Describe two general methods to determine which of two fractions is gr

Maaghu 2021-11-21 Answered
Describe two general methods to determine which of two fractions is greater. Use \(\displaystyle{\frac{{{2}}}{{{3}}}}\ {\quad\text{and}\quad}\ {\frac{{{4}}}{{{5}}}}\) to illustrate the methods.

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Expert Answer

Volosoyx
Answered 2021-11-22 Author has 1441 answers

Step 1
We will discus two methods namely "Same Denominaor Method" and "Same Numerator Method".
In same "Same Denominator Method", the fraction having larget numerator is greater.
While is "Same Numerator Method", the fraction having smaller deniminator is larger.
Step 2
Using Same Denominator Method
\(\displaystyle{\frac{{{2}}}{{{3}}}}\)
\(\displaystyle{\frac{{{2}\times{5}}}{{{3}\times{5}}}}\)
\(\displaystyle{\frac{{{10}}}{{{15}}}}\)
\(\displaystyle{\frac{{{4}}}{{{5}}}}\)
\(\displaystyle{\frac{{{4}\times{3}}}{{{5}\times{3}}}}\)
\(\displaystyle{\frac{{{12}}}{{{15}}}}\)
\(\displaystyle\Rightarrow{\frac{{{10}}}{{{15}}}}{<}{\frac{{{12}}}{{{15}}}}\)
Hence, \(\displaystyle{\frac{{{4}}}{{{5}}}}\) is greater than \(\displaystyle{\frac{{{2}}}{{{3}}}}\).
Using Same Numerator Method.
\(\displaystyle{\frac{{{2}}}{{{3}}}}\)
\(\displaystyle{\frac{{{2}\times{2}}}{{{3}\times{2}}}}\)
\(\displaystyle{\frac{{{4}}}{{{6}}}}\)
\(\displaystyle{\frac{{{4}}}{{{5}}}}\)
\(\displaystyle{\frac{{{4}}}{{{5}}}}\)
\(\displaystyle{\frac{{{4}}}{{{5}}}}\)
\(\displaystyle\Rightarrow{\frac{{{4}}}{{{6}}}}{<}{\frac{{{4}}}{{{5}}}}\)
Hence, \(\frac{4}{5}\) is greater than \(\displaystyle{\frac{{{2}}}{{{3}}}}\).

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