Question

Arrange the given fractions in ascending order of magnitude.​

$\frac{9}{16}$,$\frac{7}{12}$,$\frac{1}{4}$

Answer 1

Step 1: Finding LCM of all the numerators of all fractions​

$\begin{array}{cc}3& 9,7,1\\ 3& 3,7,1\\ 7& 1,7,1\\ & 1,1,1\end{array}$

$\therefore$ LCM of $9,7,1=3\times 3\times 7=63$

Step 2: Making the numerators of all the fraction same

$\Rightarrow \frac{9}{16}=\frac{9\times 7}{16\times 7}=\frac{63}{112}$

$\Rightarrow \frac{7}{12}=\frac{7\times 9}{12\times 9}=\frac{63}{108}$

$\Rightarrow \frac{1}{4}=\frac{1\times 63}{4\times 63}=\frac{63}{252}$

Step 3: Arranging all the fractions in ascending order

We know that if two or more fractions have same numerator then the fraction having smaller denominator is greater and greater denominator is smaller.

$\Rightarrow \frac{63}{252}<\frac{63}{112}<\frac{63}{108}$

$\Rightarrow \frac{1}{4}<\frac{9}{16}<\frac{7}{12}$

Hence $\frac{1}{4}<\frac{9}{16}<\frac{7}{12}$ is the required ascending order.