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Home > Articles > Difference Between Fraction and Rational Numbers: Definitions, Examples, Similarities, and Sample Questions
Updated on 08th August, 2023 , 6 min read
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.
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.
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.
In mathematics, fractions or fractional numbers are classified into several categories. Here are some instances of each type-
The following are some of the similarities between fractions and rational numbers-
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.
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-
Fraction | Rational Numbers |
Only whole or natural integers can be divided into fractions. | Rational numbers are those that include all of the numbers except the imaginary ones. |
Every fraction is a rational number. Numbers with no denominators have a denominator of 1. | Because fractions require both the numerator and denominator to be positive, all rational numbers are not fractions. |
Negative numbers are not classified as fractions. | Negative numbers are rational numbers as well. |
The response is not natural. | Exothermic reactions occur spontaneously. |
For Example- 16/83, 6/358, and 4/21 | For Example- 154/7, 4/-6, and -6/-12 |
NOTE:- Both are real numbers.
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.
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.
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By - Nikita Parmar 2024-09-06 10:59:22 , 6 min readAns. Although all fractions are rational numbers, not all rational numbers are fractions.
Ans. Rational numbers include 1/4, 9/-2, 12/-8, and so on. Fractions include 1/2, 1/8, 6/4, and so on.
Ans. A fraction is written as the ratio of two whole numbers, a/b and b≠0. A rational number can alternatively be written as a ratio, p/q, where the numerator and denominator are both integers and q≠0.
Ans. Proper fractions have a denominator that is bigger than the numerator. For instance, 1/2, 1/3, 1/4, 2/3, 3/4, and so on. An improper fraction is one with a numerator higher than the denominator, such as 3/2, 5/4, 7/6, and so on.
Ans. We know that a fraction is always positive in nature since it is defined as the ratio of two whole numbers, according to the distinction between fractional and rational numbers. As a result, 2/3 can be considered a fraction because both 2 and 3 are whole integers and the denominator is not 0. Also, because 2 and 3 are integers, 2/3 can be called a rational number. We also know that every fraction is a rational number; thus, 2/3 may be thought of as both a fraction and a rational number.