Answer:
[tex]\left(\left(\frac{27}{53}\right)-6\right)+\left(53\left(-\left(2^2\right)\right)\right)=-\frac{11527}{53}\quad \left(\mathrm{Decimal:\quad }\:-217.49056\dots \right)[/tex]
Step-by-step explanation:
Considering the expression
27 divided by 53 minus 6 plus 53 times -2 squared
Which can be written as
[tex]\left(\left(\frac{27}{53}\right)-6\right)+\left(53\cdot \left(-\left(2^2\right)\right)\right)[/tex]
So, solving the expression
[tex]\left(\left(\frac{27}{53}\right)-6\right)+\left(53\cdot \left(-\left(2^2\right)\right)\right)[/tex]
[tex]\mathrm{Remove\:parentheses}:\quad \left(a\right)=a[/tex]
[tex]=\frac{27}{53}-6-53\cdot \:2^2[/tex]
[tex]\mathrm{Convert\:element\:to\:fraction}:\quad \:6=\frac{6\cdot \:53}{53}[/tex]
[tex]=-\frac{6\cdot \:53}{53}+\frac{27}{53}[/tex]
[tex]\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex]
[tex]=\frac{-6\cdot \:53+27}{53}[/tex]
[tex]=\frac{-291}{53}[/tex] ∵ [tex]-6\cdot \:53+27=-291[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}[/tex]
[tex]=-2^2\cdot \:53-\frac{291}{53}[/tex]
[tex]=-212-\frac{291}{53}[/tex] ∵ [tex]53\cdot \:2^2=212[/tex]
[tex]\mathrm{Convert\:element\:to\:fraction}:\quad \:212=\frac{212\cdot \:53}{53}[/tex]
[tex]=-\frac{212\cdot \:53}{53}-\frac{291}{53}[/tex]
[tex]\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex]
[tex]=\frac{-212\cdot \:53-291}{53}[/tex]
[tex]=\frac{-11527}{53}[/tex] ∵ [tex]-212\cdot \:53-291=-11527[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}[/tex]
[tex]=-\frac{11527}{53}[/tex]
Therefore,
[tex]\left(\left(\frac{27}{53}\right)-6\right)+\left(53\left(-\left(2^2\right)\right)\right)=-\frac{11527}{53}\quad \left(\mathrm{Decimal:\quad }\:-217.49056\dots \right)[/tex]
Keywords: algebraic expression
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