Final answer:
Shannon needs a total of 5 1/4 yards of fabric for her project, which is the sum of 2 2/5 yards for a bedspread and 2 7/8 yards for curtains after converting to a common denominator and adding the fractions.
Step-by-step explanation:
To determine the total amount of fabric Shannon needs for her project, you need to add the lengths of fabric required for the bedspread and the curtains together. For the bedspread, Shannon needs 2 2/5 yards of fabric. To add fractions, you need common denominators. The fraction 2/5 has a denominator of 5, and 7/8 has a denominator of 8. The least common denominator for 5 and 8 is 40.
First, convert the mixed numbers to improper fractions. For 2 2/5 yards, multiply the whole number 2 by the denominator 5 and add the numerator 2, giving you 10 + 2 = 12. So, 2 2/5 yards is 12/5. For 2 7/8 yards, it's 2 × 8 + 7 = 23/8.
Next, convert both fractions to have the common denominator of 40. To convert 12/5, multiply both the numerator and the denominator by 8 to get 96/40. For 23/8, multiply both by 5 to get 115/40.
Now, add the two fractions: 96/40 + 115/40 = 211/40. Convert this back to a mixed number by dividing 211 by 40, which gives 5 with a remainder of 11. Therefore, 211/40 is 5 11/40, but we need a denominator of 8, so we convert 11/40 to eighths, which is 22/80 or more simply 11/20. Now, we find a common denominator for 20 and 8, which is 40. We convert 11/20 to 22/40 which is also the equivalent of 2 2/8 or 2 1/4 when both numerator and denominator are divided by 2.
So the answer is 5 2 2/8 yards, simplified to 5 1/4 yards. Thus, the correct option is (a) 5 1/4 yards.