Answer:
See explanation
Step-by-step explanation:
An art teacher has [tex]47\frac{1}{3}[/tex] pounds of clay.
He wants to give each student in his class [tex]2\frac{1}{2}[/tex] pounds of clay.
To estimate how many student the teacher can give [tex]2\frac{1}{2}[/tex] pounds of clay, just divide the whole amount of clay by [tex]2\frac{1}{2}:[/tex]
[tex]47\dfrac{1}{3}=\dfrac{47\cdot 3+1}{3}=\dfrac{142}{3}\\ \\2\dfrac{1}{2}=\dfrac{2\cdot 2+1}{2}=\dfrac{5}{2}\\ \\47\dfrac{1}{3}:2\dfrac{1}{2}=\dfrac{142}{3}:\dfrac{5}{2}=\dfrac{142}{3}\cdot \dfrac{2}{5}=\dfrac{142\cdot 2}{3\cdot 5}=\dfrac{284}{15}\\ \\\dfrac{284}{15}=\dfrac{270+14}{15}=\dfrac{18\cdot 15+14}{15}=18\dfrac{14}{15}[/tex]
This means 18 students can get [tex]2\frac{1}{2}[/tex] pounds of clay. Thus, the teacher estimation is not the best estimate.
