Lesson 3: Rational Numbers – Concepts and Basic Operations

📚 Introduction

Have you ever shared a pizza 🍕 with friends and ended up with half or a quarter? Then congratulations — you’ve already used rational numbers!

Rational numbers are numbers that can be written as fractions — meaning they have a numerator and a denominator.

In this lesson, we’ll explore what rational numbers are, how to add, subtract, multiply, and divide them — and most importantly, how they show up in real life! 🚀

🧠 Key Concepts and Explanations

1. What Are Rational Numbers?

Definition: A rational number is any number that can be written in the form where p and q are integers and q ≠ 0.

Examples of Rational Numbers	Explanation
	Two-thirds
-5	-5 can be written as
0.75	0.75 =
0	Zero is a rational number!

2. Adding and Subtracting Rational Numbers ➕➖

Same Denominators

Add or subtract the numerators. Keep the denominator the same.

Formula:

Example:

Different Denominators

First, find the Least Common Denominator (LCD), then add or subtract.

Example:

• • LCD of 5 and 3 is 15.
  • 

• Add:

3. Multiplying Rational Numbers ✖️

Multiply the numerators together and multiply the denominators together.

Formula:

Example:

4. Dividing Rational Numbers ➗

Keep the first fraction, flip the second (find its reciprocal), then multiply.

Formula:

Example:

📈 Useful Table: Quick Fraction Operations

📝 Practice Exercises

A. Add or Subtract

B. Multiply or Divide

C. Word Problems

1. Sarah ate of a cake. Then she ate more. What fraction of the cake has she eaten in total?
2. A tank holds litres of water. If litres are removed, how much is left?

✅ Answers and Explanations

Add or Subtract

Multiply or Divide

Word Problems

1. 1. of the cake eaten

1. litres left

🔄 Recap

Today you learned that rational numbers include fractions and decimals that can be written as fractions. Adding, subtracting, multiplying, and dividing fractions is easy if you follow the simple rules! 🧠

💬 Reflection

Think about this: The next time you share food, can you figure out exactly what fraction of it you ate? 🍕