60/45:45/35

To simplify the expression \( \frac{60}{45} : \frac{45}{35} \), we will first simplify the fractions and then interpret the division of the fractions.

1. Simplify \( \frac{60}{45} \):

   • The greatest common divisor (GCD) of 60 and 45 is 15.
   • So, \( \frac{60}{45} = \frac{60 \div 15}{45 \div 15} = \frac{4}{3} \).

2. Simplify \( \frac{45}{35} \):

   • The GCD of 45 and 35 is 5.
   • So, \( \frac{45}{35} = \frac{45 \div 5}{35 \div 5} = \frac{9}{7} \).

Now, we need to evaluate \( \frac{4}{3} : \frac{9}{7} \).

Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{4}{3} : \frac{9}{7} = \frac{4}{3} \times \frac{7}{9} \]

Now, multiply the fractions: \[ \frac{4 \times 7}{3 \times 9} = \frac{28}{27} \]

Therefore, the final result of the expression \( \frac{60}{45} : \frac{45}{35} \) is \( \frac{28}{27} \).