# Difference Between Fractions and Rational Numbers (2023)

Home»Difference Between Fractions and Rational Numbers: Definition, Examples

• What is the difference between fractions and rational numbers?
• What is a score?
• What are rational numbers?
• Worked example on the difference between fractions and rational numbers
• Fractions and Rational Numbers Practice Problems

## What is the difference between fractions and rational numbers?

the difference betweenrational numberyFractionSince the numerator and denominator of fractions are whole numbers$(\text{denominator} \neq 0)$, and the numerator and denominator of rational numbers are integers$(\text{denominator} \neq 0)$.

Rational numbers and fractions are two of the most used terms in mathematics. Since they look so similar, they often cause confusion. Although these basic math concepts are somewhat related, they are not the same. So what is the difference between rational numbers and fractions? We will explore in this article.

Before we understand the difference between these two terms, let's understand what fractions and rational numbers are!

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## What is a score?

Fractions represent parts of a whole. Fractions are numbers of any type.$\frac{a}{b}$, where a and b are both integers, and$b \neq 0$.

The score has two parts. The top number is called the numerator. It tells us how many equal parts have been subtracted from the whole or set. The bottom number is called the denominator. Returns the total number of equal parts of a whole or the total number of identical objects in a set.

If a circle is divided into quarters (4 equal parts), then three parts represent the fraction $\frac{3}{4}$.

If a circle is divided into 5 equal parts, the two parts represent the fraction $\frac{2}{5}$.

Depending on the value, there are different types of fractions.molecularydenominator.

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## What are rational numbers?

A rational number is a number that can be written in the form$\frac{p}{q}$, where p and q are integers and$q \neq 0$.

A rational number is any number that can be expressed as a fraction $\frac{p}{q}$ where the numerator and denominator arewhole, and the denominator is not 0. If a number cannot be represented in this way, then it is airrational number.

Any integer can be written as a rational number. Therefore, all integers are rational numbers.

For example, 5 can be represented as $\frac{5}{1}$ . Both the numerator (5) and the denominator (1) are integers and the denominator is not 0, so 5 is a rational number.

All fractions are rational numbers.

For example, $\frac{1}{2},\; \frac{4}{3}$ and $\frac{20}{450}$ are all rational numbers.

All terminal decimals are rational numbers.

For example, take the decimal number 0.5. This can be converted to $\frac{1}{2}$, which means it is a rational number.

All nonterminal but repeating decimals are rational numbers.

For example, 0.323232..., 0.6666..., etc., are all rational numbers.

## Similarities Between Fractions and Rational Numbers

• They look the same due to the similarity in rendering. Both fractions and rational numbers are expressed as ratios of numbers.
• All fractions and rational numbers are real numbers.
• Both fractions and rational numbers have a denominator of 0.

## Facts about the difference between fractions and rational numbers

• There are infinitely many rational numbers between two given integers.
• All fractions are rational numbers, but not every rational number is a fraction.
• Rational numbers that have only positive integers as numerators and denominators are fractions $(\text{denominator} \neq 0)$.
• Both fractions and rational numbers belong to the set of real numbers.
• Any positive integer (or whole number) can be written as a fraction, as long as the denominator stays at 1. More specifically, they are considered false fractions. For example: $5 = \frac{5}{1},\;9 = \frac{9}{1}$

## in conclusion

Are fractions rational numbers? The answer is yes, but not all rational numbers are fractions.

Let's tackle some examples and practice problems.

## Worked example on the difference between fractions and rational numbers

1. Identify rational numbers and fractions:$\frac{5}{4},\; \frac{-2}{3},\; \frac{7}{-8},\; \frac{6}{8},\; \frac{5}{10}$.

solution:

Rational numbers can have positive and negative integer ratios when expressed as fractions.

Therefore, $\frac{5}{4},\; \frac{6}{8},\; \frac{5}{10},\; \frac{-2}{3},\; \frac {7}{-8}$ are all rational numbers.

54 , 68 , 510 are fractions. All fractions are rational numbers. Therefore, $\frac{5}{4},\;\frac{6}{8},\; \frac{5}{10}$ are all fractions and rational numbers. $\frac{-2}{3},\; \frac{7}{-8}$ is not a fraction.

2. Determine if the following rational numbers are fractions:

(I)$\frac{1}{3}$(of the)$\frac{6}{3}$(three)$\frac{-5}{-3}$

solution:

(I)$\frac{1}{3}$

$\frac{1}{3}$ is a fraction because both the numerator (1) and denominator (3) are whole numbers. This is a unit fraction or proper fraction.

(of the)$\frac{6}{3}$

$\frac{6}{3}$ is a fraction because both the numerator (6) and denominator (3) are whole numbers. This is an incorrect punctuation.

