Step-by-step explanation:
The feet long that the board is
[tex] = 6 \frac{1}{2} \\ [/tex]
The piece of board cut off
[tex] = 1 \frac{3}{4} + 2 \frac{2}{3} \\ [/tex]
[tex] = \frac{1 \times 4 + 3}{4} + \frac{2 \times 3 + 2}{3} \\ [/tex]
[tex] = \frac{7}{4} + \frac{8}{3} \\ [/tex]
[tex] = \frac{7}{4} \times \frac{3}{3} + \frac{8}{3} \times \frac{4}{4} \\ [/tex]
[tex] = \frac{21}{12} + \frac{32}{12} \\ [/tex]
[tex] = \frac{53}{12} \\ [/tex]
The original board left
[tex] = 6 \frac{1}{2} - \frac{53}{12} \\ [/tex]
[tex] = \frac{13}{2} - \frac{53}{12} \\ [/tex]
[tex]= \frac{13}{2} \times \frac{6}{6} - \frac{53}{12} \times \frac{1}{1} \\ [/tex]
[tex] = \frac{78 - 53}{12} \\ [/tex]
[tex] = \frac{25}{12} \\ [/tex]
[tex] = 2 \frac{1}{12} \\ [/tex]
hope it helped !!!
