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Why are all rational numbers not fractions?

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  • Last Updated : 19 May, 2022
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The number system encompasses several sorts of numbers, such as prime numbers, odd numbers, even numbers, rational numbers, whole numbers, and so on. Numbers can be expressed by using these figures and words. For example, integers like 40 and 65 stated as figures can alternatively be written as forty and sixty-five.

Number System

A number system, often known as a numeral system, is a basic system for expressing numbers and figures. It is a one-of-a-kind method of representing numbers in arithmetic and algebraic structures. Numbers are used in various arithmetic values to carry out various arithmetic operations such as addition, subtraction, multiplication, and so on that are utilized in daily life for the purpose of computation. A number’s value is defined by its digit, its position in the number, and the number system’s base. Numbers, often known as numerals, are mathematical values used for counting, measuring, identifying, and quantifying basic quantities.

Rational Number 

Rational numbers are written in the form p/q, where p and q are integers and q≠0, because of the fundamental structure of numbers, the p/q form, most individuals have difficulties discriminating between fractions and rational numbers. When a rational number is split, the result is a decimal number that might be either ending or repeating. Examples of rational numbers are 2, 3, 4, and so on, which may be expressed in fraction form as 2/1, 3/1, and 4/1, respectively.

Fractions 

Fractions are defined as numerical figure that represents a part of a whole. A fraction is a component or section of any quantity taken from a whole, which can be any number, a specified value, or an item. All fractions are represented by a numerator and a denominator, which are separated by a horizontal bar called the fractional bar.

  • The denominator represents the number of parts into which the whole has been subdivided. It is positioned below the fractional bar at the lowest part of the fraction.
  • The numerator specifies how many fractional parts are represented or selected. It is positioned above the fractional bar at the upper part of the fraction.

Examples of fractions: 3/2, 7/4, 33/26, etc. 

Why are all rational numbers not fractions?

Answer: 

Rational numbers are written in the form p/q, where p and q are integers and q≠0 . Because of the fundamental structure of numbers, the p/q form, most individuals have difficulties discriminating between fractions and rational numbers. 

All rational numbers are not fraction because a rational number is defined as the ratio of integers, it cannot be called 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 conclude that every rational number cannot be a fraction. Example: 2/-5 is a rational number but it is not a fraction because its denominator is not a natural number. 

Sample Questions

Question 1: Is fraction 15/3 rational or not?

Answer: 

Rational numbers are written in the form p/q, where p and q are integers and q≠0 . Because of the fundamental structure of numbers, the p/q form, most individuals have difficulties discriminating between fractions and rational numbers. Here Given 15/3 , we can simplify it by dividing 15/3 is 5 , therefore 5 can be written as 5/1 hence its a fraction and rational number.

Question 2: Identify whether 3/-6 is a fraction or not?

Answer:

Fractions are defined as a numerical figure that represents a part of a whole. A fraction is a component or section of any quantity taken from a whole, which can be any number, a specified value, or an item.

Hence Given , 3/-6 can be written as 1/-2 its a rational number but its not a fraction as fraction only includes whole number and whole number does not include negative integers .

Question 3: Identify whether 16/3 is rational or fraction or both?

Answer:

Rational numbers are written in the form p/q, where p and q are integers and q≠0 . Because of the fundamental structure of numbers, the p/q form, most individuals have difficulties discriminating between fractions and rational numbers. Hence Given, 16/3 is rational number as well as fraction because both denominator or numerator are whole numbers.

Question 4: Identify from the numbers which are rational or which are fractions, 5/4, -2/3, 7/-8, 6/8, 5/10, 

Answer:

 Rational numbers : 5/4 , 6/8 , 5/10 ,-2/3 , 7/-8 all are rational numbers but not fractions. Fractions: 5/4 , 6/8 , 5/10 all are fractions as well as rational numbers.

Question 5: Is 35 a rational number?

Answer:  

Rational numbers are written in the form p/q, where p and q are integers and q≠0, because of the fundamental structure of numbers, the p/q form, most individuals have difficulties discriminating between fractions and rational numbers. Hence 35 here is a rational number as it can be expressed in form of p/q as 35/1.

Question 6: Identify whether it’s a fraction or not, if 4/-5 is a rational number?

Answer:

Rational numbers are written in the form p/q, where p and q are integers and q≠0 . Because of the fundamental structure of numbers, the p/q form, most individuals have difficulties discriminating between fractions and rational numbers. All rational numbers are not fraction because a rational number is defined as the ratio of integers, it cannot be called 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 conclude that every rational number cannot be a fraction. Hence. given 4/-5 is rational number but its not a fraction.

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