Question

Compare the rational numbers and choose the correct option.

$\frac{2}{5}$___$\frac{3}{4}$

• A. Cannot be determined
• B. >
• C. =
• D. <

Answer 1

The correct option is D

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To compare two rational numbers we make their denominators equal and then compare their numerators.
LCM of the denominators 4 and 5 is 20.

$\frac{2\times 4}{5\times 4}=\frac{8}{20}$

$\frac{3\times 5}{4\times 5}=\frac{15}{20}$

$\text{Comparing}\frac{8}{20}\text{and}\frac{15}{20},$

$\text{we see that}\frac{8}{20}<\frac{15}{20}$

$\text{Hence,}\frac{2}{5}<\frac{3}{4}$.