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.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. |