Lesson 1: Common Fractions – Simplification, Operations, Applications

📥 Introduction

Imagine cutting a large chocolate bar to share among friends — how do you make sure each person gets a fair piece? That’s where fractions come in! Fractions help us describe parts of a whole clearly and fairly.
In this lesson, we’ll dive deep into understanding fractions, simplifying them, and carrying out basic operations (adding, subtracting, multiplying, and dividing). You’ll see how these skills apply in real life — from sharing food to solving money problems.

🧠 Key Concepts and Explanations

1. What is a Fraction?

A fraction is a way of expressing a part of a whole or a part of a group. It is made up of two numbers separated by a line:

• Numerator: The number above the line – tells how many parts you have.
• Denominator: The number below the line – tells how many parts make the whole.

Example: means 3 parts out of 4 equal parts.

2. Types of Fractions

• Proper Fraction: Numerator is smaller than denominator ().
• Improper Fraction: Numerator is greater than or equal to denominator ().
• Mixed Number: A whole number and a proper fraction combined (e.g., ).

3. Simplifying Fractions

To simplify a fraction, divide the numerator and denominator by their greatest common factor (GCF).

Why simplify? It makes calculations easier and answers neater.

Example: Simplify .

• • GCF of 18 and 24 is 6.

• Divide both by 6:

4. Equivalent Fractions

Equivalent fractions are different fractions that represent the same value.

Example:

5. Basic Operations with Fractions

Examples:

Add same denominators:

Add different denominators:

• LCM of 4 and 6 is 12.
• Rewrite:

Multiplying fractions:

Dividing fractions:

📝 Step-by-Step Sample Walkthroughs

Example 1: Simplify

• Find GCF of 45 and 60 = 15
• Divide both:

Example 2: Subtract

• • LCM of 6 and 4 = 12
  • 

• Subtract:

✅ Practice Exercises

A. Simplify the Fractions

B. Add, Subtract, Multiply, or Divide

C. True or False?

D. Word Problems

1. Amina ate of a cake. Her brother ate . How much of the cake did they eat together?
2. A tank is filled with water. If leaks out, how much water remains?

🔁 Recap

• Fractions show parts of a whole.
• Simplify by dividing by GCF.
• Use common denominators for adding and subtracting.
• Multiply straight across; divide by flipping the second fraction.

🪞Reflection Prompt

Think about how you divide chores, money, or snacks with others. How would you write those shares as fractions?