Question

Find answers to the following. Write and indicate how you solved them.
(i) Is $\frac{5}{9}$ equal to$\frac{4}{5}$?
(ii) Is $\frac{9}{16}$ equal to $\frac{5}{9}$?
(iii) Is $\frac{4}{5}$ equal to $\frac{16}{20}$?
(iv) Is $\frac{1}{15}$ equal to $\frac{4}{30}$?

Answer 1

There are various methods by which we can compare ay two fractions $\frac{a}{b}$ and $\frac{c}{d}$. We can check whether the one fraction is equivalent to the other or not by reducing a fraction. We can also use LCM method or we ca simple compare $a\times d$ with $b\times c$.

(i) For $\frac{5}{9}$ and $\frac{4}{5}$,

$\Rightarrow 5\times 5$ and $4\times 9$

$\Rightarrow 25$ and $36$

Since, $25<36$,

$\therefore \frac{5}{9}<\frac{4}{5}$

(ii) For $\frac{9}{16}$ and $\frac{5}{9}$

$\Rightarrow 9\times 9$ ad $5\times 16$

$\Rightarrow 81$ and $80$

Since, $81>80$

$\therefore \frac{9}{16}>\frac{5}{9}$

(iii) For $\frac{4}{5}$ and $\frac{16}{20}$,

The later fraction can be reduced to its lowest form,

$\Rightarrow \frac{16}{20}=\frac{16÷4}{20÷4}=\frac{4}{5}$

Thus the two fractions are equal, $\frac{4}{5}=\frac{16}{20}$

(iv) For $\frac{1}{15}$ and $\frac{4}{30}$.

The later fraction can be reduced to its lowest form,

$\Rightarrow \frac{4}{30}=\frac{4÷2}{30÷2}=\frac{2}{15}$

Since, $\frac{2}{15}>\frac{1}{15}$

$\therefore \frac{4}{30}>\frac{1}{15}$