Question

the rational number lies between 3/7 and 2/3 is (a) 2/5 (b) 4/7 (c)3/7 (d)2/3

Answer 1

LCM of 3,7 =21

3/7=9/21

2/3=14/21

Between 9/21 and 14/21 =10/21, 11/21, 12/21, 13/21

Now only 12/21 can be reduced

So, 12/21=4/7

Therefore, 4/7 lies between 3/7 and 2/3

Answer 2

The rational number that lies between $\frac{3}{7}$ and $\frac{2}{3}$ is $\frac{4}{7}$. (option b)

Given,

Fractions: $\frac{3}{7}$ and $\frac{2}{3} .$

To find,

The rational number that lies between given fractions.

Solution,

Here, it can be seen that two fractions are given, which are,

$\frac{3}{7}$ and $\frac{2}{3} .$

To find the rational number between these 2, first, we have to convert the given unlike fractions into like fractions.

Since the LCM of 7 and 3 is 21, the given fractions can be written as

$\frac{3}{7}=\frac{3 \times 3}{7 \times 3}=\frac{9}{21}$

$\frac{2}{3} = \frac{2 \times 7}{3 \times 7} =\frac{14}{21}$

Now, we can see that the rational numbers between $\frac{9}{21}$ and $\frac{14}{21}$ or, between $\frac{3}{7}$ and $\frac{2}{3}$ will be

$\frac{10}{21},\frac{11}{21},\frac{12}{21},\frac{13}{21}.$

Among the above fractions, we can see,

$\frac{12}{21}=\frac{4}{7} ,$ and it is the only fraction that could be further simplified.

So, $\frac{4}{7}$ is the required fraction.

Therefore, the rational number that lies between $\frac{3}{7}$ and $\frac{2}{3}$ is $\frac{4}{7}$. (option b)

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