Difference Between Fraction and Rational Numbers: Explanation with Examples

Fractions and rational numbers are widely used terms in mathematics. Though fractions and rational numbers have certain things in common, or they are closely related such as for their representation, however, in reality, they are different from each other. It should always be noted that “a fractional number is always a rational number but a rational number may or may not be a fractional number”. Moreover, a fraction can only include the positive or whole Integers. On the other hand, a rational number can have both negative and positive integers in it. Here we will be discussing more the difference between fractions and rational numbers along with some examples and important questions.

Keyword takeaways: Fraction, rational numbers, integers, the difference between fractions and rational numbers.

Read More: Probability

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What is a Fraction?

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A fraction can be considered as two numbers arranged in form of a ratio, such as a/b where b is not equal to zero and both ‘a’ and ‘b’ are whole numbers. The upper number is called the numerator and the lower number is called the denominator. Moreover, it is usually taken as a part of anything whole or complete.

For example, consider a box of candies containing 20 candies of which 10 were handed over to one child and 5 to another. So the fraction given to the first child would be 10/20 (or ½, in simplest form) and 5/20 ( or ¼ ) to the second child. Some more examples of fractions: 2/5, 21/7, 8/10, and so on.

Also read: Multiplication and Division of Integers

Examples of Different Types of Fractions

Fraction or fractional numbers are divided into many types in mathematics. Here are some of the types with examples:

• Proper Fractions: In such fractions, the numerator is always smaller than the denominator. Example, 2/5 and 5/9.
• Improper fractions: In such fractions, the numerator is always larger than the denominator. Example, 10/7 and 3/8.
• Mixed Fractions: Such fractions are composed of a whole number and a fraction. Example, 3 (5/2) and 5 (3/7).
• Equivalent Fractions: In these fractions whose numerators and denominators can be divided by the same number. Example, 2/12 = 3/18 and 2/4 = 10/20.
• Like Fractions: These are the fractions with the same denominators. Example, 4/5; 2/5. 
• Unlike Fractions: These are the fractions with different denominators. Example, 3/5; 15/13.

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What are Rational Numbers?

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A rational number can be thought of as a ratio of two numbers in the form p/q where 'q' is not equal to zero and both 'p' and 'q' are integers (could be both negative or positive). Any number that is expressed in the form of a fraction is rational. Other than that it can be a whole number, a number with decimal which can further be expressed as a fraction, a natural number, or any integer. Some examples of rational numbers: 2/5, -10/2, -2/2, 0.2626, 1.5, and so on.

Also read: Rational number

Examples of Rational Numbers

Generally, rational numbers can appear in four forms- integers, whole numbers, natural numbers, and fractions. Based on this information, some of the examples are given below.

• Since the number 8 can be written as fraction 8/1, it will be a rational number.
• we can write 3/4 as a fraction since it is a rational number.
• We can write 1.5 as the ratio of 3/2. Therefore, it is also a rational number
• O.333...can be written as 1/3. Hence it is a rational number
• Recurring decimals like 0.262626..., all finite decimals, as well as all integers are also rational numbers.

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Difference between Fraction and Rational Number

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The representation for both, a fraction and a rational number is the same which is in a ratio form or a/b form and both cannot have zero as their denominator. But the main difference between both the term is, a fraction can only have whole numbers or positive integers in it whereas a rational number can have both positive and negative integers in it.

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Note: A fraction can always be a rational number but a rational number cannot always be 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 as fractions otherwise not.

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Things to Remember

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• A fraction can only have whole numbers or positive integers in its ratio.
• A rational number is expressed as fractions but unlike fractions, they can have both positive and negative integer ratios.
• All fractions are rational numbers but all rational numbers are not fractions.
• The rational numbers which only have positive integers in their ratio are fractions otherwise not.
• Their representation is the same but they differ from each other wholly.
• A fraction can always be a rational number but a rational number cannot always be a fraction.

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