Answer:
To determine how many more pieces of drippy fabric Brandon will have compared to upholstered fabric, we need to calculate the number of pieces each type of fabric can be cut into.
First, let's calculate the number of pieces Brandon can cut from the upholstered fabric.
- Brandon has 23 3/5 yards of upholstered fabric.
- He cuts the fabric into pieces that are 4 1/5 yards long.
- To find the number of pieces, we divide the total length of the fabric by the length of each piece: 23 3/5 ÷ 4 1/5.
- To simplify this division, we convert the mixed numbers to improper fractions: 23 3/5 = (5 * 23 + 3)/5 = 118/5 and 4 1/5 = (5 * 4 + 1)/5 = 21/5.
- Now we divide the fractions: (118/5) ÷ (21/5) = 118/5 * 5/21.
- Simplifying the fractions, we get: (118 * 5) / (5 * 21) = 590/105 = 118/21.
- So, Brandon can cut 118/21 pieces from the upholstered fabric.
Next, let's calculate the number of pieces Brandon can cut from the drippy fabric.
- Brandon has 18 1/2 yards of drippy fabric.
- He cuts the fabric into pieces that are 3 yards long.
- To find the number of pieces, we divide the total length of the fabric by the length of each piece: 18 1/2 ÷ 3.
- To simplify this division, we convert the mixed number to an improper fraction: 18 1/2 = (2 * 18 + 1)/2 = 37/2.
- Now we divide the fractions: (37/2) ÷ 3 = 37/2 * 1/3.
- Simplifying the fractions, we get: (37 * 1) / (2 * 3) = 37/6.
- So, Brandon can cut 37/6 pieces from the drippy fabric.
To find the difference in the number of pieces, we subtract the number of upholstered fabric pieces from the number of drippy fabric pieces:
(37/6) - (118/21) = (37 * 21 - 118 * 6) / (6 * 21) = (777 - 708) / 126 = 69/126.
Therefore, Brandon will have 69/126 more pieces of drippy fabric compared to upholstered fabric.
Explanation: