Explanation:
To solve this problem, we need to find the fraction of the project that Mariana can complete by dividing the total length of border she has by the total length of border needed.
The total length of border needed is 6 3/4 feet.
To add feet and fractions, we need to convert the whole number 6 to a fraction with the same denominator as 4.
6 = 6/1
So, 6 3/4 can be written as (6/1) + 3/4 = 24/4 + 3/4 = 27/4.
Therefore, the total length of border needed is 27/4 feet.
Now, we can find the fraction of the project Mariana can complete by dividing the total length of the border she has (3 6/7 feet) by the total length of border needed (27/4 feet).
Let's convert 3 6/7 to an improper fraction.
3 6/7 = (3 * 7 + 6)/7 = 21/7 + 6/7 = 27/7.
So, Mariana has 27/7 feet of border.
Now, divide 27/7 by 27/4.
(27/7) / (27/4) = (27/7) * (4/27) = (27 * 4) / (7 * 27) = 108/189.
Therefore, Mariana can complete 108/189 of the project.
But, we can simplify this fraction.
Both 108 and 189 are divisible by 9. We can divide both the numerator and denominator by 9.
108/189 = (108/9)/(189/9) = 12/21.
Finally, the simplified fraction representing the fraction of the project Mariana can complete is 12/21.
Thus, Mariana can complete 12/21 of the project.