What is a rational number? Give an example.

In one line

The rule

A rational number is a number that can be expressed in the form p/q, where p and q are integers and q ≠ 0.

There is no special formula, but the key part is:

• p/q where:
• p = any integer (like −3, 0, 5)
• q = any integer except 0 (like 1, −2, 7)

Let's understand it simply

Imagine you are sharing 8 ladoos among 4 friends. Each friend gets 2 ladoos. You can write this as 8/4 = 2. Here, 8/4 is a rational number. Even if you share 1 ladoo among 2 friends, each gets 1/2 ladoo. That 1/2 is also a rational number. So, any number you can write as a part of something (like 3/5, −7/2, 0/1) is a rational number.

How it works

1. Take any two integers (whole numbers, can be negative or zero), call them p and q.
2. Make sure the bottom number (q) is not zero (because you can't divide by zero).
3. Write the number as p/q. This is a rational number.
4. If you can write a number like this, it is rational. If not, it is not rational.

The story behind it

The word "rational" comes from "ratio". Long ago, people needed to show parts of things, like half a roti or one-third of a cricket team. Mathematicians realised that not all numbers are whole, so they made this group called rational numbers. It helps us talk about sharing, measuring, and dividing things in real life.

Where you see it in real life

• Splitting a bill: If 3 friends share a ₹60 bill, each pays ₹20 (60/3 = 20).
• Measuring ingredients: 1/4 teaspoon of salt in a recipe is a rational number.
• Cricket averages: If a batsman scores 45 runs in 9 matches, average = 45/9 = 5.
• Dividing land: If 2 brothers get 7 acres, each gets 7/2 = 3.5 acres.
• Bus seats: If 5 people share 2 seats, each gets 2/5 of a seat (not possible, but the number is rational!).
• School marks: Scoring 17 out of 20 in a test is 17/20, a rational number.

Why it matters

• Rational numbers help you solve equations that whole numbers cannot.
• They let you talk about parts, sharing, and averages in daily life.
• Many chapters in maths (fractions, decimals, ratios, percentages) use rational numbers.
• Rational numbers are the base for more advanced maths, like algebra and number theory.

Common mistakes

• Thinking only fractions like 1/2 or 3/4 are rational. But 5 (which is 5/1) and −2 (which is −2/1) are also rational numbers.
• Forgetting that the bottom number (q) cannot be zero. 4/0 is NOT a rational number.
• Mixing up rational numbers with decimal numbers. Only decimals that end or repeat (like 0.5 or 0.333...) are rational.

Remember it

If you can write a number as a fraction (p/q), it is a rational number. Example: 7/3, −4/5, 2, 0.

Example: 3/4 is a rational number because 3 and 4 are integers and 4 ≠ 0.