Answer:
To find the new length of the string, we need to add the length of the existing string (9 3/4 feet) to the length of the additional piece of string (2.5 feet).
First, we need to convert the mixed number, 9 3/4 feet, to an improper fraction. The improper fraction equivalent of 9 3/4 is (4 * 9 + 3)/4 = 39/4.
Now, we can add the fractions: 39/4 + 2 1/2 = 39/4 + (2 * 2 + 1)/2 = 39/4 + 5/2.
To add these fractions, we need a common denominator. The least common multiple of 4 and 2 is 4, so we can rewrite 5/2 as 10/4.
Now, we can add the fractions: 39/4 + 10/4 = 49/4.
To convert the improper fraction back to a mixed number, we divide the numerator (49) by the denominator (4). The quotient is the whole number, and the remainder is the numerator of the fraction part.
49 ÷ 4 = 12 with a remainder of 1. So, the new length of the string is 12 1/4 feet.
Therefore, the correct answer is (A) 12 1/4 feet.
Explanation: