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A board is 6 1/2 feet long. You cut off a 1 3/4-foot piece and a 2 2/3 foot piece. How much of the original board is left?

A Board Is 6 12 Feet Long You Cut Off A 1 34foot Piece And A 2 23 Foot Piece How Much Of The Original Board Is Left class=

Sagot :

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 !!!

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