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

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. 

Examples of Rational Numbers

3, 4, 5, and so on are some examples of rational numbers as they can be expressed in fraction form as 3/1, 4/1, and 5/1. 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 the 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.

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

Solution:

Approach 1:

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

The equivalent fraction for −2⁄5 can be −4⁄10 and for 1⁄2 can be 5⁄10.

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

The ratio of numerator and denominator of the required number should be between the given number.

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.

The formula to calculate the mean is given as:

m = sum of the terms/number of the 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.

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