Question

Fill in the boxes with the symbols $=,$$>$ or $<$.

$\frac{4}{9}$$\square$$\frac{17}{19}$

Answer 1

Two or more fractions are said to be like fractions if they have same denominator. For like fraction, the fraction with greater numerator is greater.

Here, the given fractions are $\frac{4}{9}$ and $\frac{17}{19}$. Since the denominator of both fractions are not the same, therefore the given fractions are unlike fractions. The unlike fractions are compared by converting them into like fractions. They are converted into like fractions by taking their equivalent forms with denominator as the LCM of denominators of unlike fractions.

Here, the LCM of denominators i.e. $9$ and $19$ is $171$. Therefore, the equivalent forms of $\frac{4}{9}$ and $\frac{17}{19}$ must have denominator $171$.

To obtain an equivalent form of $\frac{4}{9}$ with denominator $171$, we have

$\frac{4}{9}=\frac{4\times 19}{9\times 19}$ [multiplying numerator and denominator by $19$]

$=\frac{76}{171}$

To obtain an equivalent form of $\frac{17}{19}$ with denominator $171$, we have

$\frac{17}{19}=\frac{17\times 9}{19\times 9}$ [multiplying numerator and denominator by $9$]

$=\frac{153}{171}$

Now, the two fractions are $\frac{76}{171}$ and $\frac{153}{171}$, which are like fractions. Therefore, the fraction with a greater denominator is greater.

Hence, $\frac{76}{171}$ $<$ $\frac{153}{171}$ or $\frac{4}{9}$ $<$$\frac{17}{19}$.