Final answer:
To determine the number of banners Scott can make with 10 1/2 yards of fabric, when each banner requires 1 3/4 yards, convert the mixed numbers to improper fractions, divide the total fabric length by the amount needed per banner, and simplify the fraction to find that Scott can make 6 banners.
Step-by-step explanation:
The student's question pertains to finding out how many banners Scott can make with a given amount of fabric. He has 10 1/2 yards of fabric to make banners for the community fair and needs 1 3/4 yards for each banner. To find out the number of banners Scott can make, we need to divide the total fabric length by the fabric required for each banner:
- Convert mixed numbers to improper fractions: 10 1/2 yards becomes 21/2 yards and 1 3/4 yards becomes 7/4 yards.
- Divide the total yardage by the yardage required per banner: (21/2) / (7/4).
- Simplify the division by multiplying by the reciprocal of the divisor: (21/2) * (4/7) which equals 84/14.
- Now, simplify the fraction: 84/14 reduces to 6.
Scott can make 6 banners from the fabric he has for the community fair.