Find: `2(1)/(2)-1(5)/(18)`

Answer

To solve the problem \(2\frac{1}{2} - 1\frac{5}{18}\), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

For \(2\frac{1}{2}\):
- Multiply the whole number (2) by the denominator (2): \(2 \times 2 = 4\)
- Add the numerator (1): \(4 + 1 = 5\)
- The improper fraction is \(\frac{5}{2}\).

For \(1\frac{5}{18}\):
- Multiply the whole number (1) by the denominator (18): \(1 \times 18 = 18\)
- Add the numerator (5): \(18 + 5 = 23\)
- The improper fraction is \(\frac{23}{18}\).

### Step 2: Rewrite the Expression
Now we can rewrite the expression using the improper fractions:
\[ \frac{5}{2} - \frac{23}{18} \]

### Step 3: Find the Least Common Multiple (LCM)
Next, we need to find the least common multiple (LCM) of the denominators (2 and 18) to perform the subtraction.

- The multiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, 18...
- The multiples of 18 are: 18, 36, 54...

The LCM of 2 and 18 is 18.

### Step 4: Convert Fractions to Have a Common Denominator
Now we convert each fraction to have the common denominator of 18.

For \(\frac{5}{2}\):
- Multiply the numerator and denominator by 9 (since \(2 \times 9 = 18\)):
\[ \frac{5 \times 9}{2 \times 9} = \frac{45}{18} \]

For \(\frac{23}{18}\), it already has the denominator of 18, so it remains:
\[ \frac{23}{18} \]

### Step 5: Subtract the Fractions
Now we can subtract the fractions:
\[ \frac{45}{18} - \frac{23}{18} = \frac{45 - 23}{18} = \frac{22}{18} \]

### Step 6: Simplify the Result
Finally, we simplify \(\frac{22}{18}\) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2:
\[ \frac{22 \div 2}{18 \div 2} = \frac{11}{9} \]

### Final Answer
The final answer is:
\[ \frac{11}{9} \]