Questions that require simplifying or evaluating a purely numerical expression involving fractions, decimals, or mixed numbers with no variables or surds.
A tablet screen; when "large icons" is selected in the display settings is divided into 3 rows and 4 columns into identical compartments, and when "small icons" is selected, it is divided into 5 rows and 6 columns into identical compartments as shown in Figure 2. In both cases, at most one application icon is placed in each compartment. When "large icons" is selected in the display settings, it is observed that the icons of all applications on the tablet are located in $\frac{2}{3}$ of the compartments on the screen. If the display settings are changed to "small icons", in what fraction of the compartments on the screen will the icons of all applications on the tablet be located? A) $\frac{1}{5}$ B) $\frac{1}{6}$ C) $\frac{3}{10}$ D) $\frac{4}{15}$ E) $\frac{7}{30}$
A mathematics teacher asked students to find the decimal representation of the number $\frac{13}{20}$. Sude, who found this representation correctly, accidentally swapped the tenths and hundredths digits when writing the number she found on the board. Accordingly, the number Sude wrote on the board is equal to which of the following? A) $\frac{5}{8}$ B) $\frac{9}{20}$ C) $\frac{14}{25}$ D) $\frac{23}{40}$ E) $\frac{27}{50}$