Lesson 2: Fractions

1⃣ What Is a Fraction?

A fraction represents a part of a whole. It consists of two numbers separated by a fraction line.

🔹 Examples of Fractions:

• ⅕ (one out of five parts)

• ½ (one out of two parts)

• 3/4 (three out of four parts)

📌 Real-Life Example:

If you ride the bus one day out of five, you have ridden ⅕ of the time.

Fractions Can Be Written in Three Ways:

1. ⅕ (with a fraction symbol)

2. 1/5 (written with a slash)

3. Visual Representation: (shown with shaded parts in a diagram)

2⃣ Numerators and Denominators

Each fraction has two parts:

✔ Numerator (top number): Represents how many parts are taken.

✔ Denominator (bottom number): Represents the total number of equal parts.

📌 Memory Trick: Denominator starts with “D” like “Down” → It goes down below the fraction line.

🔹 Example:

• In 3/4, 3 is the numerator (3 parts taken), and 4 is the denominator (4 total parts).

3⃣ Proper, Improper, and Mixed Fractions

Proper Fractions (Less than 1)

A proper fraction has a numerator that is smaller than the denominator.

🔹 Examples:

• ½

• 3/4

• 7/8

Improper Fractions (Greater than 1)

An improper fraction has a numerator that is greater than the denominator.

🔹 Examples:

• 7/5

• 8/2

• 63/7

📌 Why Do Improper Fractions Exist?

Even though they are greater than a whole, we use improper fractions in calculations before simplifying them into whole or mixed numbers.

Mixed Numbers (Whole Number + Fraction)

A mixed number includes a whole number and a proper fraction.

🔹 Examples:

• 2 ½

• 5 ⅓

• 7 ¾

📌 Conversion: Improper fractions can be converted into mixed numbers. We will learn how to do this in a later lesson.

4⃣ Adding and Subtracting Fractions

Step 1: Check for Like Denominators

Fractions must have the same denominator before adding or subtracting.

🔹 Example:

• 3/4 + 1/4

• The denominators are the same (4), so we add the numerators:

• (3 + 1)/4 = 4/4 = 1

📌 Rule: The denominator stays the same when adding or subtracting fractions.

Step 2: Subtracting Fractions

• 5/6 - 4/6 = (5 - 4)/6 = 1/6

• The denominator stays 6, and we subtract the numerators.

📌 Key Concept: When the numerator and denominator are the same (like 4/4 or 6/6), the fraction equals 1 whole.

5⃣ What If the Denominators Are Different?

You cannot add or subtract fractions with different denominators.

First, you must find a common denominator (a later lesson will cover this in detail).

🔹 Example:

• 1/3 + 1/4

• Since the denominators (3 and 4) are different, we must adjust them to be the same before adding.

📌 Coming Soon: Learn how to find the least common denominator to solve these problems.

6⃣ Test-Taking Tip: Understand the Question

When solving math problems, pay close attention to the wording.

✔ Look for Clues (Key Words):

• “Half,” “percentage,” “left over,” “total” → Addition or subtraction.

• “Per,” “product,” “average” → May involve multiplication or division.

✔ Check What You Have

• Write down the given numbers to see what’s missing.

✔ Use Diagrams & Tables

• Sometimes, the answer is easier to spot in a picture.

✔ Look at Answer Choices

• The answer options can sometimes hint at what the question is asking.

📌 Lesson Recap

✔ A fraction is a part of a whole number.

✔ Numerator (top number) represents parts taken.

✔ Denominator (bottom number) represents total parts.

✔ Proper fractions are less than 1, while improper fractions are greater than 1.

✔ Mixed numbers include a whole number and a fraction.

✔ Adding and subtracting fractions requires like denominators.

✔ A denominator must be the same before adding or subtracting fractions.

✔ Understanding the question is key to solving fraction problems correctly.