A fraction is a way to represent a part of a whole or a part of a group. It is written in the form a/b, where:

• Numerator (a): The number of parts we have.
• Denominator (b): The total number of equal parts the whole is divided into.

Key Terms

✔ Numerator (top number) → How many parts we have.
✔ Denominator (bottom number) → How many equal parts the whole is divided into.
✔ Unit Fraction → A fraction where the numerator is 1 (e.g., ½, ⅓, ¼).
✔ Equal Parts → Fractions only work when the whole is divided into equal sections.

Examples

Example 1: ½ (One-Half)

• Meaning: 1 part out of 2 equal parts.
• Real-Life Example:
  • If a pizza is cut into 2 equal slices, eating 1 slice means you ate ½ of the pizza.

Example 2: ¾ (Three-Fourths)

• Meaning: 3 parts out of 4 equal parts.
• Real-Life Example:
  • If a chocolate bar is divided into 4 equal pieces and you eat 3 pieces, you have eaten ¾ of the chocolate.

Example 3: ⅖ (Two-Fifths)

• Meaning: 2 parts out of 5 equal parts.
• Real-Life Example:
  • If you have 5 apples and take 2, you have taken ⅖ of the apples.

Types of Fractions

1. Proper Fractions → Numerator < Denominator (e.g., ⅔, ⅜).
2. Improper Fractions → Numerator ≥ Denominator (e.g., 5/4, 7/3).
3. Mixed Numbers → A whole number + a fraction (e.g., 1½, 2⅔).

Visual Examples

1. Pizza Example:
   • If a pizza is cut into 4 equal slices and you eat 1 slice, you have eaten ​ of the pizza. If you eat 2 slices, you have eaten or ​ of the pizza.
2. Pie Example:
   • Imagine a pie cut into 8 equal slices. If you have 3 slices, you have of the pie.

Fractions are everywhere—from slicing a cake to measuring ingredients. By understanding the numerator and denominator, you can easily interpret and use fractions in daily life. Keep practicing with real-world examples, and soon, fractions will become second nature!

Fractions on a Number Line

What Is a Number Line?

A number line is a straight, horizontal line with numbers placed at equal distances. It helps visualize numbers, including whole numbers and fractions, in order from smallest to largest.

Key Features of a Number Line:

✔ Equal spacing → Each segment represents the same value.
✔ Zero (0) as the starting point → Numbers increase as you move right.
✔ Fractions between whole numbers → Helps compare sizes of fractions.

How to Place Fractions on a Number Line

Step 1: Divide the Number Line

• The denominator (bottom number) tells you how many equal parts to divide the line between two whole numbers.
  • Example: For ¼, divide the space between 0 and 1 into 4 equal parts.

Step 2: Locate the Fraction

• The numerator (top number) tells you how many parts to count from 0.
  • Example: ¾ means 3 parts out of 4 from 0 toward 1.

Visualizing Fractions on a Number Line

Example 1: ½ (One-Half)

1. Draw a line from 0 to 1.
2. Divide it into 2 equal parts.
3. ½ is the first mark after 0.

📌 Position: Exactly halfway between 0 and 1.

Example 2: ¼ (One-Fourth)

1. Draw a line from 0 to 1.
2. Divide it into 4 equal parts.
3. ¼ is the first mark after 0.

📌 Position: One small step from 0 toward 1.

Example 3: ¾ (Three-Fourths)

1. Draw a line from 0 to 1.
2. Divide it into 4 equal parts.
3. ¾ is the third mark after 0.

📌 Position: Just one step before 1.

Comparing Fractions Using a Number Line

A number line makes it easy to see which fraction is larger or smaller.

Example: ½ vs. ¼

• ½ is farther to the right than ¼, so ½ > ¼.

Example: ⅔ vs. ⅗

• If you divide the same space (0 to 1) into 3rds and 5ths, you’ll see that ⅔ is closer to 1 than ⅗, meaning ⅔ > ⅗.

Fraction Number Lines (0 to 1) with Examples

1. Halves (½) on a Number Line

Denominator = 2 → Divide the line into 2 equal parts.

0      ½       1
|------|------|

• ½ is exactly in the middle between 0 and 1.

2. Thirds (⅓, ⅔) on a Number Line

Denominator = 3 → Divide the line into 3 equal parts.

0      ⅓       ⅔       1
|------|------|------|

• ⅓ = First mark after 0.
• ⅔ = Second mark, closer to 1.

3. Fourths (¼, ½, ¾) on a Number Line

Denominator = 4 → Divide the line into 4 equal parts.

0      ¼       ½       ¾       1
|------|------|------|------|

• ¼ = First small mark after 0.
• ½ = Second mark (same as ½ in the first example).
• ¾ = Third mark, just before 1.

4. Fifths (⅕, ⅖, ⅗, ⅘) on a Number Line

Denominator = 5 → Divide the line into 5 equal parts.

0     ⅕     ⅖     ⅗     ⅘     1
|-----|-----|-----|-----|-----|

• ⅕ = First small step from 0.
• ⅗ = Three steps from 0 (more than halfway).
• ⅘ = Very close to 1.

Number lines make fractions easy to understand by turning numbers into visual steps. Whether you’re comparing sizes or adding fractions, this method builds a strong math foundation!