Question

Asha and Samuel have bookshelves of the same size partly filled with books. Asha’s shelf is $\frac{5}{6}$th full and Samuel’s shelf is $\frac{2}{5}$ th full. Whose bookshelf is more full? By what fraction?

Answer 1

Here, we have to compare two unlike fractions,

Methodology to compare unlike fractions:

Step$1$: Find LCM of denominators of the given fractions:

$\therefore$ LCM $\left(6,5\right)=30$

Step 2: Multiply the numerator and denominator of each fraction by a suitable number so that the denominator in each case becomes equal to LCM obtained in Step $1$:

$\therefore$ $\frac{5}{6}=\frac{5\times 5}{6\times 5}=\frac{25}{30}$

$\frac{2}{5}=\frac{2\times 6}{5\times 6}=\frac{12}{30}$

Step 3: Step $2$ would convert all fractions to like fractions and therefore the fraction with the greater numerator is greater:

$\because$ $25>12$

$\therefore$ $\frac{5}{6}>\frac{2}{5}$

Hence, Asha's bookshelf is filled more than Samuel's bookshelf.

$\Rightarrow$To find by what fraction Asha's shelf is full more, we will find the difference in their fractions.

$\therefore$ Difference$=\frac{5}{6}-\frac{2}{5}$

$=$ $\frac{25}{30}-\frac{12}{30}=\frac{13}{30}$

Therefore, Asha’s bookshelf is more full than Samuel’s bookshelf by $\frac{13}{30}$ the fraction.