Question

# Convert each fraction into like fractions. $\frac{5}{9},\frac{12}{81},\frac{2}{27},\frac{1}{3}$

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Solution

## Step 1 : Finding the LCM of denominatorsLike 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 $\left(9,81,27,3\right)$ $9=3×3\phantom{\rule{0ex}{0ex}}81=3×3×3×3\phantom{\rule{0ex}{0ex}}27=3×3×3\phantom{\rule{0ex}{0ex}}3=3×1$From the above choose each factor with the highest exponent.LCM$\left(9,81,27,3\right)$ $=$$3×3×3×3$LCM$\left(9,81,27,3\right)$$=$$81$Step 2: Converting the fractions into like fractionsChange all fractions to equivalent fractions such that their denominators are equal to $81.$ $\frac{5}{9}=\frac{5×9}{9×9}=\frac{45}{81}\phantom{\rule{0ex}{0ex}}\frac{12}{81}=\frac{12}{81}\phantom{\rule{0ex}{0ex}}\frac{2}{27}=\frac{2×3}{27×3}=\frac{6}{81}\phantom{\rule{0ex}{0ex}}\frac{1}{3}=\frac{1×27}{3×27}=\frac{27}{81}$Therefore,$\frac{45}{81},\frac{12}{81},\frac{6}{81}$ and $\frac{27}{81}$ are like fractions.

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