Which one of the following will have minimum change in its value if 5 is added to both numerator and the…
Which one of the following will have minimum change in its value if 5 is added to both numerator and the denominator of the fractions 2/3, 3/4, 4/5 and 5/6?
2/3
3/4
4/5
5/6
Solution
Adding 5 to numerator and denominator moves a fraction toward 1. The change equals the difference between the new and old fraction. 2/3: $7/8 - 2/3 = 5/24 \approx 0.208$. 3/4: $8/9 - 3/4 = 5/36 \approx 0.139$. 4/5: $9/10 - 4/5 = 1/10 = 0.1$. 5/6: $10/11 - 5/6 = 5/66 \approx 0.076$. The smallest change is for 5/6.