Convert the fractions `5/6,7/9,11/12` into like fractions

Answer

To convert the fractions \( \frac{5}{6}, \frac{7}{9}, \frac{11}{12} \) into like fractions, we need to find a common denominator for all three fractions. Here’s how to do it step by step:

### Step 1: Find the LCM of the denominators
The denominators of the fractions are 6, 9, and 12. We need to find the least common multiple (LCM) of these numbers.

- **Prime factorization**:
- \( 6 = 2 \times 3 \)
- \( 9 = 3^2 \)
- \( 12 = 2^2 \times 3 \)

- **LCM Calculation**:
- Take the highest power of each prime factor:
- For \( 2 \): highest power is \( 2^2 \) (from 12)
- For \( 3 \): highest power is \( 3^2 \) (from 9)

Thus, the LCM is:
\[ LCM = 2^2 \times 3^2 = 4 \times 9 = 36 \]

### Step 2: Convert each fraction to have the common denominator
Now that we have the LCM, which is 36, we will convert each fraction.

1. **Convert \( \frac{5}{6} \)**:
- We need to multiply the denominator by \( 6 \) to get \( 36 \).
- Multiply both the numerator and denominator by \( 6 \):
\[ \frac{5 \times 6}{6 \times 6} = \frac{30}{36} \]

2. **Convert \( \frac{7}{9} \)**:
- We need to multiply the denominator by \( 4 \) to get \( 36 \).
- Multiply both the numerator and denominator by \( 4 \):
\[ \frac{7 \times 4}{9 \times 4} = \frac{28}{36} \]

3. **Convert \( \frac{11}{12} \)**:
- We need to multiply the denominator by \( 3 \) to get \( 36 \).
- Multiply both the numerator and denominator by \( 3 \):
\[ \frac{11 \times 3}{12 \times 3} = \frac{33}{36} \]

### Step 3: Write the like fractions
Now that we have converted all fractions to have the same denominator, we can write them as:
\[ \frac{30}{36}, \frac{28}{36}, \frac{33}{36} \]

### Final Answer:
The like fractions are \( \frac{30}{36}, \frac{28}{36}, \frac{33}{36} \).

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