## The Difference Between Rational Numbers and Fractions

When it comes to mathematics, there are many terms that can be confusing. Two of those terms are rational numbers and fractions. While they both represent numbers that can be expressed as ratios, they are not the same thing.

### What is a Rational Number?

A rational number is a number that can be expressed as the quotient or fraction of two integers. This means that it can be written in the form of p/q, where p and q are integers and q is not equal to zero. Some examples of rational numbers include:

– 1/2

– 5/8

– -3/4

– 0

– 6

Note that both positive and negative numbers, as well as zero, can be rational numbers.

### What is a Fraction?

On the other hand, a fraction is a number that represents a part of a whole. It is also expressed as a ratio of two numbers, but unlike a rational number, a fraction can be written in various forms, such as:

– Proper fraction: a fraction where the numerator is less than the denominator, like 2/3

– Improper fraction: a fraction where the numerator is greater than or equal to the denominator, like 7/4

– Mixed number: a combination of a whole number and a proper fraction, like 2 1/3

Some examples of fractions include:

– 1/4

– 2/5

– 7/2

– 2 1/2

– 0 (represented as 0/1)

### The Main Difference

The main difference between rational numbers and fractions is that while all rational numbers can be expressed as fractions, not all fractions are rational numbers. For example, decimal numbers like 1.5 and repeating decimals like 0.666… cannot be expressed as fractions and are not rational numbers.

In conclusion, while both rational numbers and fractions are expressed as ratios, their definitions and applications differ. When you encounter these terms in math problems, make sure to understand the context to solve the equation accurately.

## Table difference between rational number and fraction

Rational Number |
Fraction |
---|---|

A number that can be expressed as a ratio of two integers | A number that represents a part of a whole, also expressed as a ratio of two integers |

Includes integers, terminating decimals, and repeating decimals | Includes proper fractions, improper fractions, and mixed numbers |

Can be expressed in decimal form, but not always | Can always be expressed in decimal form and may either terminate or repeat |

Examples: 2/3, 4, 0.6, -3/4 | Examples: 1/4, 7/8, 3 1/2, -2/3 |