Question

find five rational number between 1/2 and 1/3

Answer 1

find the LCM of 2&3..

LCM is 6..

1/2=3/6

1/3=2/6

now how many rational numbers u want ..
add 1 to the numbers of rational u want.....

3/6×6/6=18/36

2/6×6/6=12/36....

rational no.. between
1/3=2/6=12/36 < [13/36 < 14/36 < 15/36 < 16/36 < 17/36]<18/36=3/6=1/2



answer is in brackets...

Answer 2

Given: Two rational numbers $\frac{1}{2}$ and $\frac{1}{3}$

To find: Five rational numbers between the given numbers

Solution: The given rational numbers have different denominators. First we need to make their denominators same.

LCM of their denominators 2 and 3 = 6

To convert the rational numbers with same denominators, we have

$\frac{1}{2} = \frac{1}{2}$ × $\frac{3}{3} = \frac{3}{6}$ and $\frac{1}{3} = \frac{1}{3}$ × $\frac{2}{2} = \frac{2}{6}$

To insert five rational numbers, we need to multiply both numerator and denominator of each rational number by 5 + 1 i.e., 6.

$\frac{2}{6} = \frac{2}{6}$ × $\frac{6}{6} = \frac{12}{36}$ and $\frac{3}{6} = \frac{3}{6}$ × $\frac{6}{6} = \frac{18}{36}$

We see thet 13, 14, 15, 16 and 17 are five integers between 12 and 18.

i.e., $\frac{12}{36} < \frac{13}{36} < \frac{14}{36} < \frac{15}{36} < \frac{16}{36} < \frac{17}{36} < \frac{18}{36}$

Hence, five rational numbers between $\frac{1}{2}$ and $\frac{1}{3}$ are:

$\frac{13}{36}, \frac{14}{36}, \frac{15}{36}, \frac{16}{36} \ and \ \frac{17}{36}$