Question

Ila read 25 pages of a book containing 100 pages and Lalita read $\frac{2}{5}$of the same book. What can be concluded from this? (4 marks)

Answer 1

As per the question, Ila read 25 pages out of 100 pages.
Fraction of the pages read by Ila$=\frac{25}{100}$ (0.5 mark)

25 is the common factor of both 25 and 100, so divide the numerator and denominator by 25, we get
$\frac{25}{100}=\frac{25÷25}{100÷25}=\frac{1}{4}$
So, Ila read ${\frac{1}{4}}^{th}$part of book. (1 mark)

Given that Lalita read ${\frac{2}{5}}^{th}$ part of book

To compare both the fractions, let us convert them into like fractions.
LCM of the denominators of $\frac{1}{4}$ and $\frac{2}{5}$ , i.e., LCM of 4 and 5 is 20. (0.5 mark)
Now, writing $\frac{1}{4}$ and $\frac{2}{5}$ as equivalent fractions having same denominator which is 20, we get
$\frac{1}{4}=\frac{1\times 5}{4\times 5}=\frac{5}{20}$ and $\frac{2}{5}=\frac{2\times 4}{5\times 4}=\frac{8}{20}$ (1 mark)
On comparing the numerators, we have
5 < 8
$\therefore \frac{5}{20}<\frac{8}{20}$
Therefore, Ila read less than Lalitha. (1 mark)