Which integer is closest in value to $\frac{35}{4}$ ?
(A) 10
(B) 8
(C) 9
(D) 7
(E) 6
Solution 1

Written as a mixed fraction, $\frac{35}{4}=8 \frac{3}{4}$.

Since $\frac{3}{4}$ is closer to 1 than it is to 0 , then $8 \frac{3}{4}$ is closer to 9 than it is to 8 .

The integer closest in value to $\frac{35}{4}$ is 9 .

Solution 2

Written as a decimal $\frac{35}{4}=35 \div 4=8.75$.

Since 0.75 is closer to 1 than it is to 0 , then 8.75 is closer to 9 than it is to 8 .

The integer closest in value to $\frac{35}{4}$ is 9 .

Answer: (C)