Question

find six rational number between one by two and two by three​

Answer 1

Given two rational numbers $\frac{1}{2}$ and $\frac{2}{3}$ and we are required to find six rational numbers between the two numbers.

To find six rational numbers, we need to multiply $7$ on both the numerator and the denominator.

So, we get $\frac{1\times7}{2\times7}\:and\: \frac{2\times7}{3\times7}$.

$= \frac{7}{14} \: and \: \frac{14}{21}$

Here, the LCM of $14$ and $21$ is $42$.

$\frac{7 \times 3}{14 \times 3} \: and \: \frac{14 \times 2}{21 \times 2}$

$\frac{21}{42} \: and \: \frac{28}{42}$

So, the six rational numbers between $\frac{1}{2}\:and\: \frac{2}{3}$ are $\frac{22}{42} \frac{23}{42} \frac{24}{42} \frac{25}{42} \frac{25}{42}\: and \: \frac{26}{42}$.

Answer 2

Step-by-step explanation:

Given two rational numbers \frac{1}{2}

2

1

and \frac{2}{3}

3

2

and we are required to find six rational numbers between the two numbers.

To find six rational numbers, we need to multiply 77 on both the numerator and the denominator.

So, we get \frac{1\times7}{2\times7}\:and\: \frac{2\times7}{3\times7}

2×7

1×7

and

3×7

2×7

.

= \frac{7}{14} \: and \: \frac{14}{21}=

14

7

and

21

14

Here, the LCM of 1414 and 2121 is 4242 .

\frac{7 \times 3}{14 \times 3} \: and \: \frac{14 \times 2}{21 \times 2}

14×3

7×3

and

21×2

14×2

\frac{21}{42} \: and \: \frac{28}{42}

42

21

and

42

28

So, the six rational numbers between \frac{1}{2}\:and\: \frac{2}{3}

2

1

and

3

2

are \frac{22}{42} \frac{23}{42} \frac{24}{42} \frac{25}{42} \frac{25}{42}\: and \: \frac{26}{42}

42

22

42

23

42

24

42

25

42

25

and

42

26

.