Question

Which ratio is greater $7:8or2:\hspace{0.17em}3$?

Answer 1

Comparison of ratios:

We can write $7:8or2:\hspace{0.17em}3$ as $\frac{7}{8}or\frac{2}{3}$

We will have to equalise the denominators and then multiply by LCM of the denominators

Firstly, taking LCM of the denominators $3and8$.

By prime factorisation method:

$3=3\times 1$

$8=2^3\times 1$

$LCM(3,8)=2^3\times 3\times 1=8\times 3=24$

Now, multiplying the LCM in both terms:

$\frac{7}{8}\times 24and\frac{2}{3}\times 24$

$7\times 3and2\times 8$

$21and16$

Since, $21>16$

Therefore, $\frac{7}{8}>\frac{2}{3}$ or $7:8>2:\hspace{0.17em}3$

Hence, $7:8$ is the greater ratio.