Are mixed numbers rational numbers?

Last Updated : 23 Jun, 2022

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Rational numbers are the numbers or fractions that can be represented in the form of x/y, where x and y are integers and y is not equal to zero i.e. (y ≠0). Most people have difficulty distinguishing between fractions and rational numbers because of the fundamental structure of numbers, the x/y form. When a rational number is divided then the result will be a decimal value that can be either terminated or repeated.

Rational numbers include 55, -20, 15, -15, 4, and so on, which can be expressed as 55/1, -20/1, and 4/1, respectively.

A rational number is a type of real number with the formula x/y where y does not equal zero (y ≠0). When a rational number is divided, the result is a decimal number that can be terminated or repeated infinitely.

The conditions below are helpful to identify if a number is rational or not.

It is written in the form x/y, where y≠0.
The x/y ratio can be simplified further and represented in decimal form.

Rational numbers are the sets of

Positive, negative, and zero numbers are included in the set of rational numerals
They can be expressed as a fraction.

Examples of Rational Numbers are: 6/5, 4/9, -2/6, etc

Mixed Numbers

The fraction that has both a whole number and a fractional part is termed a Mixed fraction. It can be formed by combining a whole number and a fraction. A mixed fraction is a fraction that is expressed by its quotient and remainder.

Example: $5{\Large\frac{2}{4}}$ is a mixed fraction in which 5 is the quotient and 2 is the remainder. Therefore, A mixed fraction is the product of a whole number and a proper fraction.

Are Mixed numbers rational numbers?

Solution:

A rational number is a type of real number with the formula a/b where b does not equal zero (b ≠0). When a rational number is divided, the result is a decimal number that can be terminated or repeated.

An Improper Fraction, which is a quotient of two integers, can be expressed as a Mixed Fraction with both Integer and Fractional Parts. Therefore , we can say that every Mixed Fraction can be expressed as a Rational Number.

For Example:

$6{\Large\frac{4}{5}}$ is a mixed fraction or mixed number and it can be re-written as 34/5. Here, 34/5 is in form of improper fraction. All decimals which are either terminating or showing repeating pattern after some point are rational numbers, therefore 34/5 is rational number .

Sample Problems

Problem 1: Identify $32{\Large\frac{3}{4}}$ mixed number is rational or not ?

Solution:

A mixed fraction is a fraction that has both a whole number and a fractional part. A mixed fraction is one that is formed by combining a whole number and a fraction. A mixed fraction is fractionn which is expressed by its quotient and remainder.

here , $32{\Large\frac{3}{4}}$ we can write it as : 131/4 in fraction therefore it is rational number .

Problem 2: Is $3{\Large\frac{1}{3}}$ mixed number is rational number or not ?

Solution:

A mixed fraction is a fraction that has both a whole number and a fractional part. A mixed fraction is one that is formed by combining a whole number and a fraction. A mixed fraction is fractionn which is expressed by its quotient and remainder.

here , $3{\Large\frac{1}{3}}$ we can write it as : 10/3 in fraction therefore it is rational number .

Problem 3: Is $12{\Large\frac{2}{5}}$ mixed number a rational number or not?

Solution:

A mixed fraction is a fraction that has both a whole number and a fractional part. A mixed fraction is one that is formed by combining a whole number and a fraction. A mixed fraction is fractionn which is expressed by its quotient and remainder.

here , $12{\Large\frac{2}{5}}$ , we can write it as : 62/5 in fraction therefore it is rational number .

Problem 4: Examine whether $4{\Large\frac{2}{7}}$ is a rational number or not?

Solution:

A rational number is a type of real number with the formula a/b where b does not equal zero (b ≠0). When a rational number is divided, the result is a decimal number that can be terminated or repeated.

A mixed fraction is a fraction that has both a whole number and a fractional part. A mixed fraction is one that is formed by combining a whole number and a fraction. A mixed fraction is fractionn which is expressed by its quotient and remainder.

here , $4{\Large\frac{2}{7}}$ , we can write it as : 30/7 in fraction therefore it is rational number .

Problem 5: Examine whether $5{\Large\frac{5}{7}}$ is a rational number or not?

Solution:

A rational number is a type of real number with the formula a/b where b does not equal zero (b ≠0). When a rational number is divided, the result is a decimal number that can be terminated or repeated.

A mixed fraction is a fraction that has both a whole number and a fractional part. A mixed fraction is one that is formed by combining a whole number and a fraction. A mixed fraction is fractionn which is expressed by its quotient and remainder.

here , $5{\Large\frac{5}{7}}$ , we can write it as : 40/7 in fraction therefore it is rational number .

Problem 6: Examine whether $7{\Large\frac{2}{6}}$ is a rational number or not?

Solution:

A rational number is a type of real number with the formula a/b where b does not equal zero (b ≠0). When a rational number is divided, the result is a decimal number that can be terminated or repeated.

A mixed fraction is a fraction that has both a whole number and a fractional part. A mixed fraction is one that is formed by combining a whole number and a fraction. A mixed fraction is fractionn which is expressed by its quotient and remainder.

here , $7{\Large\frac{2}{6}}$ , we can write it as : 44/6 in fraction therefore it is rational number .

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