Question

Arrange the given fractions in ascending order.

$\frac{17}{30},\frac{5}{17},\frac{8}{10},\frac{9}{15}$

Answer 1

First we make their denominators same by finding the L.C.M of denominators i.e. $7,12,24,13$ and then we can simply compare their numerators as the denominators are the same now.

$$\begin{gathered} 30=2\times 3\times 5 \\ 17=17\times 1 \\ 10=2\times 5 \\ 15=3\times 5 \\ L.C.M=2\times 3\times 5\times 17=510 \end{gathered}$$

Now,

$$\begin{gathered} \frac{17}{30}=\frac{17\times 17}{30\times 17}=\frac{289}{510} \\ \frac{5}{17}=\frac{5\times 30}{17\times 30}=\frac{150}{510} \\ \frac{8}{10}=\frac{8\times 51}{10\times 51}=\frac{408}{510} \\ \frac{9}{15}=\frac{9\times 34}{15\times 34}=\frac{306}{510} \end{gathered}$$

When two fractions having the same denominator are compared, then the fraction with the greater numerator will be the greater fraction.

Hence $150<289<306<408$

So we can say that,

$\frac{5}{17}<\frac{17}{30}<\frac{9}{15}<\frac{8}{10}$