Difference Between Fraction And Rational Number, Important Topics For JEE
Difference Between Fraction And Rational Number : Read everything you need to know about the numbers. Learn the basic difference between fraction and rational number.
Shrivastav 17 Jan, 2024
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Difference Between Fraction And Rational Number : The two words in mathematics that are most often used are fractions and rational numbers. Because they have somewhat similarities, they often cause confusion.
There is a significant difference between fraction and rational number, although certain conceptual similarities between two essential mathematical terms. We will be discussing the basic difference between fraction and rational number in the content below. The difference between fraction and rational number is considerable. Although they are distinct in many ways, the concepts of "fractional numbers" and "rational numbers" are closely connected. A rational number may or may not be a fractional number, but a fractional number is always a rational number, it should be noted. Achieve JEE excellence with PW JEE Online Course . Join now to fulfill your engineering dreams. Before we discuss the difference between fraction and rational number, let’s first discuss the meaning and characteristics of both of them.What Is Fraction
What Is Fraction: The definition of a fraction is parts of a whole number. It may be seen as a segment, part, or piece of the overall entity. A fraction is defined mathematically as the ratio of two whole integers, where the denominator is always a whole number that is not zero. For instance, 6/7, 1/2, etc.Types of Fractions
There are many various types of fractions or fractional numbers in mathematics. Proper Fractions: The numerator is always less than the denominator. Example: 3/8 and 7/9. Improper fractions have the numerator always being greater than the denominator. Examples are 9/2 and 7/5. Mixed fractions: Mixed fractions are made up of both a whole number and a fraction. For example, 3 (3/2) and 5 (2/7). Equivalent fractions: Equivalent fractions are those that have numerators and denominators that can be divided by the same number. 2/12 equals 3/18, and 5/10 equals 10/20. Like fractions: Like fractions, they are fractional numbers with the same denominator. Example: 2/5; 3/5. Unlike Fractions: Fractions with distinct denominators. Example: 2/3; 15/13.Definition of Rational Number
Definition of Rational Number : In terms of mathematical representation, rational numbers are extremely similar to fractions and are a subset of real numbers. A rational number is defined mathematically as the ratio of two integers, where the denominator is always an integer that is not zero. For instance, - 2/3, 7/8, and so on.Key Difference Between Fraction and Rational Number
Key Difference Between Fraction and Rational Number : Let's look into the following table showing the key difference between a fraction and rational number:| Difference Between Fraction and Rational Number | ||
| Particulars | Fraction | Rational Number |
| Range of Numbers | Fractions cover parts from 1/∞ to ∞/1. | Rational numbers include fractions and other numbers expressible as ratios of integers. |
| Types | Proper, improper, and mixed fractions. | Terminating and non-terminating rational numbers. |
| Operations | Addition, subtraction, multiplication, division. | Similar operations as fractions; may involve converting irrational numbers to fractions. |
| Simplification | GCF used to simplify by dividing the numerator and denominator. | Reduce to lowest terms; irrational numbers cannot be simplified. |
| Representation | Ratio, mixed number, or decimal (terminating/non-terminating). | Fraction, decimal, or percent (terminating/non-terminating). |
| Irrational Numbers | Cannot represent irrational numbers. Examples: √2, π, e. | Exclude irrational numbers but can approximate them. |
| Prime Factorization | GCF found by prime factorization. | GCF used for simplification; prime factorization helps find GCF. |
| Equivalent Numbers | Fractions representing the same part. Example: 2/4 = 1/2. | Rational numbers are equivalent if they have the same value. Example: 0.5 = 1/2. |
| Recurring Decimals | Can result in recurring decimals. Example: 4/3 = 1.3333… | Rational numbers can also have recurring decimals. Example: 1/7 = 0.142857142857… |
| Real Numbers | A subcategory of real numbers on the number line. | A subcategory of the real numbers expressed as a ratio of two integers. |
| Irrational Numbers (again) | Cannot represent irrational numbers. Examples: √2, π, e. | Do not include irrational numbers but can approach them with rational numbers. |
| Decimal Expansion | Can be terminated or non-terminating. Examples: 1/4 = 0.25, 1/3 = 0.3333… | Rational numbers can also have terminating or non-terminating decimals. Example: 3/5 = 0.6. |
| Comparing Numbers | Compare by finding a common denominator. Example: 2/5 vs. 3/4. | Compare by finding a common denominator or converting to a common form. |
| Absolute Value | Fractions don't have an absolute value. | Rational numbers have a positive absolute value, the distance from zero on the number line. |
| Mixed Numbers | A combination of a whole number and a proper fraction. Example: 2 1/2. | Rational numbers can be expressed as mixed numbers, e.g., 7/3 as 2 1/3. |
Similarities Between Fraction and Rational Numbers
The previous part discussed the difference between fraction and rational number. Now let's talk about the similarities between the two.- The set of real numbers includes both rational numbers and fractions.
- Ratios of numbers serve as the mathematical representation for both rational and fractional numbers.
- There is a non-zero denominator for rational numbers and fractions equally.
Difference Between Fraction And Rational Number FAQs
Q1: Is 2 a fraction or not?
Ans. The integer 2 may be expressed as the improper fraction 2/1, and its multiples are all improper fractions.
Q2: What do Fractions Mean?
Ans. A fraction is a part, or more generally, a collection of parts, that are all equal. A number is expressed in arithmetic as a quotient when the numerator and denominator are divided.
Q3: What is a rational number that isn't a fraction, for example?
Ans. The number 1 is one example of a rational number that isn't a fraction. This is so because there is no way to describe the number one as a fraction.
Q4: Is 3.14 a rational number?
Ans. 3.14 is a rational number. A rational number is one that can be expressed as a fraction, a / b, with a and b being integers. Pi is an irrational number.
Q5: Is Pi a non-real number?
Ans. Pi cannot be described as a simple fraction, this means it is an irrational number. We know that any irrational number is a real number. Pi is a real number, therefore.
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