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

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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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 $$\displaystyle{\frac{{{2}}}{{{3}}}}$$.