What should be subtracted from `17 3/4` to get `11 2/3`?

Answer

To find out what should be subtracted from \( 17 \frac{3}{4} \) to get \( 11 \frac{2}{3} \), we can set up the equation:

\[ 17 \frac{3}{4} - x = 11 \frac{2}{3} \]

### Step 1: Convert the mixed numbers to improper fractions

1. Convert \( 17 \frac{3}{4} \) to an improper fraction:
- Multiply the whole number (17) by the denominator (4): \( 17 \times 4 = 68 \)
- Add the numerator (3): \( 68 + 3 = 71 \)
- Therefore, \( 17 \frac{3}{4} = \frac{71}{4} \)

2. Convert \( 11 \frac{2}{3} \) to an improper fraction:
- Multiply the whole number (11) by the denominator (3): \( 11 \times 3 = 33 \)
- Add the numerator (2): \( 33 + 2 = 35 \)
- Therefore, \( 11 \frac{2}{3} = \frac{35}{3} \)

### Step 2: Set up the equation with improper fractions

Now we have:

\[ \frac{71}{4} - x = \frac{35}{3} \]

### Step 3: Isolate \( x \)

To isolate \( x \), we can rearrange the equation:

\[ x = \frac{71}{4} - \frac{35}{3} \]

### Step 4: Find a common denominator

The denominators are 4 and 3. The least common multiple of 4 and 3 is 12.

Convert both fractions:

1. Convert \( \frac{71}{4} \) to have a denominator of 12:
- \( \frac{71}{4} \times \frac{3}{3} = \frac{213}{12} \)

2. Convert \( \frac{35}{3} \) to have a denominator of 12:
- \( \frac{35}{3} \times \frac{4}{4} = \frac{140}{12} \)

### Step 5: Subtract the fractions

Now we can subtract:

\[ x = \frac{213}{12} - \frac{140}{12} = \frac{213 - 140}{12} = \frac{73}{12} \]

### Step 6: Convert back to a mixed number (if necessary)

To convert \( \frac{73}{12} \) back to a mixed number:
- Divide 73 by 12: \( 73 \div 12 = 6 \) remainder \( 1 \)
- So, \( \frac{73}{12} = 6 \frac{1}{12} \)

### Final Answer

Thus, the value that should be subtracted from \( 17 \frac{3}{4} \) to get \( 11 \frac{2}{3} \) is:

\[ \boxed{6 \frac{1}{12}} \]