Reduce the following fractions to simplest form

Question

(i) 78/91

Answer 1

To reduce the fraction \( \frac{78}{91} \) to its simplest form, we first need to find the greatest common divisor (GCD) of the numerator and the denominator.

1. Factor 78 and 91:

   • The factors of 78: \( 78 = 2 \times 39 = 2 \times 3 \times 13 \)
   • The factors of 91: \( 91 = 7 \times 13 \)

2. Identify the GCD:

   • The common factor between 78 and 91 is 13.

3. Divide both the numerator and the denominator by the GCD: \[ \frac{78 \div 13}{91 \div 13} = \frac{6}{7} \]

Thus, the fraction \( \frac{78}{91} \) in simplest form is \( \frac{6}{7} \).