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 numbers 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. 

We can find unlimited rational numbers between two rational numbers. A number between two rational numbers can be a rational number or a whole number. A rational number is a real number that can be expressed as P/Q, where P and Q are any integers and Q ≠ 0.

When we speak about whole numbers, then between any two whole numbers, there are limited numbers only. For example, between 3 and 7, there are only three whole numbers, i.e. 4, 5 and 6. But there is no limit to finding the rational numbers between two rational numbers.

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.

There are two methods to find the rational number between other rational numbers.

Approach 1: When Denominators are Same

As we already know, the arithmetic operations on rational numbers become easy when the denominators are the same. Hence, it also applies to finding the rational numbers between two rational numbers. Follow the steps:

Step 1: Check the values on the numerators of the rational numbers

Step 2: Find by how many values, the numerators differ from each other

Step 3: Since, the denominators are the same for the two rational numbers, therefore, we can write the rational numbers between the two given rationals, in the increasing order of numerator, if the difference between the two numerators is more.

Step 4: If the difference between two numerators is less, and we need to find more rational numbers, then multiply the numerator and denominator of the given rational numbers by multiples of 10.

Approach 2: When Denominators are Different

We have already discussed above to find the rational numbers, when the given two rational numbers have the same denominators. But what if the denominators are different? Here we apply the same rule, what we have applied while finding the sum and difference of two rational numbers.

Suppose we have two rational numbers with different denominators, then follow the below steps to find the rational numbers between them.

Step 1: Find the LCM of two rational numbers first.

Step 2: Multiply and divide the two rational numbers, by the value that results in the denominators equal to the obtained LCM.

Step 3: Once the denominators become the same, follow the same rules as we have discussed for the rational numbers with the same denominators.

Finding Next Rational Numbers

To find the next rational numbers for a given pattern of rational numbers, we have to check the common factors of numerator and denominator.

Suppose the given pattern of rational numbers are: -⅓, -2/6, -3/9, -4/12,….

• -⅓
• -2/6 = -⅓ × (2/2)
• -3/9 = -⅓ × (3/3)
• -4/12 = -⅓ × (4/4)

Thus, we can see, each time, the rational number -⅓ is multiplied by increasing order of numbers both in numerator and denominator.

Hence, to find the next rational numbers, we can multiply -⅓ by 5/5, 6/6, and so on.

• -⅓ × 5/5 = -5/15
• -⅓ × 6/6 = -6/18
• -⅓ × 7/7 = -7/21

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.