2-26/27 : 39/45

To simplify the ratio \( \frac{2 - \frac{26}{27}}{\frac{39}{45}} \), we will first simplify each part separately.

1. Calculate \( 2 - \frac{26}{27} \):

   • Convert 2 into a fraction with a denominator of 27: \[ 2 = \frac{54}{27} \]
   • Now subtract: \[ 2 - \frac{26}{27} = \frac{54}{27} - \frac{26}{27} = \frac{54 - 26}{27} = \frac{28}{27} \]

2. Simplify \( \frac{39}{45} \):

   • Find the greatest common divisor (GCD) of 39 and 45, which is 3: \[ \frac{39}{45} = \frac{39 \div 3}{45 \div 3} = \frac{13}{15} \]

3. Now substitute back into the ratio: \[ \text{The ratio is } \frac{\frac{28}{27}}{\frac{13}{15}} \]

4. Dividing two fractions: \[ \frac{28}{27} \div \frac{13}{15} = \frac{28}{27} \times \frac{15}{13} = \frac{28 \times 15}{27 \times 13} \]

5. Calculate \( 28 \times 15 \) and \( 27 \times 13 \):

   • \( 28 \times 15 = 420 \)
   • \( 27 \times 13 = 351 \)

6. Final ratio: \[ \frac{420}{351} \]

7. Simplify \( \frac{420}{351} \):

   • The GCD of 420 and 351 is 3: \[ \frac{420 \div 3}{351 \div 3} = \frac{140}{117} \]

Thus, the simplified form of the original expression \( \frac{2 - \frac{26}{27}}{\frac{39}{45}} \) is \( \frac{140}{117} \).