A store has 7 3/8 yd on one roll of fabric, and 10 3/4 yd on another roll. The store sells 4 pieces of fabric. Each piece sold is 4 5/8 yards long. How many yards of the fabric is left after the sale?

Question

This deals with fundamentals of fractions, up to and including borrowing.

Answer 1

To solve this problem, we will change all the mixed numbers into improper fractions with the same denominator. The first roll of fabric has 7 3/8 yd, which is equal to 7 + 3/8 = (7*8)/8 + 3/8 = 56/8 + 3/8 = 59/8. The second roll of fabric has 10 3/4 yd, which is equal to 10 + 3/4 = (10*8)/8 + (3*2)/8 = 80/8 + 6/8 = 86/8. Thus, the store has a total of 59/8 + 86/8 = 145/8 yd of fabric. Now each piece sold is 4 5/8 yd, which is equal to (4*8)/8 + 5/8 = 32/8 + 5/8 = 37/8 yd. Since we sell 4, we need to do 4 * 37/8 = (4*37)/8 = 148/8. But, the store only has 145/8yd of fabric. Thus, the store cannot sell that much fabric and needs an extra 3/8 yd (or if they sell if they will have -3/8yd).

Answer 2

Using the fundamentals for fractions, including borrowing, we can determine the answer to the problem in the following manner.

1) Since we have two separate rolls, let's begin with the first, smaller roll that has 7 3/8 yds of fabric.

1. Because each piece sold is 4 5/8 yds long, let's subtract that from the first roll.
2. 7 3/8 - 4 5/8 requires borrowing 1 from the whole number in the first mixed number so we can subtract the fractional parts. So, 7 3/8 becomes 6 3/8 + 8/8 which equals 6 11/8
3. Therefore, we get 6 11/8 - 4 5/8 = 2 6/8 which equals 2 3/4 yds.
4. This smaller roll of fabric now only has 2 3/4 yds left so no other pieces can be cut from it that is 4 5/8 yds.

2) The second, larger roll has 10 3/4 yds which is equal to 10 6/8 (we make a common denominator so we can subtract).

1. If one piece is cut from this roll, we would subtract and get 10 6/8 - 4 5/8 = 6 1/8
2. If another piece is cut from this roll, we would subtract again and get 6 1/8 - 4 5/8
3. Borrowing is required once again in order to subtract so the first fraction becomes 5 1/8 + 8/8 which equals 5 9/8
4. Subtracting then gives us 5 9/8 - 4 5/8 = 1 4/8 or 1 1/2yds
5. Since we only have 1 1/2 yds left on the second roll, no more pieces 4 5/8 yds can be cut.

3) It is not possible for the store to have sold 4 pieces of fabric of 4 5/8 yds each with the initial, stated amount of fabric.

1. The first roll has 2 3/4 yds of fabric left
2. The second roll has 1 1/2 yds of fabric left
3. The store was only able to cut and sell 3 pieces of fabric 4 5/8 yds long from the given amount.

Answer 3

1. Calculate the total initial amount of fabric.
2. Calculate the total amount of fabric sold.
3. Subtract the total amount sold from the total initial amount.

Step 1: Total Initial Amount of Fabric

We start with two rolls of fabric:

1. One roll has 738783​ yards.
2. The other roll has 10341043​ yards.

First, we convert these mixed numbers to improper fractions: 738=7×8+38=56+38=598783​=87×8+3​=856+3​=859​1034=10×4+34=40+34=4341043​=410×4+3​=440+3​=443​

Next, we find a common denominator to add these fractions. The least common denominator of 8 and 4 is 8:434=43×24×2=868443​=4×243×2​=886​

Now we can add the two fractions: 598+868=59+868=1458859​+886​=859+86​=8145​

Convert the improper fraction back to a mixed number: 1458=18188145​=1881​

So, the total initial amount of fabric is 18181881​ yards.

Step 2: Total Amount of Fabric Sold

Each piece of fabric sold is 458485​ yards long, and the store sells 4 pieces.

Convert the mixed number to an improper fraction: 458=4×8+58=32+58=378485​=84×8+5​=832+5​=837​

Multiply this by 4 to find the total amount sold: 4×378=4×378=14884×837​=84×37​=8148​

Convert this improper fraction to a mixed number: 1488=1848=18128148​=1884​=1821​

So, the total amount of fabric sold is 18121821​ yards.

Step 3: Calculate the Remaining Fabric

Subtract the total amount sold from the total initial amount: 1818−18121881​−1821​

Convert both mixed numbers to improper fractions with a common denominator of 8: 1818=14581881​=8145​1812=1848=14881821​=1884​=8148​

Subtract the fractions: 1458−1488=145−1488=−388145​−8148​=8145−148​=8−3​

The result is a negative fraction, meaning more fabric was sold than initially available by 3883​ yards.