Find Five Rational Numbers Between 3/5 and 4/5

# Find Five Rational Numbers Between 3/5 and 4/5

## How to Find Rational Numbers Between Two Rational Numbers?

Can you find the integers between –4 and 1? They are –3, –2, –1 and 0. It is observed

that there are finite number of integers lying between two given integers.

Now, let us find the rational numbers lying between 3/10 and 7/10.

You can find that they are 4/10, 5/10 and 6/10.

You can also write 3/10 as 30/100 and 7/10 as 70/100.

Now the numbers 31/100, 32/100, 33/100, … , 69/100 are all lying between 3/10 and 7/10, i.e., there are 39 rational numbers.

In the same way, we can go on inserting more and more rational numbers between two given rational numbers. Thus, the number of rational numbers lying between two rational numbers is not finite as there are countless rational numbers lying between two given rational numbers.

Now, to find a rational number between any two given rational numbers, follow these steps:

Method 1: If and are two rational numbers and b, then ½(b) is a rational number lying between and b.

Further, a rational number between and ½(b) is ½[+ ½(b)]. Also a rational number between ½(b) and is ½[½(b) + b].

Thus, we can find infinite number of rational numbers between two given rational numbers.

Method 2: Write the given rational numbers as equivalent rational numbers by making the same denominator which is equal to the LCM of both the denominators.

Write the required number of rational numbers by choosing numbers lying between the numbers.

## Find Five Rational Numbers Between 3/5 and 4/5

Here, we will use Method 2 to find five rational numbers between 3/5 and 4/5. We should use method 1 in case we have to find 2 to 3 rational numbers between the given rational numbers. But here we have to find 5 rational numbers between 3/5 and 4/5.

Using method 2, write the equivalent rational numbers of 3/5 and 4/5 with denominator 50.

So, multiply the numerator and the denominator of 3/5 and 4/5 by 10 to get 30/50 and 40/50.

Now, five rational numbers between 30/50 and 40/50 are:

31/50, 32/50, 33/50, 34/50, 35/50

These rational numbers lie between 3/5 and 4/5.

So, five rational numbers between 3/5 and 4/5 are 31/50, 32/50, 33/50, 34/50 and 35/50.

## How many rational numbers lies between two rational numbers?

How many rational numbers can you write between 2/5 and 4/5?

Of course, we can write one rational number 3/5 between 2/5 and 4/5.

If we write the equivalent rational numbers of 2/5 and 4/5 by multiplying the numerator and the denominator of both the rational numbers by 10, we get 20/50 and 40/50.

Between 20/50 and 40/50, we write 19 rational numbers, i.e., 21/50, 22/50, 23/50, 24/50, ……., 39/50.

If we write the equivalent rational numbers of 2/5 and 4/5 by multiplying the numerator and the denominator of both the rational numbers by 100, we get 200/500 and 400/500.

Between 200/500 and 400/500, we can write 199 rational numbers, i.e., 201/500, 202/500, 203/500, 204/500, ……., 399/500.

Similarly, between 2000/5000 and 4000/5000, we can write 1999 rational numbers, i.e., 2001/5000, 2002/5000, 2003/5000, 2004/5000, ……., 3999/5000.

In the same way, we can write infinite number of rational numbers between these two rational numbers.

Thus, there are infinite rational numbers lie between two given rational numbers.