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Answer :
Ben built a total of 13(5)/(8) ft of railing.
To find the total length of the railing, we need to add the initial length of 10(3)/(4) ft and the additional length of 2(1)/(8) ft.
Starting with the initial length, 10(3)/(4) ft can be converted to an improper fraction as (40+3)/(4) ft, which simplifies to 43/4 ft.
Similarly, the additional length of 2(1)/(8) ft can be converted to an improper fraction as (16+1)/(8) ft, which simplifies to 17/8 ft.
Now, to find the total length, we add the two fractions together:
[tex]43/4 ft + 17/8 ft = (43*2 + 17)/8 ft = 103/8 ft.[/tex]
To convert the fraction to a mixed number, we divide the numerator (103) by the denominator (8) and get a quotient of 12 with a remainder of 7. So the total length of the railing is 12(7)/(8) ft, which can also be written as 13(5)/(8) ft.
In conclusion, Ben built a total of 13(5)/(8) ft of railing.
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