---
title: Rational Numbers - Definition, Properties & Operations
description: "Learn about rational numbers (ℚ): their definition as fractions (p/q), how to represent them, basic operations, and key properties like density."
url: https://astra-ai.co/videos/rational-numbers/
locale: en
type: video-topic
keywords:
  - rational numbers
  - fractions
  - decimals
  - repeating decimals
published: 2026-10-01T09:45:44.201Z
updated: 2026-10-04T21:53:17.759Z
alternates:
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  da: https://astra-ai.co/da/videos/rationale-tal/
  de: https://astra-ai.co/de/videos/rationale-zahlen/
  el: https://astra-ai.co/el/videos/ritoi-arithmoi/
  en: https://astra-ai.co/videos/rational-numbers/
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  id: https://astra-ai.co/id/videos/bilangan-rasional/
  it: https://astra-ai.co/it/videos/numeri-razionali/
  ja: https://astra-ai.co/ja/videos/rational-numbers-ja/
  km: https://astra-ai.co/km/videos/rational-numbers/
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  ms-BN: https://astra-ai.co/ms-BN/videos/nombor-rasional/
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  nl: https://astra-ai.co/nl/videos/rationele-cijfers/
  no: https://astra-ai.co/no/videos/rasjonale-tall/
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  pt: https://astra-ai.co/pt/videos/numeros-racionais/
  pt-TL: https://astra-ai.co/pt-TL/videos/numeros-racionais/
  ro: https://astra-ai.co/ro/videos/numere-rationale/
  sk: https://astra-ai.co/sk/videos/racionalne-cisla/
  sl: https://astra-ai.co/sl/videos/racionalna-stevila/
  sr: https://astra-ai.co/sr/videos/racionalni-brojevi/
  sv: https://astra-ai.co/sv/videos/rationella-tal/
  th: https://astra-ai.co/th/videos/chamnuan-trakka/
  tr: https://astra-ai.co/tr/videos/rasyonel-say-lar/
  uk: https://astra-ai.co/uk/videos/uk-topic-18/
  vi: https://astra-ai.co/vi/videos/vi-topic-18/
  zh-HK: https://astra-ai.co/zh-HK/videos/shuxue-kecheng-018/
  zh-TW: https://astra-ai.co/zh-TW/videos/rational-numbers/
---

# Rational Numbers

> Rational numbers are numbers that can be written as a fraction of two integers. This topic covers fractions, decimals, and how to compare them.

Rational numbers are numbers that can be written as a fraction p/q, where p and q are integers, and q ≠ 0. This set includes integers, decimal numbers with a finite length (terminating decimals), and infinite repeating decimals. Rational numbers are denoted by ℚ.

## REPRESENTATION OF RATIONAL NUMBERS

Every rational number can be written in various ways. For example:

- 1/2 = 0.5

- 3/4 = 0.75

- 1/3 = 0.3333… (or 0.(3))

Rational numbers can be divided into positive, negative, and zero. All integers are rational because they can be expressed as n/1 (e.g., 5 = 5/1).

## BASIC ARITHMETIC OPERATIONS

Rational numbers allow for all four basic arithmetic operations:

- **ADDITION:** 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2

- **SUBTRACTION:** 5/4 – 3/4 = 2/4 = 1/2

- **MULTIPLICATION:** (2/3) × (3/4) = 6/12 = 1/2

- **DIVISION:** (3/5) ÷ (2/7) = (3/5) × (7/2) = 21/10 = 2.1

## PROPERTIES OF RATIONAL NUMBERS

- **DENSITY:** Between any two distinct rational numbers, there is always another rational number.

- **CLOSURE:** The set ℚ is closed under addition, subtraction, multiplication, and division (except for division by 0).

- **RECIPROCAL (MULTIPLICATIVE INVERSE):** Every rational number p/q (except 0) has a multiplicative inverse q/p.

## CONCLUSION

Rational numbers are a key part of number sets, as they allow for the precise expression of parts of a whole. Their properties and calculations with them are the basis for understanding decimal numbers, fractions, and algebra.