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 \( \frac{140}{117} \).