Problem: The number halfway between 1/81 / 81/8 and 1/101 / 101/10 is
Answer Choices:
A. 180\dfrac{1}{80}801
B. 140\dfrac{1}{40}401
C. 118\dfrac{1}{18}181
D. 19\dfrac{1}{9}91
E. 980\dfrac{9}{80}809
Solution:
The desired number is the arithmetic average or mean:
12(18+110)=12⋅1880=980.\dfrac{1}{2}\left(\dfrac{1}{8}+\dfrac{1}{10}\right)=\dfrac{1}{2} \cdot \dfrac{18}{80}=\dfrac{9}{80} . 21(81+101)=21⋅8018=809.