Evaluate: c. `4 (11)/(15) - 2 (7)/(20)`

Answer

To evaluate the expression \( 4 \frac{11}{15} - 2 \frac{7}{20} \), we will follow these steps:

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

For \( 4 \frac{11}{15} \):
- Multiply the whole number (4) by the denominator (15):
\[ 4 \times 15 = 60 \]
- Add the numerator (11):
\[ 60 + 11 = 71 \]
- So, \( 4 \frac{11}{15} = \frac{71}{15} \).

For \( 2 \frac{7}{20} \):
- Multiply the whole number (2) by the denominator (20):
\[ 2 \times 20 = 40 \]
- Add the numerator (7):
\[ 40 + 7 = 47 \]
- So, \( 2 \frac{7}{20} = \frac{47}{20} \).

### Step 2: Rewrite the Expression
Now we can rewrite the expression using the improper fractions:
\[ \frac{71}{15} - \frac{47}{20} \]

### Step 3: Find the Least Common Multiple (LCM)
Next, we need to find the least common multiple (LCM) of the denominators (15 and 20) to perform the subtraction.

- The prime factorization of 15 is \( 3 \times 5 \).
- The prime factorization of 20 is \( 2^2 \times 5 \).

The LCM is found by taking the highest power of each prime:
- LCM = \( 2^2 \times 3^1 \times 5^1 = 60 \).

### Step 4: Convert Fractions to Have a Common Denominator
Now we convert both fractions to have the common denominator of 60.

For \( \frac{71}{15} \):
- Multiply the numerator and denominator by 4:
\[ \frac{71 \times 4}{15 \times 4} = \frac{284}{60} \]

For \( \frac{47}{20} \):
- Multiply the numerator and denominator by 3:
\[ \frac{47 \times 3}{20 \times 3} = \frac{141}{60} \]

### Step 5: Subtract the Fractions
Now we can subtract the two fractions:
\[ \frac{284}{60} - \frac{141}{60} = \frac{284 - 141}{60} = \frac{143}{60} \]

### Step 6: Final Answer
The final answer is:
\[ \frac{143}{60} \]

This fraction cannot be simplified further, so this is our final result.