Question

Asha and Samuel have bookshelves of the same size. Asha's shelf is $\frac{5}{6}th$ full and Samuel's shelf is $\frac{2}{5}th$ full. Whose bookshelf is more full and by what fraction?

Answer 1

Step 1: Find whose bookshelf is more full:

Given Asha's shelf is $\frac{5}{6}th$ full

Samuel's shelf is $\frac{2}{5}th$ full.

To find whose bookshelf is more full

Consider

$$\begin{gathered} \frac{5}{6}?\frac{2}{5} \\ 5\times 5?2\times 6 \\ 25?12 \\ 25>12 \end{gathered}$$

Since $25$ is greater than $12$

Hence, $\frac{5}{6}>\frac{2}{5}$

Hence, Asha's bookshelf is more full

Step 2: Find what fraction Asha's shelf is more:

To find what fraction of Asha's shelf is more

Consider

$$\begin{gathered} \frac{5}{6}-\frac{2}{5} \\ =\frac{5\times 5}{6\times 5}-\frac{2\times 6}{5\times 6} \\ =\frac{25}{30}-\frac{12}{30} \\ =\frac{25-12}{30} \\ =\frac{13}{30} \end{gathered}$$

Hence, the fraction Asha's shelf is more by $\frac{13}{30}th$