Find a rational number between 3/5 and 2/3

A rational number between 3/5 and 2/3 is 19/30.

What are Rational Number?

A rational number is a sort of real number that has the form p/q where q ≠ 0 in mathematics. We may also classify any fraction as a rational number if the denominator and numerator are both integers and the denominator is not equal to zero. When a rational number is split, the result is a decimal number, which can be either a terminating or a recurring decimal.

The number “0” is also rational since it may be represented in a variety of ways, including 0/1, 0/2, 0/3, and so on. However, 1/0, 2/0, 3/0, and so on are irrational because they give us unlimited values.

How to Find a Rational Numbers between Two Rational Numbers?

Between two rational numbers, there exist “n” numbers of rational numbers. Two alternative approaches can be used to find the rational numbers between two rational numbers. Let’s have a look at the two distinct approaches.

Approach 1:

Calculate the equivalent fractions of the given rational numbers and calculate the rational numbers in between them. Those figures should be the necessary reasonable figures.

Approach 2:

Calculate the mean of the two rational numbers supplied. The necessary rational number should be the mean value. Repeat the method with the old and newly obtained rational numbers to find more rational numbers.

Find a Rational Number Between 3/5 and 2/3

Solution:

To find a rational number between 3/5 and 2/3 , we can take the average of these two numbers.

Average = (3/5 + 2/3)/2

To add these fractions, we need a common denominator, which is 15 in this case.

so, 3/5 × 3/3= 9/15 and 2/3 × 5/5=10/15

Now, we can add them:

9/15 + 10/15 =19/15

Now, we divide by 2 to find the average:

(19/15) / 2 = 19/15 × 1/2 = 19/30

Therefore, 19/30 is a rational number between 3/5 and 2/3.

There are infinite numbers of rational numbers between two given rational numbers is because between any two distinct rational numbers, there are infinitely many other rational numbers.

Since both the denominators and the numerators of the rational number will be integers, this makes sense. There will be no zero in the denominator. Decimal numbers that may be terminating or repeating may arise if there are any rational numbers in splits. Since zero may be expressed in a variety of ways, such as 0/1, 0/2, and others, it is thought to be rational. It won’t make sense to invert the representation to get values that are infinite, such as 1/0, 2/0, and so on.

Finding more than rational numbers between 3/5 and 2/3

In order to find more than one rational numbers between 3/5 and 2/3 , we have to considered the following solution:

To find 5 rational numbers between 3/5 and 2/3 , we have to make there denominator equal.

we need a common denominator, which is 15 in this case.

so, 3/5 × 3/3= 9/15 and 2/3 × 5/5=10/15

Now, we can see no rational number exist between 9/15 and 10/15, so we have increase the denominator of the two numbers:

lets multiply the numerator and denominator by 10

9/15 × 10/10= 90/150 and 10/15 × 10/10= 100/150

From here we can easily find 5 rational numbers between 90/150 and 100/150 ,i.e, 91/150 , 92/150, 93/150, 94/150, 95/150

Therefore, there are infinite numbers of rational numbers between two given rational numbers is because between any two distinct rational numbers, there are infinitely many other rational numbers.

Similar Questions

Question 1: What is the rational number between 1⁄2 and 1⁄4?

Solution:

Here, the given terms are 1⁄2 and 1⁄4, so the mean is:

mean = ((1 ⁄ 2) + (1 ⁄ 4)) / 2

= 3 / 8

The required rational number is 3/8.

Question 2: What is the rational number between 2⁄5 and 3⁄4?

Solution:

Here, the given terms are 2⁄5 and 3⁄4, so the mean is:

mean = {(2 ⁄ 5) + (3 ⁄ 4)}/ 2

= {(8+15)/20}/2

= 23 / 40

The required rational number is 23/40.