Answer:
Fraction of the original board left = [tex]\frac{2}{15}[/tex]
Step-by-step explanation:
Let the length of the board is = l feet
Marty saws off [tex]\frac{1}{5}[/tex] of a wooden board.
Length of the board left = l - [tex](\frac{1}{5})l[/tex]
= [tex](\frac{4}{5})l[/tex] feet
He saws off [tex]\frac{3}{4}th[/tex] of the remaining board,
Board left = [tex](\frac{4}{5})l-[(\frac{4}{5})l\times (\frac{3}{4})][/tex]
= [tex]\frac{4}{5}l-\frac{3}{5}l[/tex]
= [tex]\frac{1}{5}l[/tex] feet
He finally saws off [tex]\frac{1}{3}[/tex]rd of the remaining board.
Board left = [tex]\frac{1}{5}l-[\frac{1}{5}\times \frac{1}{3}]l[/tex]
= [tex](\frac{1}{5}-\frac{1}{15})l[/tex]
= [tex]\frac{2}{15}l[/tex] feet
Fraction of the original board left = [tex]\frac{\frac{2}{15}l}{l}[/tex]
= [tex]\frac{2}{15}[/tex]
