Aspect	Fraction	Rational Number
Definition	Represents a part of a whole or ratio of two numbers	Any number expressible as the quotient of two integers.
Form	Written as numerator over denominator (e.g., 4/7)	Can be written in fraction form or as a decimal (e.g., 0.59)
Examples	2/5, 3/4	3/4, 0.45, -0.57
Can it be Negative?	Yes, if numerator or whole fraction is negative	Yes, if the number itself is negative
Simplicity	Fractions represent values in their simplest form, with the numerator and denominator having no common factors other than 1	Rational numbers may be expressed in various forms, some of which may not be in their simplest form
Applications	Common in everyday life	Widely used in Mathematics and Everyday life

Note: Fractions are subset of Rational Numbers.

Read: Applications of Rational Numbers

Similarities between Fraction and Rational Number

While fractions and rational numbers have distinct definitions, they share several similarities:

• Both fractions and rational numbers represent parts of a whole or ratios of two quantities.

• They can be positive, negative, or zero.

• They can be added, subtracted, multiplied, and divided using the same arithmetic operations.

Is every Fraction a Rational Number?

Yes, every fraction is indeed a rational number! This is because the definition of a rational number includes any number that can be expressed as a fraction of two integers, where the denominator is not zero. Since a fraction fits this definition perfectly (it’s literally written as a fraction of two integers), it is always considered a rational number.

For example, let’s take the fraction 2/3. This fraction represents two parts out of three equal parts. It can also be written as the rational number 0.666…, which is a repeating decimal. So, 2/3 fits the definition of a rational number because it can be expressed as the quotient of two integers.

Is every Rational Number a Fraction?

Not necessarily. While every fraction is a rational number, not every rational number is a fraction. Rational numbers include integers and non-integer values that can be expressed as the quotient of two integers. Integers, for example, are rational numbers but are not typically written in fraction form.

For example, consider the rational number 0.5. While it may not look like a fraction at first glance, it can be expressed as [Tex]\frac{1}{2}[/Tex], which is a fraction. 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.

Related:

• Whole Numbers
• Natural Numbers
• Real Numbers

Practice Questions on Fractions and Rational Numbers

Q1. Determine whether the following numbers are fractions, rational numbers, or both:

• -2/5
• 0.6
• -5
• 2/5

Q2. Express the rational number −1.25 as a fraction in simplest form.

Q3. Identify which of the following numbers are rational numbers but not fractions:

• 5/2
• 2.5
• -5/2
• -0.54

Q4. Simplify the following fraction and express it as a rational number: 12/18

Q5. Determine whether the number -8/4 is a fraction, a rational number, or both.

FAQs on Difference between Fraction and Rational Number

Can a fraction have a negative denominator?

No, a fraction cannot have a negative denominator. However, the entire fraction can be negative if the numerator is negative.

Are all integers rational numbers?

Yes, all integers are rational numbers because they can be expressed as fractions with a denominator of 1.

Is zero a rational number?

Yes, zero is a rational number because it can be expressed as 0/1, where the numerator is zero and the denominator is any non-zero integer.

What is the difference between a fraction and an irrational number?

• Fractions are subset of rational numbers that include numbers like, 1/2, 3/4. etc.
• Irrational Numbers are different from rational number and they are not represented in form of fractions they include numbers such as, √2, √3, π, etc.