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Are mixed numbers rational numbers?

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  • 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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