Insert three fractions between \[\dfrac{2}{5}\] and \[\dfrac{4}{9}\].

Hint: We need to find three fractions in between the given fractions. Mathematically, fractions are used to represent ratios and division. Adding the numerator and the denominator of the two given fractions gives another fraction. And by repeating this method , we can find the three fractions between the given fractions.

Complete answer:
We need to find the fractions between \[\dfrac{2}{5}\] and \[\dfrac{4}{9}\]
First we can find the fraction between \[\dfrac{2}{5}\ \] and \[\dfrac{4}{9}\] by adding the numerator and the denominator,
\[\dfrac{2 + 4}{5 + 9} = \dfrac{6}{13}\]
By simplifying,
We get,
 \[\dfrac{3}{7}\]
The first fraction between \[\dfrac{2}{5}\ \] and \[\dfrac{4}{9}\] is \[\dfrac{3}{7}\]
Now we can obtain the next fraction between \[\dfrac{2}{5}\ \] and \[\dfrac{3}{7}\]
 \[\dfrac{2 + 3}{5 + 7} = \dfrac{5}{12}\]
Therefore the second fraction is \[\dfrac{5}{12}\]
Now we can obtain the next fraction between \[\dfrac{3}{7}\] and \[\dfrac{4}{9}\]
\[\dfrac{3 + 4}{7 + 9} = \dfrac{7}{16}\]
Therefore the third fraction is \[\dfrac{7}{16}\]
Hence the three fraction between \[\dfrac{2}{5}\] and \[\dfrac{4}{9}\] are \[\dfrac{3}{7}\ ,\dfrac{5}{12}\ ,\dfrac{7}{16}\]
Final answer :
The three fraction between \[\dfrac{2}{5}\] and \[\dfrac{4}{9}\] are \[\dfrac{3}{7}\ ,\dfrac{5}{12}\ ,\dfrac{7}{16}\].

Note:
Fraction basically represents the whole part or a number of equal parts . Generally the fraction consists of numerator and denominator, both numerator and denominator are natural numbers. There are many types of fractions namely proper fraction, improper fraction ,etc… .