Reduce the following fractions into their lowest terms :
(i) `36/60 " (ii) " 135/81" (iii) " 117/26`

Answer

To reduce the given fractions into their lowest terms, we will follow these steps for each fraction:

### (i) Reduce 36/60

1. **Find the GCD (Greatest Common Divisor)**:
- The GCD of 36 and 60 is 12.

2. **Divide both the numerator and denominator by the GCD**:
- \( \frac{36 \div 12}{60 \div 12} = \frac{3}{5} \)

3. **Check if the fraction is in lowest terms**:
- The numerator (3) and the denominator (5) have no common factors other than 1.

**Final Result**: \( \frac{3}{5} \)

### (ii) Reduce 135/81

1. **Find the GCD**:
- The GCD of 135 and 81 is 9.

2. **Divide both the numerator and denominator by the GCD**:
- \( \frac{135 \div 9}{81 \div 9} = \frac{15}{9} \)

3. **Further reduce the fraction**:
- The GCD of 15 and 9 is 3.
- \( \frac{15 \div 3}{9 \div 3} = \frac{5}{3} \)

4. **Check if the fraction is in lowest terms**:
- The numerator (5) and the denominator (3) have no common factors other than 1.

**Final Result**: \( \frac{5}{3} \)

### (iii) Reduce 117/26

1. **Find the GCD**:
- The GCD of 117 and 26 is 13.

2. **Divide both the numerator and denominator by the GCD**:
- \( \frac{117 \div 13}{26 \div 13} = \frac{9}{2} \)

3. **Check if the fraction is in lowest terms**:
- The numerator (9) and the denominator (2) have no common factors other than 1.

**Final Result**: \( \frac{9}{2} \)

### Summary of Results:
- (i) \( \frac{36}{60} = \frac{3}{5} \)
- (ii) \( \frac{135}{81} = \frac{5}{3} \)
- (iii) \( \frac{117}{26} = \frac{9}{2} \)