Answer: 0
Step-by-step explanation:
Conversion of Mixed fraction to improper :
[tex]a\dfrac{b}{c}=\dfrac{a\timesc+b}{c}[/tex] , where a, b, c are integers and not equal to zero.
The given expression : [tex]3\dfrac{1}{4}+(-2\dfrac{2}{3})[/tex] ..(i)
Here , [tex]3\dfrac{1}{4}=\dfrac{3\times4+1}{4}=\dfrac{13}{4}[/tex] ..(ii)
[tex]-2\dfrac{2}{3}=-\dfrac{2\times3+2}{3}=-\dfrac{6+2}{3}=-\dfrac{8}{3}[/tex] ...(iii)
Now substitute (ii) and (iii) in (i) , we get
[tex]\dfrac{13}{4}-\dfrac{8}{3}=\dfrac{13\times3-8\times4}{4\times3}\\\\=\dfrac{39-34}{12}\\\\=\dfrac{7}{12}=0.583333333333\approx0 [\text{Nearest given option}][/tex]
Hence the best estimate for the give expression would be 0.
