Question

Convert the following fractions into like fractions.

$3\frac{5}{6},1\frac{1}{9},1\frac{7}{12}$

Answer 1

Step 1: Converting mixed fractions into improper fractions

Given fraction are $3\frac{5}{6},1\frac{1}{9},1\frac{7}{12}$

$$\begin{gathered} 3\frac{5}{6}=\frac{6\times 3+5}{6}=\frac{18+5}{6}=\frac{23}{6} \\ 1\frac{1}{9}=\frac{9\times 1+1}{9}=\frac{9+1}{9}=\frac{10}{9} \\ 1\frac{7}{12}=\frac{12\times 1+7}{12}=\frac{12+7}{12}=\frac{19}{12} \end{gathered}$$

The improper fractions are $\frac{23}{6},\frac{10}{9},\frac{19}{12}$.

Step 2: Converting the fractions into like fractions

To express these fractions as like fractions, we must make all the denominators the same by taking the LCM of all the denominators, that is $6,9$ and $12$.

$$\begin{gathered} 6=2\times 3 \\ 9=3\times 3 \\ 12=2\times 2\times 3 \end{gathered}$$

From the above choose each factor with the highest factor.

LCM$\left(6,9,12\right)=2\times 2\times 3\times 3$

LCM$\left(6,9,12\right)=36$

Now make the denominators as $36$ for all the fractions.

$$\begin{gathered} \frac{23}{6}=\frac{23\times 6}{6\times 6}=\frac{138}{36} \\ \frac{10}{9}=\frac{10\times 4}{9\times 4}=\frac{40}{36} \\ \frac{19}{12}=\frac{19\times 3}{12\times 3}=\frac{57}{36} \end{gathered}$$

Therefore, the like fractions are $\frac{138}{36},\frac{40}{36},\frac{57}{36}$