Difference Between Fraction and Rational Numbers: Definitions, Examples, Similarities, and Sample Questions

Difference Between Fraction and Rational Number Overview

In mathematics, the two most widely used terms are fractions and rational numbers. They frequently confuse people due to their similar appearances. Although the conceptions of these critical mathematical components are linked in some ways, they differ significantly. Furthermore, a fraction can only include positive or full integers. A rational number, on the other hand, can contain both negative and positive integers.

Difference Between Fraction and Rational Numbers Definitions

Fraction

A fraction is any number of the type a/b, where a and b are both whole numbers, as is b≠0. It denotes a portion of a whole or any number of equal portions. It may alternatively be defined as the ratio of two integers, where the higher number (numerator) indicates the number of equal parts into which the whole is split and the lower number (denominator) indicates the number of equal parts into which the whole is divided. In other words, a fraction is a divisional expression in which the divisor and dividend are integers and the divisor is not equal to zero. 

Rational Number

A rational number, on the other hand, is a number with the form p/q, where both "p" and "q" are integers and q≠0. A rational number can alternatively be expressed as a/b, where b is not zero and a and b are integers.

Difference Between Fraction and Rational Number Examples

Examples of Fractions

In mathematics, fractions or fractional numbers are classified into several categories. Here are some instances of each type-

1. Proper fractions have a numerator that is always less than the denominator. For example, 2/5 and 5/9.
2. Improper fractions have a numerator that is always greater than the denominator. For example, 10/7 and 3/8.
3. Mixed Fractions: These are fractions that are made up of a whole number and a fraction.  For example, 3¾ and 5⅓.
4. Equivalent fractions have numerators and denominators that can be divided by the same number.  For example, 2/4 and 3/6 are equivalent fractions, because they are both equal to the ½.
5. Similar Fractions: These are fractions that have the same denominator. For example, 4/5; 2/5.
6. Differentiating Fractions: These are fractions with various denominators. For Example, 3/5; 15/13.

Examples of Rational number

1. Rational numbers may be found in four different forms: integers, whole numbers, natural numbers, and fractions. Some examples are provided below based on this knowledge. 
2. The number 8 is a rational number because it may be expressed as the fraction 8/1.
3. Because 3/4 is a rational number, we can express it as a fraction.
4. We can write 1.5 as a 3/2 ratio. As a result, it is also a rational number.
5. 0.333... is also known as 1/3. As a result, it is a rational number.
6. All recurring decimals, such as 0.262626..., all finite decimals, and all integers are rational numbers.

Read more about Rational Numbers.

Difference Between Fraction and Rational Numbers Similarities

The following are some of the similarities between fractions and rational numbers-

1. Real numbers include both fractions and rational numbers.
2. Both fractions and rational numbers are mathematically represented as ratios of numbers.
3. A non-zero denominator exists in both fractions and rational numbers.

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Why is it that every fraction is a rational number but not the other way around?

All fractions may be called rational numbers, but not all rational numbers can be called fractions. Only rational numbers with positive integers "p" and "q" are called fractions. Allow a/b to be any fraction. a and b are now natural numbers. Because all natural numbers are integers, a and b are integers as well. Thus, a/b is the quotient of two numbers, such that b = 0. As a result, a/b is a rational number. One example of a number that is a rational number but not a fraction is- Take a look at the fraction 12/-32. Because the denominator (n) is not a natural number, it is a rational number but not a fraction.

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Difference Between Fraction and Rational Numbers

A fraction is always a rational number because it always has positive integers in its ratio, which is possible for a rational number as well. But not all rational numbers are fractions because not all of them have positive integers in their ratio. So, the integers that only have positive integers in them can be considered fractions; otherwise, they cannot. 

The following table gives details about the difference between fractions and rational numbers-

NOTE:- Both are real numbers.

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Is it true that every Rational Number is a Fraction?

Because a rational number is defined as the ratio of integers, it cannot be considered a fraction. As a result, if we take the ratio of a negative integer to a positive integer, such as - 4/9 or - 31/70, we do not receive a fraction since a fraction can only be the ratio of two whole numbers, and all whole numbers are positive. As a result, it is possible to deduce that no rational number can be a fraction.

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Sample Questions for the Difference Between Fraction and Rational Number

Sample Question 1: There are 27 male instructors and 19 female teachers at Green Valley School. What percentage of the total number of instructors are female?

Ans. The fraction's numerator (p) equals the number of female instructors, and the fraction's denominator (q) equals the total number of instructors in the school. So, the fraction of female teachers is the number of female teachers divided by the total number of instructors.

= 19/ (27 + 19)

= 19/46

Sample Question 2: What distinguishes a fraction from a rational number? Use an example to demonstrate.

Ans. A fraction is a portion of a whole number, but a rational number can be a portion of any whole number. For example, 5/5 is unquestionably a rational number but not a fraction.

Consider the following example: 24/-68. Let us now determine if it is a fraction of a rational number. The denominator of the number 24/-68 is negative, indicating that it is not a natural number, whereas a number considered to be a fraction of its denominator is a natural number. As a result, it is evident that the number 24/-68 is a rational number rather than a fraction.

Sample Question 3: The number 6½ is a mixed fraction. Determine whether or not it is a rational number.

Ans. 13/2 is the simple form of 6½.

Where,

13 is an integer in the numerator, and 2 in the denominator is an integer that is not equal to zero (0). As a result, we may conclude that 6½ = 7/2 is a rational number.

Sample Question 4: Give an example of the difference between a fraction and a rational number. 

Ans. A fraction is always a rational number since it has positive integers in its ratio, which a rational number can also have. However, not all rational numbers are fractions since their ratios do not always contain positive integers. As a result, integers that only include positive integers can be deemed fractions; otherwise, they cannot. Both a fraction and a rational number have the same representation, which is in ratio form or a/b form, and neither can have zero as their denominator. The major distinction between the two terms is that a fraction may only contain whole numbers or positive integers, but a rational number can contain both positive and negative integers.

Sample Question 5: Determine whether the number 8 is a rational number, a fraction, or both.

Ans. 8 is a fraction since it may be stated as 16/2, which is a positive number ratio. It is also a rational number. However, if it is taken as 8, it is not a fraction. As a result, 8 represented as 16/2 is both a fraction and a rational number.

Sample Question 6: Rita brought a total of 35 chocolates to distribute for her birthday. 10 chocolates were distributed, with the remaining 8 remaining with her. What is the percentage of chocolates remaining with her? 

Ans. There were 25 chocolates left here. She brought a total of 35 chocolates with her. In its simplest form, the fraction would be 25/35 or 5/7.

Sample Question 7: Identify the following number as a rational number fraction. 7/7.

Ans. Because the denominator is non-zero, 7/7 is a rational number. It is not, however, a fraction because it does not meet the criteria of being a portion of a whole. As a result, 7/7 is a rational number.

Points to Remember

1. A fraction's ratio can only contain whole numbers or positive integers.
2. A rational number is written as a series of fractions, but unlike fractions, it can contain both positive and negative integer ratios.
3. All rational numbers are fractions, but not all fractions are rational numbers.
4. Rational numbers with only positive integers in their ratio are fractions; otherwise, they are not.
5. Their representations are the same, but they are completely different.
6. A rational number may always be a fraction, but a fraction cannot always be a rational number.