Solution 1.1:1a
From Förberedande kurs i matematik 1
(Difference between revisions)
(Ny sida: {{NAVCONTENT_START}} Eftersom det inte finns några parenteser eller multiplikationer/ divisioner så finns det inget deluttryck som vi måste räkna ut först, utan vi kan påbörja beräk...) |
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{{NAVCONTENT_START}} | {{NAVCONTENT_START}} | ||
- | + | Because there are no brackets nor multiplications/divisions there is no subexpression that needs to be calculated first, so we can start calculating the expression from left to right. First we perform the subtraction of the two leftmost numbers | |
:<math>\bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5=\bbox[#FFEEAA;,1.5pt]{\,-4\,}-4+6-5</math>. | :<math>\bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5=\bbox[#FFEEAA;,1.5pt]{\,-4\,}-4+6-5</math>. | ||
{{NAVCONTENT_STEP}} | {{NAVCONTENT_STEP}} | ||
- | + | The next step is to subtract the two new leftmost numbers | |
:<math>\phantom{\bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5}{}=\firstcbox{#FFEEAA;}{\,-4-4\,}{-8}+6-5</math> | :<math>\phantom{\bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5}{}=\firstcbox{#FFEEAA;}{\,-4-4\,}{-8}+6-5</math> | ||
{{NAVCONTENT_STEP}} | {{NAVCONTENT_STEP}} | ||
:<math>\phantom{\bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5}{}=\secondcbox{#FFEEAA;}{\,-4-4\,}{-8}+6-5</math> | :<math>\phantom{\bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5}{}=\secondcbox{#FFEEAA;}{\,-4-4\,}{-8}+6-5</math> | ||
{{NAVCONTENT_STEP}} | {{NAVCONTENT_STEP}} | ||
- | + | and we continue in the same way to work with the two left-most terms in the expression that arises | |
:<math>\phantom{\bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5}{}=\firstcbox{#FFEEAA;}{\,-8+6\,}{-2}-5</math> | :<math>\phantom{\bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5}{}=\firstcbox{#FFEEAA;}{\,-8+6\,}{-2}-5</math> | ||
{{NAVCONTENT_STEP}} | {{NAVCONTENT_STEP}} | ||
:<math>\phantom{\bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5}{}=\secondcbox{#FFEEAA;}{\,-8+6\,}{-2}-5</math>. | :<math>\phantom{\bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5}{}=\secondcbox{#FFEEAA;}{\,-8+6\,}{-2}-5</math>. | ||
{{NAVCONTENT_STEP}} | {{NAVCONTENT_STEP}} | ||
- | + | Finally we have an expression which we can calculate in one step | |
:<math>\phantom{\bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5}{}=-2-5</math> | :<math>\phantom{\bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5}{}=-2-5</math> | ||
{{NAVCONTENT_STEP}} | {{NAVCONTENT_STEP}} | ||
:<math>\phantom{\bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5}{}=-7</math>. | :<math>\phantom{\bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5}{}=-7</math>. | ||
- | {{NAVCONTENT_STEP}} | ||
- | Det går också att skriva hela uttrycket som en summa av positiva och negativa tal, | ||
- | |||
- | <center><math>3+(-7)+(-4)+6+(-5)</math></center> | ||
- | {{NAVCONTENT_STEP}} | ||
- | och addera ihop termerna i valfri ordning | ||
- | |||
- | :<math>\phantom{\bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5}{} = \firstcbox{#FFEEAA;}{\,3+(-7)\,}{(-4)}+(-4)+\firstcbox{#FFEEAA;}{\,6+(-5)\,}{1}</math> | ||
- | {{NAVCONTENT_STEP}} | ||
- | :<math>\phantom{\bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5}{} = \secondcbox{#FFEEAA;}{\,3+(-7)\,}{(-4)}+(-4)+\secondcbox{#FFEEAA;}{\,6+(-5)\,}{1}</math> | ||
- | {{NAVCONTENT_STEP}} | ||
- | :<math>\phantom{\bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5}{} = (-4)+\firstcbox{#FFEEAA;}{\,(-4)+1\,}{(-3)}</math> | ||
- | {{NAVCONTENT_STEP}} | ||
- | :<math>\phantom{\bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5}{} = (-4)+\secondcbox{#FFEEAA;}{\,(-4)+1\,}{(-3)}</math> | ||
- | {{NAVCONTENT_STEP}} | ||
- | :<math>\phantom{\bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5}{} = -7</math>. | ||
{{NAVCONTENT_STOP}} | {{NAVCONTENT_STOP}} |
Current revision
Because there are no brackets nor multiplications/divisions there is no subexpression that needs to be calculated first, so we can start calculating the expression from left to right. First we perform the subtraction of the two leftmost numbers
- \displaystyle \bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5=\bbox[#FFEEAA;,1.5pt]{\,-4\,}-4+6-5.
The next step is to subtract the two new leftmost numbers
- \displaystyle \phantom{\bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5}{}=\firstcbox{#FFEEAA;}{\,-4-4\,}{-8}+6-5
- \displaystyle \phantom{\bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5}{}=\secondcbox{#FFEEAA;}{\,-4-4\,}{-8}+6-5
and we continue in the same way to work with the two left-most terms in the expression that arises
- \displaystyle \phantom{\bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5}{}=\firstcbox{#FFEEAA;}{\,-8+6\,}{-2}-5
- \displaystyle \phantom{\bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5}{}=\secondcbox{#FFEEAA;}{\,-8+6\,}{-2}-5.
Finally we have an expression which we can calculate in one step
- \displaystyle \phantom{\bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5}{}=-2-5
- \displaystyle \phantom{\bbox[#FFEEAA;,1.5pt]{\,3-7\,}-4+6-5}{}=-7.