Question

Convert each fraction into like fractions.

$\frac{5}{9},\frac{12}{81},\frac{2}{27},\frac{1}{3}$

Answer 1

Step 1 : Finding the LCM of denominators

Like fractions: The fractions having the same denominators are called like fractions.

Given fraction are $\frac{5}{9},\frac{12}{81},\frac{2}{27},\frac{1}{3}$

First, find the LCM of all the denominators $\left(9,81,27,3\right)$

$$\begin{gathered} 9=3\times 3 \\ 81=3\times 3\times 3\times 3 \\ 27=3\times 3\times 3 \\ 3=3\times 1 \end{gathered}$$

From the above choose each factor with the highest exponent.

LCM$\left(9,81,27,3\right)$ $=$$3\times 3\times 3\times 3$

LCM$\left(9,81,27,3\right)$$=$$81$

Step 2: Converting the fractions into like fractions

Change all fractions to equivalent fractions such that their denominators are equal to $81.$

$$\begin{gathered} \frac{5}{9}=\frac{5\times 9}{9\times 9}=\frac{45}{81} \\ \frac{12}{81}=\frac{12}{81} \\ \frac{2}{27}=\frac{2\times 3}{27\times 3}=\frac{6}{81} \\ \frac{1}{3}=\frac{1\times 27}{3\times 27}=\frac{27}{81} \end{gathered}$$

Therefore,$\frac{45}{81},\frac{12}{81},\frac{6}{81}$ and $\frac{27}{81}$ are like fractions.