To find the length of the shortened ribbon, we first need to subtract the length cut off from the original length of the ribbon.
-
Original length of the ribbon: \( 6 \frac{1}{8} \) feet
To convert this to an improper fraction:
\( 6 \frac{1}{8} = \frac{6 \times 8 + 1}{8} = \frac{48 + 1}{8} = \frac{49}{8} \) feet -
Length cut off: \( 2 \frac{1}{12} \) feet
To convert this to an improper fraction:
\( 2 \frac{1}{12} = \frac{2 \times 12 + 1}{12} = \frac{24 + 1}{12} = \frac{25}{12} \) feet
Now we can perform the subtraction: \[ \text{Length of shortened ribbon} = \frac{49}{8} - \frac{25}{12} \]
To subtract these fractions, we need a common denominator. The least common multiple of 8 and 12 is 24.
Next, we convert both fractions: \[ \frac{49}{8} = \frac{49 \times 3}{8 \times 3} = \frac{147}{24} \] \[ \frac{25}{12} = \frac{25 \times 2}{12 \times 2} = \frac{50}{24} \]
Now we can subtract: \[ \frac{147}{24} - \frac{50}{24} = \frac{147 - 50}{24} = \frac{97}{24} \]
Next, we can convert \( \frac{97}{24} \) into a mixed number:
- Divide 97 by 24, which goes 4 times (since \( 4 \times 24 = 96 \)).
- The remainder is \( 97 - 96 = 1 \).
- So, \( \frac{97}{24} = 4 \frac{1}{24} \).
Thus, the length of the shortened ribbon is \( 4 \frac{1}{24} \) feet.
Among the options provided, the closest corresponding form is: 4 and 1 over 24 feet.