(three)$\frac{-5}{3}$

$\frac{-5}{3}$ is not a fraction because the numerator (-5) is not an integer.

3. A drama camp has 16 art instructors and 13 drama instructors. What percentage of the total number of professors teaches drama?

solution:

Fraction Numerator $(p) =$ Number of Theater Tutors

The denominator of the fraction $(q) =$ total number of camp instructors.

Percentage of theater tutors$=$Number of drama teachers/total number of teachers

$\frac{p}{q} = \frac{13}{16 +13}$

$\frac{p}{q} = \frac{13}{29}$

4. Determine if 7 is a rational number, a fraction, or both.

solution:

7 can be expressed as $\frac{7}{1}$, which is a positive ratio. So it's a score. This is an incorrect punctuation. It is also a rational number because it can be written as $\frac{p}{q},\;ask \neq 0$,where p and q are both integers.

5. and$\frac{2}{-5}$a small part? Is it a rational number?

solution:

The number $\frac{2}{-5}$ is rational because it has the form $\frac{p}{q},\;ask \neq 0$,Both p and q are integers.

However, it is not a fraction, since fractions are always positive. Note that $\frac{2}{5}$ is a fraction (true fraction).

## Fractions and Rational Numbers Practice Problems

1

### All ____ are rational numbers.

Fraction

Real number

irrational number

plural

correctIncorrect

All fractions are rational numbers.

2

### ________ cannot have a negative numerator or denominator.

Fraction

rational number

irrational number

None of the above.

correctIncorrect

Fractions cannot have negative numerators or denominators. Therefore, both the numerator and denominator of fractions are whole numbers $(\text{denominator} \neq 0)$.

3

### Which of the following statements is incorrect?

Fractions represent parts of a whole.

Rational numbers and fractions are real numbers.

All rational numbers are fractions.

All fractions are rational numbers.

correctIncorrect

The correct answer is: All rational numbers are fractions.
All fractions are rational numbers, but not all rational numbers are fractions.

4

### Which of the following is not a rational number?

$\frac{-1}{5}$

$-\;1$

$\pi$

correctIncorrect

The correct answer is: $\pi$
$\pi$ is not a rational number. Its decimal expansion is neither final nor cyclical, and cannot be expressed as a ratio.

5

### $\frac{-99}{100}$ is a ________.

Fraction

rational number

a y B

None of the above

correctIncorrect

The correct answer is: rational numbers
$\frac{-99}{100}$ is a rational number.

Converting $\sqrt{2}$ to a decimal value, we get $\sqrt{2} = 1.414213562$...

1.414213562 is a nonrecurring and nonterminating decimal. Therefore, this is not a rational number. This is an irrational number.

There are four rational numbers. These are the scoresdecimal point, whole,terminating decimaland rational numbers.

Fractions are of the form $\frac{a}{b},\;b \neq 0$ where a and b are whole numbers. Note that all integers are also integers. therefore, All fractions are rational numbers. They can be expressed as $\frac{p}{q},\;q \neq 0$ Both p and q are integers.

Rational numbers are written in the form $\frac{p}{q}$, where p and q are integers and $q \neq 0$.

Therefore, if we take the ratio of a negative integer to a positive integer, such as $\frac{-2}{9}$ or $\frac{-20}{67}$, we get no score because fractions cannot be negative.

Therefore, every rational number cannot be a fraction. For example: $\frac{3}{-7}$ is a rational number, but it is not a fraction.

All fractions are rational numbers.

0 is a rational number. A rational number is a number that can be written in the form $\frac{p}{q}$, where p and q are integers and $q \neq 0$. We can represent 0 as $\frac{0}{1}$.

## FAQs

### Difference Between Fractions and Rational Numbers? ›

A fraction's ratio can only contain whole numbers or positive integers. A rational number is written as a series of fractions, but unlike fractions, it can contain both positive and negative integer ratios. All rational numbers are fractions, but not all fractions are rational numbers.

What is the difference between a rational number and a fraction answer? ›

A fraction is any number of the form a/b where both “a” and “b” are whole numbers and b≠0. On the other hand, a rational number is a number which is in the form of p/q where both “p” and “q” are integers and q≠0. Thus, a fraction is written in the form of m/n, where n is not 0 and m & n are whole (or natural numbers).

Mixed Fraction consisting of both Integer Part and Fractional Part can be expressed as an Improper Fraction, which is a quotient of two integers. Hence, we can say every Mixed Fraction is a Rational Number. Thus, Every Fraction is a Rational Number.

What is the difference between rational numbers and in rational numbers? ›

A rational number includes any whole number, fraction, or decimal that ends or repeats. An irrational number is any number that cannot be turned into a fraction, so any number that does not fit the definition of a rational number.

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