What are the ways to calculate the difference between fractions where

nuais6lfp 2021-11-21 Answered
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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Expert Answer

Kara Dillon
Answered 2021-11-22 Author has 84 answers
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 \(\displaystyle-{\frac{{{1}}}{{{18}}}}\).
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