Question

Insert six rational number between 1/2 and 2/5

Answer 1

Answer:

• 1/2 and 2/5

LCM is 10

1/2 × 5/5 = 5/10

2/5 × 2/2 = 4/10

There are not enough rational number between them

5/10 × 3/3 = 15/30

4/10 × 3/3 = 12/30

Rational number between them are 13/30, 13/30.

Step-by-step explanation:

# Hope it help.

Answer 2

Given: Two rational numbers-  $\frac{1}{2}$ and $\frac{2}{5}$

To find: Six 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 5 = 10

To convert the rational numbers with same denominators, we have

$\frac{1}{2} = \frac{1}{2}$ × $\frac{5}{5} = \frac{5}{10}$ and $\frac{2}{5} = \frac{2}{5}$ × $\frac{2}{2} = \frac{4}{10}$

To insert six rational numbers, we need to multiply both numerator and denominator of each rational number by 6 + 1 i.e., 7.

We get  $\frac{4}{10} = \frac{4}{10}$ × $\frac{7}{7} = \frac{28}{70}$ and $\frac{5}{10} = \frac{5}{10}$ × $\frac{7}{7} = \frac{35}{ 70}$

We see that 29, 30, 31, 32, 33 and 34 are six integers between 28 and 35.

i.e.,  $\frac{28}{70} < \frac{29}{70} < \frac{30}{70} < \frac{31}{70} < \frac{32}{70} < \frac{33}{70} < \frac{34}{70} < \frac{35}{70}$

Hence, six rational numbers between $\frac{1}{2} \ and \ \frac{2}{5}$ are:

$\frac{29}{70}, \frac{30}{70}, \frac{31}{70}, \frac{32}{70}, \frac{33}{70} \ and \ \frac{34}{70}$