Question

Find at least 5 numbers between 1/2 and 1/3

Answer 1

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Answer 2

The five rational numbers between $\bold{\frac{1}{2} \text { and } \frac{1}{3} \text { are } \frac{13}{36}, \frac{14}{36}, \frac{15}{36}, \frac{16}{36}, \frac{17}{36}}$.  

To find the rational numbers between $\frac{1}{2} \text { and } \frac{1}{3}$

The first step is to change the fractions in to like fractions.

To change the fractions in to like fractions  

Take Least Common Multiple (LCM) for two fractions  

The LCM of 2 and 3 is 6  

$\frac{1}{2}=\frac{1 \times 3}{2 \times 3}=\frac{3}{6} \quad \text { and } \quad \frac{1}{3}=\frac{1 \times 2}{3 \times 2}=\frac{2}{6}$

Hence the fraction becomes $\frac{3}{6} \text { and } \frac{2}{6}$

From this it is not possible to find five rational numbers between them.  

Multiplying numerator and denominator by 6 from the  

$\begin{array}{l}{\frac{3}{6} \times \frac{6}{6}=\frac{18}{36}} \\ {\frac{2}{6} \times \frac{6}{6}=\frac{12}{36}}\end{array}$

From this we can write 5 rational numbers  

∴ 5 numbers between $\frac{12}{36} \text { and } \frac{18}{36} \text { can be }=\frac{13}{36}, \frac{14}{36}, \frac{15}{36}, \frac{16}{36}, \frac{17}{36}$.

Hence , 5 numbers between $\bold{\frac{1}{2} \text { and } \frac{1}{3} \text { are } \frac{13}{36}, \frac{14}{36}, \frac{15}{36}, \frac{16}{36}, \frac{17}{36}}$.