Question

Arrange the following in ascending order.

$\frac{2}{9},\frac{6}{7},\frac{1}{10},\frac{3}{5},\frac{7}{11}$

Answer 1

Given fractions,

$\frac{2}{9},\frac{6}{7},\frac{1}{10},\frac{3}{5},\frac{7}{11}$

To arrange the ascending order, first, we have to find the LCM of denominators $\left(9,7,10,5,11\right)$

$$\begin{gathered} 9=3\times 3 \\ 7=7\times 1 \\ 10=5\times 2 \\ 5=5\times 1 \\ 11=11\times 1 \end{gathered}$$

Choose each factor with the highest exponent.

LCM$\left(9,7,10,5,11\right)$$=$$2\times 3\times 3\times 5\times 7\times 11$

LCM$\left(9,7,10,5,11\right)$$=6930$

Now we have to make the denominators equal.

$$\begin{gathered} \frac{2}{9}=\frac{2\times 770}{9\times 770}=\frac{1540}{6930} \\ \frac{6}{7}=\frac{6\times 990}{7\times 990}=\frac{5940}{6930} \\ \frac{1}{10}=\frac{1\times 693}{10\times 693}=\frac{693}{6930} \\ \frac{3}{5}=\frac{3\times 1386}{5\times 1386}=\frac{4158}{6930} \\ \frac{7}{11}=\frac{7\times 630}{11\times 630}=\frac{4410}{6930} \end{gathered}$$

Now since the denominators are the same, we can compare the numerators to arrange them in ascending order.

$\frac{630}{6930}<\frac{1540}{6930}<\frac{4158}{6930}<\frac{4410}{6930}<\frac{5940}{6930}$

Therefore, ascending order $\frac{1}{10},\frac{2}{9},\frac{3}{5},\frac{7}{11},\frac{6}{7}$