Find the difrence
`2(7)/(9)-1(8)/(15)`

Answer

To find the difference \( \frac{2 \times 7}{9} - \frac{1 \times 8}{15} \), we can follow these steps:

### Step 1: Convert the mixed numbers to improper fractions
The first term is \( 2 \frac{7}{9} \) which can be converted to an improper fraction:
\[ 2 \frac{7}{9} = \frac{2 \times 9 + 7}{9} = \frac{18 + 7}{9} = \frac{25}{9} \]
The second term is \( 1 \frac{8}{15} \) which can be converted similarly:
\[ 1 \frac{8}{15} = \frac{1 \times 15 + 8}{15} = \frac{15 + 8}{15} = \frac{23}{15} \]

### Step 2: Write the subtraction
Now, we can write the subtraction:
\[ \frac{25}{9} - \frac{23}{15} \]

### Step 3: Find the least common multiple (LCM) of the denominators
The denominators are 9 and 15. To find the LCM:
- The prime factorization of 9 is \( 3^2 \).
- The prime factorization of 15 is \( 3^1 \times 5^1 \).
- The LCM is \( 3^2 \times 5^1 = 9 \times 5 = 45 \).

### Step 4: Convert each fraction to have the same denominator
Now we convert both fractions to have the denominator of 45:
- For \( \frac{25}{9} \):
\[ \frac{25}{9} = \frac{25 \times 5}{9 \times 5} = \frac{125}{45} \]
- For \( \frac{23}{15} \):
\[ \frac{23}{15} = \frac{23 \times 3}{15 \times 3} = \frac{69}{45} \]

### Step 5: Subtract the fractions
Now we can subtract:
\[ \frac{125}{45} - \frac{69}{45} = \frac{125 - 69}{45} = \frac{56}{45} \]

### Step 6: Simplify if necessary
The fraction \( \frac{56}{45} \) is already in its simplest form. We can also express it as a mixed number:
\[ \frac{56}{45} = 1 \frac{11}{45} \]

### Final Answer
The final answer is:
\[ 1 \frac{11}{45} \]

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