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 \(\displaystyle-{\frac{{{1}}}{{{18}}}}\).

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 \(\displaystyle-{\frac{{{1}}}{{{18}}}}\).