Solve the following expressions:
`6/55 - 7/88`

Answer

To solve the expression \( \frac{6}{55} - \frac{7}{88} \), we will follow these steps:

### Step 1: Find the Least Common Multiple (LCM) of the Denominators
The denominators are 55 and 88. We need to find the LCM to make the denominators equal.

- The prime factorization of 55 is \( 5 \times 11 \).
- The prime factorization of 88 is \( 2^3 \times 11 \).

To find the LCM, we take the highest power of each prime factor:
- From 55: \( 5^1 \) and \( 11^1 \)
- From 88: \( 2^3 \) and \( 11^1 \)

Thus, the LCM is:
\[ LCM = 2^3 \times 5^1 \times 11^1 = 8 \times 5 \times 11 = 440 \]

### Step 2: Rewrite Each Fraction with the Common Denominator
Now that we have the LCM (440), we will convert each fraction to have this common denominator.

For \( \frac{6}{55} \):
\[ \frac{6}{55} = \frac{6 \times 8}{55 \times 8} = \frac{48}{440} \]

For \( \frac{7}{88} \):
\[ \frac{7}{88} = \frac{7 \times 5}{88 \times 5} = \frac{35}{440} \]

### Step 3: Subtract the Two Fractions
Now we can subtract the two fractions:
\[ \frac{48}{440} - \frac{35}{440} = \frac{48 - 35}{440} = \frac{13}{440} \]

### Step 4: Simplify the Result (if necessary)
The fraction \( \frac{13}{440} \) cannot be simplified further since 13 is a prime number and does not divide 440.

### Final Answer
Thus, the final answer is:
\[ \frac{13}{440} \]

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