Question

Arrange the following in ascending order.

$\frac{4}{5},\frac{7}{11},\frac{9}{16},\frac{6}{8},\frac{5}{12}$

Answer 1

Given fractions,

$\frac{4}{5},\frac{7}{11},\frac{9}{16},\frac{6}{8},\frac{5}{12}$

To arrange the ascending order, first, we have to find the LCM of denominators $\left(5,11,16,8,12\right)$

$$\begin{gathered} 5=5\times 1 \\ 11=11\times 1 \\ 16=2\times 2\times 2\times 2 \\ 8=2\times 2\times 2 \\ 12=2\times 2\times 3 \end{gathered}$$

Choose each factor with the highest exponent.

LCM$\left(5,11,16,8,12\right)$$=$$2\times 2\times 2\times 2\times 3\times 5\times 11$

LCM$\left(5,11,16,8,12\right)$$=$$2640$

Now we have to make the denominators equal.

$$\begin{gathered} \frac{4}{5}=\frac{4\times 528}{5\times 528}=\frac{2112}{2640} \\ \frac{7}{11}=\frac{7\times 240}{11\times 240}=\frac{1680}{2640} \\ \frac{9}{16}=\frac{9\times 165}{16\times 165}=\frac{1485}{2640} \\ \frac{6}{8}=\frac{6\times 330}{8\times 330}=\frac{1980}{2640} \\ \frac{5}{12}=\frac{5\times 220}{12\times 220}=\frac{1100}{2640} \end{gathered}$$

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

$\frac{1100}{2640}<\frac{1485}{2640}<\frac{1680}{2640}<\frac{1980}{2640}<\frac{2112}{2640}$

Therefore, ascending order $\frac{5}{12},\frac{9}{16},\frac{7}{11},\frac{6}{8},\frac{4}{5}$