Final answer:
After subtracting the 4 1/4 yards for Clutch's own shirt from the total 65 yards purchased, we are left with 60 3/4 yards of fabric, from which Clutch can make 27 fan shirts, with each shirt requiring 2 1/4 yards of fabric.
Step-by-step explanation:
The question is concerned with determining the number of fan shirts that can be made from a specified amount of fabric. Clutch initially bought 65 yards of fabric but wants to use 4 1/4 yards for his own shirt. To find out how much fabric will be left for the fan shirts, we subtract 4 1/4 yards from 65 yards:
65 yards - 4 1/4 yards = 60 3/4 yards remaining
Each fan shirt requires 2 1/4 yards of fabric. To find out how many fan shirts can be made, we divide the remaining fabric by the amount needed per shirt:
60 3/4 yards ÷ 2 1/4 yards per shirt
Firstly, we convert the mixed fractions to improper fractions:
60 3/4 yards = 243/4 yards
2 1/4 yards = 9/4 yards
Now we divide the two improper fractions:
(243/4) ÷ (9/4) = 243/4 × 4/9 = 27 shirts
Clutch can make 27 fan shirts from the remaining fabric.