Madelyn bought 12 5/8 yards of fabric. She used 6 7/8 yards of the fabric for a costume. How much fabric did Madelyn have left?
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To find out how much fabric Madelyn has left, we need to subtract the amount of fabric she used for the costume from the total amount of fabric she bought.
The total amount of fabric Madelyn bought is 12 5/8 yards. To work with mixed numbers like 12 5/8, we need to convert them into improper fractions.
To convert the whole number to an improper fraction, we multiply the whole number (12) by the denominator of the fraction (8) and then add the numerator (5). This gives us: 12 * 8 + 5 = 96 + 5 = 101.
So, the total amount of fabric Madelyn bought in improper fraction form is 101/8 yards.
Now, let's find how much fabric she used for the costume. The amount of fabric used for the costume is 6 7/8 yards. Following the same process as above, we convert it to an improper fraction: 6 * 8 + 7 = 48 + 7 = 55/8 yards.
To find the amount of fabric Madelyn has left, we subtract the fabric used for the costume from the total amount of fabric bought: 101/8 - 55/8.
To subtract fractions with the same denominator, we subtract their numerators and keep the denominator the same: (101 - 55)/8 = 46/8.
Now, we simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2 in this case: 46/8 = (23/4).
Therefore, Madelyn has 23/4 yards of fabric left. However, it's more common to express this as a mixed number. To convert the improper fraction 23/4 to a mixed number, we divide the numerator (23) by the denominator (4):
23 ÷ 4 = 5 remainder 3.
The whole number is the result of division (5), and the remainder (3) becomes the numerator of the fraction part, with the same denominator as before. So, the fabric Madelyn has left is 5 3/4 yards.
Therefore, Madelyn has 5 3/4 yards of fabric left.