Which of the following rational number lies between −4/5 and −2/3 ?

Concept: A rational number lies between two given rational numbers only when, after writing all three numbers on the same scale (a common denominator, or decimal form), its value is strictly greater than the smaller (more negative) bound and strictly less than the larger bound.

Method: Convert the two bounds and every option to a common denominator, then compare.

1. Write the two bounds with denominator 45: −4/5 = −36/45 and −2/3 = −30/45. Since −36/45 < −30/45, the required value V must satisfy −36/45 < V < −30/45.

2. Convert −3/5 to denominator 45: −3/5 = −27/45.

3. Convert −7/9 to denominator 45: −7/9 = −35/45.

4. Convert −1/3 to denominator 45: −1/3 = −15/45.

5. −13/45 is already in denominator 45.

6. Compare each converted value against the range −36/45 to −30/45: only −35/45 falls strictly inside it. −27/45, −15/45, and −13/45 are all greater than −30/45, so they lie outside the range on the higher side.

Cross-check (decimals): −4/5 = −0.8, −2/3 is approximately −0.667, and −7/9 is approximately −0.778, confirming −0.8 < −0.778 < −0.667.

Answer: −7/9 is the only option lying between −4/5 and −2/3.