Question

Insert five rational number between 1/3and2/3

Answer 1

CONCEPT OF RATIONAL NUMBERS

These numbers are in p/q form where q is not equal to 0.

There is infinite number of rational number between any two rational numbers.

e.g. 1.5 is in between 1 and 2

1.25 is in between 1 and 1.5

*Even in such questions every student would get different and unique answers

METHOD - 1

Add both the no. and divide it by 2. Again follow same procedure with obtained result to get more rational numbers.

1/3 & 2/3

= (1/3 + 2/3) ÷ 2

= 1/2

we got one result and we would be following it as;

(1/2 + 1/3) ÷ 2

= 5/6÷2

= 5/12

again,

(1/2 + 2/3) ÷ 2

= 7/6 ÷ 2

= 7/12

again, (7/12 + 2/3)/2 = 15/12÷2 = 15/24

= 5/8

and similarly,

(5/12 + 1/3)÷2 = 9/12÷2 = 9/24 = 3/8

Ans is 3/8, 5/8, 1/2, 7/12 and 5/12

METHOD-2

We would be simply write the decimal intermediates like

1/3 = 0.3333333....

2/3 = 0.6666666....

so numbers in between these can be,

0.34,0.35...,0.4, 0.456...., 0.5555,0.5, 0.567,0.6, 0.62,0.65777 .

you can choose any of your wish