Find the difference:
`23(5)/(8)-16(5)/(6)`

Answer

To find the difference between the mixed fractions \(23\frac{5}{8}\) and \(16\frac{5}{6}\), we will follow these steps:

### Step 1: Convert mixed fractions to improper fractions
1. For \(23\frac{5}{8}\):
- Multiply the whole number (23) by the denominator (8):
\[ 23 \times 8 = 184 \]
- Add the numerator (5):
\[ 184 + 5 = 189 \]
- So, \(23\frac{5}{8} = \frac{189}{8}\).

2. For \(16\frac{5}{6}\):
- Multiply the whole number (16) by the denominator (6):
\[ 16 \times 6 = 96 \]
- Add the numerator (5):
\[ 96 + 5 = 101 \]
- So, \(16\frac{5}{6} = \frac{101}{6}\).

### Step 2: Find a common denominator
- The denominators are 8 and 6. The least common multiple (LCM) of 8 and 6 is 48.

### Step 3: Convert the fractions to have the common denominator
1. Convert \(\frac{189}{8}\) to a fraction with a denominator of 48:
- Multiply both the numerator and denominator by 6:
\[ \frac{189 \times 6}{8 \times 6} = \frac{1134}{48} \]

2. Convert \(\frac{101}{6}\) to a fraction with a denominator of 48:
- Multiply both the numerator and denominator by 8:
\[ \frac{101 \times 8}{6 \times 8} = \frac{808}{48} \]

### Step 4: Subtract the fractions
Now we can subtract the two fractions:
\[ \frac{1134}{48} - \frac{808}{48} = \frac{1134 - 808}{48} = \frac{326}{48} \]

### Step 5: Simplify the result (if necessary)
To convert \(\frac{326}{48}\) into a mixed fraction:
1. Divide 326 by 48:
- \(48\) goes into \(326\) a total of \(6\) times (since \(48 \times 6 = 288\)).
- The remainder is \(326 - 288 = 38\).

So, we can express \(\frac{326}{48}\) as:
\[ 6\frac{38}{48} \]

### Step 6: Simplify the fractional part
The fraction \(\frac{38}{48}\) can be simplified:
- The greatest common divisor (GCD) of 38 and 48 is 2.
- Divide both the numerator and denominator by 2:
\[ \frac{38 \div 2}{48 \div 2} = \frac{19}{24} \]

Thus, the final answer is:
\[ 6\frac{19}{24} \]

### Final Answer
The difference \(23\frac{5}{8} - 16\frac{5}{6} = 6\frac{19}{24}\).

---