Evaluate: b. `5 (5)/(11) - 1 (5)/(12) - 2 (7)/( 24)`

Answer

To evaluate the expression \( 5 \frac{5}{11} - 1 \frac{5}{12} - 2 \frac{7}{24} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we convert each mixed number into an improper fraction.

1. \( 5 \frac{5}{11} = \frac{5 \times 11 + 5}{11} = \frac{55 + 5}{11} = \frac{60}{11} \)
2. \( 1 \frac{5}{12} = \frac{1 \times 12 + 5}{12} = \frac{12 + 5}{12} = \frac{17}{12} \)
3. \( 2 \frac{7}{24} = \frac{2 \times 24 + 7}{24} = \frac{48 + 7}{24} = \frac{55}{24} \)

So, the expression becomes:
\[ \frac{60}{11} - \frac{17}{12} - \frac{55}{24} \]

### Step 2: Find the Least Common Multiple (LCM)
Next, we need to find the LCM of the denominators \( 11, 12, \) and \( 24 \).

- The prime factorization of \( 11 \) is \( 11 \).
- The prime factorization of \( 12 \) is \( 2^2 \times 3 \).
- The prime factorization of \( 24 \) is \( 2^3 \times 3 \).

The LCM is found by taking the highest power of each prime:
- \( 2^3 \) from \( 24 \)
- \( 3^1 \) from \( 12 \)
- \( 11^1 \) from \( 11 \)

Thus, the LCM is:
\[ 2^3 \times 3^1 \times 11^1 = 8 \times 3 \times 11 = 264 \]

### Step 3: Convert Each Fraction to Have the Same Denominator
Now we convert each fraction to have the denominator of \( 264 \).

1. For \( \frac{60}{11} \):
\[ \frac{60}{11} \times \frac{24}{24} = \frac{1440}{264} \]

2. For \( \frac{17}{12} \):
\[ \frac{17}{12} \times \frac{22}{22} = \frac{374}{264} \]

3. For \( \frac{55}{24} \):
\[ \frac{55}{24} \times \frac{11}{11} = \frac{605}{264} \]

### Step 4: Combine the Fractions
Now we can combine the fractions:
\[ \frac{1440}{264} - \frac{374}{264} - \frac{605}{264} = \frac{1440 - 374 - 605}{264} \]

### Step 5: Perform the Subtraction
Now we perform the subtraction in the numerator:
\[ 1440 - 374 = 1066 \]
\[ 1066 - 605 = 461 \]

So we have:
\[ \frac{461}{264} \]

### Final Answer
The final answer is:
\[ \frac{461}{264} \]