# What are the ways to calculate the difference between fractions where

What are the ways to calculate the difference between fractions where the denominators are different?
For example,
$$\displaystyle{\frac{{{4}}}{{{9}}}}{\frac{{{27}}}{{{54}}}}$$

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Kara Dillon
Step 1
To calculate the difference between fractions where the denominators are different, write the fraction with common denominators
$$\displaystyle{\frac{{{4}}}{{{9}}}}-{\frac{{{27}}}{{{54}}}}$$
In this question, the fraction have different denominator 9 and 54.
Calculate the lowest common multiple (LCM) of 9 and 54.
Multiple of $$\displaystyle{9}={9},{18},{27},{36},{45},{54},{63}$$ .........
Multiple of $$\displaystyle{54}={54},{108},{162}$$ .........
The LCM is 54.
Calculate the equivalent of each fraction with the denominator 54.
Multiply numerator and denominator of $$\displaystyle{\frac{{{4}}}{{{9}}}}$$ by 6.
Step 2
$$\displaystyle{\frac{{{4}}}{{{9}}}}={\frac{{{4}\times{6}}}{{{9}\times{6}}}}$$
$$\displaystyle={\frac{{{24}}}{{{54}}}}$$
In term $$\displaystyle{\frac{{{27}}}{{{54}}}}$$ is already contains 54 in denominator.
$$\displaystyle{\frac{{{4}}}{{{9}}}}-{\frac{{{27}}}{{{54}}}}={\frac{{{24}}}{{{54}}}}-{\frac{{{27}}}{{{54}}}}$$
$$\displaystyle={\frac{{{24}-{27}}}{{{54}}}}$$
$$\displaystyle=-{\frac{{{3}}}{{{54}}}}$$
$$\displaystyle=-{\frac{{{1}}}{{{18}}}}$$
Answer $$\displaystyle-{\frac{{{1}}}{{{18}}}}$$.