To find the length of the shortened ribbon, we need to subtract the length that was cut off from the original length of the ribbon.
The original length of the ribbon is \( 6 \frac{1}{8} \) feet, and the length cut off is \( 2 \frac{1}{12} \) feet.
First, let's convert both mixed numbers to improper fractions:
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Convert \( 6 \frac{1}{8} \): \[ = 6 \times 8 + 1 = 48 + 1 = 49 \implies \frac{49}{8} \]
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Convert \( 2 \frac{1}{12} \): \[ = 2 \times 12 + 1 = 24 + 1 = 25 \implies \frac{25}{12} \]
Now, we need to subtract \( \frac{25}{12} \) from \( \frac{49}{8} \).
To do this, we need a common denominator. The least common multiple of 8 and 12 is 24.
Now convert both fractions:
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Convert \( \frac{49}{8} \) to a denominator of 24: \[ \frac{49}{8} = \frac{49 \times 3}{8 \times 3} = \frac{147}{24} \]
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Convert \( \frac{25}{12} \) to a denominator of 24: \[ \frac{25}{12} = \frac{25 \times 2}{12 \times 2} = \frac{50}{24} \]
Now, we can subtract: \[ \frac{147}{24} - \frac{50}{24} = \frac{147 - 50}{24} = \frac{97}{24} \]
Now, we can convert \( \frac{97}{24} \) back to a mixed number: \[ 97 รท 24 = 4 \quad \text{(remainder } 1\text{)} \] So, \[ \frac{97}{24} = 4 \frac{1}{24} \]
Since this is not one of the options given, we need to double-check the given options. Based on the calculation:
- The shortened ribbon's length is \( 4 \frac{1}{24} \) feet.
Thus, none of the responses listed in the question match the answer we calculated. The correct length of the shortened ribbon is \( 4 \frac{1}{24} \) feet.