Compare the fractions given below:
`(11)/(12), (13)/(15)`

Answer

To compare the fractions \( \frac{11}{12} \) and \( \frac{13}{15} \), we can follow these steps:

### Step 1: Find the Least Common Multiple (LCM) of the Denominators
The denominators of the fractions are 12 and 15. We need to find the LCM of these two numbers.

- **Prime factorization of 12**:
- \( 12 = 2^2 \times 3^1 \)

- **Prime factorization of 15**:
- \( 15 = 3^1 \times 5^1 \)

To find the LCM, we take the highest power of each prime factor:
- For \( 2 \): highest power is \( 2^2 \)
- For \( 3 \): highest power is \( 3^1 \)
- For \( 5 \): highest power is \( 5^1 \)

So, the LCM is:
\[ LCM = 2^2 \times 3^1 \times 5^1 = 4 \times 3 \times 5 = 60 \]

### Step 2: Convert Each Fraction to Have the Same Denominator
Now that we have the LCM, we will convert both fractions to have a denominator of 60.

- For \( \frac{11}{12} \):
\[ \frac{11}{12} = \frac{11 \times 5}{12 \times 5} = \frac{55}{60} \]

- For \( \frac{13}{15} \):
\[ \frac{13}{15} = \frac{13 \times 4}{15 \times 4} = \frac{52}{60} \]

### Step 3: Compare the Converted Fractions
Now we can compare the two fractions:
\[ \frac{55}{60} \quad \text{and} \quad \frac{52}{60} \]

Since \( 55 > 52 \), we conclude that:
\[ \frac{11}{12} > \frac{13}{15} \]

### Final Answer
Thus, \( \frac{11}{12} \) is greater than \( \frac{13}{15} \).

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