Write any 5 rational numbers between -2⁄5 and ½

Five rational numbers between -2/5 and 1/2:

1. -1/4
2. -1/5
3. -1/6
4. 0
5. 1/4

Now let’s learn about rational number in brief.

What are Rational Numbers?

A rational number is a type of real number of the form p/q where q is not equal to zero in mathematics. Any fraction can be classified as a rational number if the denominator and numerator are both integers and the denominator is not zero. A decimal number, which can be either a terminating or recurring decimal, is the result of dividing a rational number. 

How to Find 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.

Approach 2:

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

Write any 5 Rational Numbers between -2⁄5 and 1/2

Approach 1:

Let us follow the first approach to find out the rational numbers between -2⁄5 and 1⁄2.

Equivalent fraction for

-2⁄5 = -4⁄10

1⁄2 = 5⁄10

Now, the numbers are -4⁄10 and 5⁄10, so the required rational number can be in between these numbers.

Hence, the five rational numbers between −2⁄5 and 1⁄2 are -3⁄10, -1⁄10, 0, 2⁄10 and 4⁄10. In decimal form, these numbers can be expressed as -0.3, -0.1, 0, 0.2 and 0.4.

Approach 2:

Let us follow the second approach to find out the rational numbers between -2⁄5 and 1⁄2.

Formula to calculate mean is:

m = sum of terms/number of terms

Here, the given terms are -2⁄5 and 1⁄2, so the mean is:

m = (-2 ⁄ 5 + 1 ⁄ 2) / 2 = 1/20 = 0.05

Now, the mean of −2⁄5 and 1⁄20 is:

m = (-2 ⁄ 5 + 1 ⁄ 20) / 2 = (-0.4 + 0.05) / 2 = -0.175

Now, the mean of -2⁄5 and -0.175 is:

m = (-0.4 −0.175) / 2 = -0.575/2 = -0.2875

Now, the mean of 1⁄2 and 1⁄20 is:

m = (0.5 + 0.05) / 2 = 0.55 / 2 = 0.275

Now, the mean of 1 ⁄ 2 and 0.275 is:

m = (0.5 + 0.275) / 2 = 0.775 / 2 = 0.3875

Hence, the five rational numbers between -2⁄5 and 1⁄2 are -0.2875, -0.175, 0.05, 0.275 and 0.3875.

Similar Questions

Problem 1: What are the three rational numbers between 4 and 7?

Solution:

Here, the given terms are 4 and 7, so the mean is:

m = (7 + 4) / 2 = 11 / 2 = 5.5

Now, the mean of 7 and 5.5 is:

m = (7 + 5.5) / 2 = 12.5 / 2 = 6.25

Now, the mean of 5.5 and 4 is:

m = (5.5 + 4) / 2 = 9.5 / 2 = 4.75

Hence, the three rational numbers between 4 and 7 are 4.75, 5.5, and 6.25.

Problem 2: What are the two rational numbers between 1 and 2?

Solution:

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

m = (1 + 2) / 2 = 3 / 2 = 1.5

Now, the mean of 1 and 1.5 is:

m = (1 + 1.5) / 2 = 2.5 / 2 = 1.25

Hence, the two rational numbers between 1 and 2 are 1.25 and 1.5.