Question

How many rational numbers are there between 1/2 and 1/5​

Answer 1

Step-by-step explanation:

Given:-

1/2 and 1/5

To find:-

How many rational numbers are there between 1/2 and 1/5 ?

Solution:-

Given numbers are 1/2 and 1/5

The rational number between a and b is (a+b)/2

by Mean method

=>[(1/2)+(1/5)]/2

LCM of 2 and 5 = 10

=> [(5+2)/10]/2

=> (7/10)/2

=>7/(10×2)

=> 7/20

The rational number between 1/2 and 1/5 = 7/20

and

1/2 = (1/2)×(5/5)=5/10

1/5=(1/5)×(2/2)=2/10

Rational numbers between 5/10 and 2/10

3/10 and 4/10

If we do like this we get infinite number of rational numbers .

Answer:-

There are infinitely many rational numbers between 1/2 and 1/5

Used Concept:-

Densitive Property:-

There are infinitely many rational numbers between any two numbers.

Answer 2

Answer:

There are infinite rational numbers between two rational numbers.

You can find as much you want to find .

To find more than 1 rational numbers the formula is

d = b - a / n + 1 (where n is no. rational numbers required)

For example Find 4 rational numbers between 1/2 and 1/5

Step - by - step - explanation:-

Solution:-

Let a = 1/5 and b = 1/2

d = b - a / n + 1

d = (1/2 - 1/5) / 4 + 1

d = 10 - 2

--------

5

-------———

5

d = 8

—— = 8 × 1

5 ----- ——

——— 5 5

5

d = 8

---—

25

4 rational numbers between 1 and 1 are :-

—— ——

2 5

a+d , a+2d , a +3d , a + 4d

1 8 1 8 1 8 1 8

--- + --- , --- + 2 × --- , --- + 3 × --- , --- + 4 × ---

5 25 5 25 5 25 5 25

5 + 8 5 + 16 5 + 24 5 + 32

——— , ———— , ———— , ————

25 25 25 25

13 21 29 37

——— , ——— , ——— , ———

25 25 25 25

There these are 4 rational numbers between 1 and 1

—— —

2 5

You can find as much rational numbers

If you want to find then you have to write upto a +10d

If you want to find 20 the you have to write upto a +20d

I hope you have understand.