-5)\,}{(-2)}</math>. | ||
+ | {{NAVCONTENT_STEP}} | ||
+ | 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> | ||
+ | {{NAVCONTENT_STEP}} | ||
+ | ::<math>\phantom{3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{(4+6)}/(-5)}{} = -21+2</math> | ||
+ | {{NAVCONTENT_STEP}} | ||
+ | ::<math>\phantom{3\cdot(-7)-\bbox[#FFEEAA;,1.5pt]{(4+6)}/(-5)}{} = -19</math>. | ||
{{NAVCONTENT_STOP}} | {{NAVCONTENT_STOP}} | ||
+ | <!--<center> [[Image:1_1_2d.gif]] </center>--> |
Current revision
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.