Greg has a piece of string that is $$ 31 / 3 $$ yards long. If he cuts off $$ 3 / 4 $$ yard, how many yards of the string will be left? a. $$ 1 / 4 $$ yards To get the amount of string left we need to multiply only the fraction portions of the equation to get the remaining string length. b. $$ 21 / 4 $$ yards To get the amount of string left we need to multiply the whole number byt the fraction he cuts of to get the remaining string length. c. $$ 4 / 9 $$ yards To get the amount of string left we need to divide only the fraction portions of the equation to get the remaining string length: d. $$ 27 / 12 $$ yards To get the amount of string Greg has left we need toFind the LCD of $$ 1 / 3 $$ and $$ 3 / 4 $$ and rewrite to solve with the equivalent fractions and then combine the whole fraction

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To find out how many yards of string Greg has left after cutting off $$ \frac{3}{4} $$ yard from $$ \frac{31}{3} $$ yards, we can follow these steps:

1. **Convert the mixed number to an improper fraction**: 
   - The length of the string is $$ \frac{31}{3} $$ yards.
   - The amount cut off is $$ \frac{3}{4} $$ yards.

2. **Subtract the amount cut off from the total length**:
   $$
   \text{Remaining length} = \frac{31}{3} - \frac{3}{4}
   $$

3. **Find a common denominator**: 
   - The denominators are 3 and 4. The least common denominator (LCD) is 12.

4. **Convert each fraction to have the common denominator**:
   - Convert $$ \frac{31}{3} $$ to twelfths:
     $$
     \frac{31}{3} = \frac{31 \times 4}{3 \times 4} = \frac{124}{12}
     $$
   - Convert $$ \frac{3}{4} $$ to twelfths:
     $$
     \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
     $$

5. **Subtract the two fractions**:
   $$
   \text{Remaining length} = \frac{124}{12} - \frac{9}{12} = \frac{124 - 9}{12} = \frac{115}{12}
   $$

Now, let's summarize the calculations and find the final answer.

The remaining length of the string is $$ \frac{115}{12} $$ yards.

Now, let's check the options provided:
- a. $$ \frac{1}{4} $$ yards
- b. $$ \frac{21}{4} $$ yards
- c. $$ \frac{4}{9} $$ yards
- d. $$ \frac{27}{12} $$ yards

None of the options match $$ \frac{115}{12} $$ yards.

Thus, the correct answer is $$ \frac{115}{12} $$ yards, which is not listed among the options.
The remaining length of the string is $$ \frac{115}{12} $$ yards.

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