Question

Fill up the blank in the following statement using $\text{'}<\text{'}$, $\text{'}>\text{'}$ or $\text{'}=\text{'}$ :

$11:19$_____ $19:21$

Answer 1

Step 1: Express the given ratios as fractions

We have to compare the given ratios: $11:19$and $19:21$.

Ratios can be compared by expressing each of them as fractions and then comparing the fractions.

$11:19$and $19:21$can be written as fractions $\frac{11}{19}$and $\frac{19}{21}$.

Step 2: Compare the fractions

To compare fractions, we make the denominators of both the fractions equal and then compare the numerators.

The L.C.M of denominators, $19$ and $21$ , is $399$.

Let's make the denominator of both the fractions $399$.

$\frac{11\times 21}{19\times 21}=\frac{231}{399}$ and $\frac{19\times 19}{21\times 19}=\frac{361}{399}$

$\frac{231}{399}$$<$$\frac{361}{399}$

So, $\frac{11}{19}$$<$$\frac{19}{21}$.

Hence, $11:19$$<$$19:21$.