# Find a rational number between 1/2 and 3/4

In arithmetic, **a rational number **is one that can be written as the quotient **p⁄q** of two numbers with **q ≠ 0**. The set of rational numbers also contains all integers, which can be represented as a quotient with the integer as the numerator and 1 as the denominator. Rational numbers are either terminating or recurring decimals in decimal form.

**Examples of Rational Numbers**

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1/2, 1/5, 3/4, and so on are some examples of rational numbers. 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.

### Find a rational number between 1/2 and 3/4

**Solution:**

Approach 1:Let us follow the first approach to find out the rational number between 1⁄2 and 3⁄4.

The equivalent fraction for 1⁄2 can be 2⁄4 and for 3⁄4 can be 6⁄8.

Now, the numbers are 2⁄4 and 6⁄8, so the required rational number can be in between these numbers.

The numerator and denominator of the required number should be between the given number, i.e., numerator can be 3 and denominator can be 5.

Hence, the rational between 1⁄2 and 3⁄4 is

3⁄5.

Approach 2:Let us follow the second approach to find out the rational number between 1⁄2 and 3⁄4.

The formula to calculate the mean is given as:

m = sum of the terms/number of the termsHere, the given terms are 1⁄2 and 3⁄4, so the mean is:

m = ((1 ⁄ 2) + (3 ⁄ 4)) / 2 = 5 / 8

Hence, the rational number between 3 and 4 is

5/8.

### Similar Questions

**Problem 1: What is the rational number between 1⁄5 and 1⁄4?**

**Solution:**

Here, the given terms are 1⁄5 and 1⁄4, so the mean is:

m = ((1 ⁄ 5) + (1 ⁄ 4)) / 2 = 9 / 40

**Problem 2: What is the rational number between 3⁄8 and 1⁄3?**

**Solution:**

Here, the given terms are 3⁄8 and 1⁄3, so the mean is:

m = ((3 ⁄ 8) + (1 ⁄ 3)) / 2 = 17 / 48