(a) Find the HCF of `(2)/(5),(12)/(5) and (3)/(4)`

Answer

To find the HCF (Highest Common Factor) of the fractions \( \frac{2}{5} \), \( \frac{12}{5} \), and \( \frac{3}{4} \), we can follow these steps:

### Step 1: Identify the numerators and denominators
The fractions given are:
- \( \frac{2}{5} \) (numerator = 2, denominator = 5)
- \( \frac{12}{5} \) (numerator = 12, denominator = 5)
- \( \frac{3}{4} \) (numerator = 3, denominator = 4)

### Step 2: Find the HCF of the numerators
Now, we need to find the HCF of the numerators 2, 12, and 3.

- The factors of 2 are: 1, 2
- The factors of 12 are: 1, 2, 3, 4, 6, 12
- The factors of 3 are: 1, 3

The common factors of 2, 12, and 3 are: 1. Therefore, the HCF of the numerators is 1.

### Step 3: Find the LCM of the denominators
Next, we need to find the LCM (Lowest Common Multiple) of the denominators 5 and 4.

- The multiples of 5 are: 5, 10, 15, 20, 25, 30, ...
- The multiples of 4 are: 4, 8, 12, 16, 20, 24, ...

The smallest common multiple of 5 and 4 is 20. Therefore, the LCM of the denominators is 20.

### Step 4: Form the HCF of the fractions
Now, we can form the HCF of the fractions using the HCF of the numerators and the LCM of the denominators.

The HCF of the fractions is given by:
\[ \text{HCF} = \frac{\text{HCF of numerators}}{\text{LCM of denominators}} = \frac{1}{20} \]

### Final Answer:
The HCF of \( \frac{2}{5} \), \( \frac{12}{5} \), and \( \frac{3}{4} \) is \( \frac{1}{20} \).

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