5. Which of the following numbers is the largest?
A $\frac{397}{101}$
B $\frac{487}{121}$
C $\frac{596}{153}$
D $\frac{678}{173}$
E $\frac{796}{203}$
SolUTION
B
Commentary
Without the use of a calculator it is not feasible in the time available to answer this question by calculating the values of these fractions to an appropriate number of decimal places.
It would also not be reasonable to decide the relative sizes of, for example, $\frac{397}{101}$ and $\frac{487}{121}$ by using the fact that
$$
\frac{397}{101}\frac{484}{121}=4 \\
\frac{596}{153}<\frac{612}{153}=4 \\
\frac{678}{173}<\frac{692}{173}=4
\end{array}
$$
and
$$
\frac{796}{203}<\frac{812}{203}=4 \text {. }
$$

These calculations show that the fraction given as option $\mathrm{B}$ is the only one that is greater than 4 , and hence is the largest of the given numbers.