Answer:
[tex]-\frac{11}{2}[/tex] is the number which represents the expression [tex]-2+\left(\frac{-7}{2}\right)[/tex].
i.e.
[tex]-2+\left(\frac{-7}{2}\right)=-\frac{11}{2}[/tex]
Step-by-step explanation:
Given the expression
[tex]-2+\left(\frac{-7}{2}\right)[/tex]
[tex]\mathrm{Remove\:parentheses}:\quad \left(a\right)=a[/tex]
[tex]=-2+\frac{-7}{2}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}[/tex]
[tex]=-2-\frac{7}{2}[/tex]
[tex]\mathrm{Convert\:element\:to\:fraction}:\quad \:2=\frac{2\cdot \:2}{2}[/tex]
[tex]=-\frac{2\cdot \:2}{2}-\frac{7}{2}[/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{2\cdot \:2}{2}-\frac{7}{2}[/tex]
[tex]=\frac{-2\cdot \:2-7}{2}[/tex]
[tex]=\frac{-11}{2}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}[/tex]
[tex]=-\frac{11}{2}[/tex]
Therefore, [tex]-\frac{11}{2}[/tex] is the number which represents the expression [tex]-2+\left(\frac{-7}{2}\right)[/tex].
i.e.
[tex]-2+\left(\frac{-7}{2}\right)=-\frac{11}{2}[/tex]
