Introduction
Ever divided a chocolate bar between friends or measured half a cup of sugar? You were using fractions! They're not just numbers they're essential tools used in cooking, timekeeping, shopping, and school. Understanding fractions helps children develop number sense and lays the foundation for topics like decimals, percentages, and ratios.
This easy-to-follow guide covers:
- What are fractions?
- Types of fractions (with real-life examples)
- Adding, subtracting, multiplying, and dividing fractions
- Converting fractions to decimals and percentages
- Common student mistakes and how to fix them
- Practice questions and activities
What Is a Fraction?
A fraction is a number that represents a part of a whole. It is written in the form:
Numerator / Denominator
The numerator (top number) tells how many parts you have. The denominator (bottom number) tells how many equal parts the whole is divided into.
Examples:
- ½ — one out of two equal parts
- ¾ — three out of four parts
- 5⁄8 — five parts out of eight
Fractions are used in time (¼ hour = 15 mins), shopping (½ price), and cooking (⅓ cup of milk).
Types of Fractions
| Type | Example | Description |
|---|---|---|
| Proper Fraction | ⅔ | Numerator is smaller than denominator |
| Improper Fraction | ⁷⁄₄ | Numerator is equal to or larger than denominator |
| Mixed Fraction | 1¾ | Whole number plus proper fraction |
| Equivalent Fraction | ½ = 2⁄4 = 4⁄8 | Different forms, same value |
| Like Fractions | 3⁄5 and 2⁄5 | Same denominator |
| Unlike Fractions | ½ and ⅓ | Different denominators |
How to Calculate Fractions
Addition
Same denominator: ⅓ + ⅓ = ⅔
Different denominator: ½ + ⅓ → LCM = 6 → 3⁄6 + 2⁄6 = 5⁄6
Subtraction
¾ − ¼ = 2⁄4 = ½
Multiplication
⅔ × ¾ = (2×3)/(3×4) = 6⁄12 = ½
Division
Flip the second fraction and multiply: ½ ÷ ¼ = ½ × ⁴⁄₁ = 4⁄2 = 2
Fractions, Decimals & Percentages
- ½ = 0.5 = 50%
- ¼ = 0.25 = 25%
- ¾ = 0.75 = 75%
To convert a decimal to a fraction: 0.75 = 75⁄100 → Simplify → ¾
Mixed & Improper Fractions
Convert Mixed to Improper: 1¾ → (1×4 + 3)⁄4 = ⁷⁄₄
Convert Improper to Mixed: ⁹⁄₄ → 9 ÷ 4 = 2 remainder 1 = 2¼
Real-Life Uses of Fractions
- Time: ¾ of an hour = 45 minutes
- Cooking: ½ tsp of salt, ⅓ cup sugar
- Shopping: 25% off = ¼ price
- Sports: A team won 3 out of 4 matches = ¾
- School: Test score: 17/20
Common Mistakes with Fractions
- Adding numerators and denominators directly: ❌ ⅓ + ½ ≠ 4⁄5
- Not converting to like denominators
- Confusing mixed and improper forms
- Forgetting to simplify
Practice Questions (with Answers)
- What is ¾ + ⅙? → LCM = 12 → 9⁄12 + 2⁄12 = 11⁄12
- Convert 0.8 into a fraction and percent. → 0.8 = ⁸⁄₁₀ = ⁴⁄₅ = 80%
- Which is greater: ⅖ or 3⁄8? → Convert to decimal: 0.4 vs 0.375 → ⅖
- Simplify 36⁄60: → GCD = 12 → 3⁄5
- Convert 2⅓ to improper: → (2×3 + 1)⁄3 = ⁷⁄₃
Fun Facts About Fractions
- Fractions date back to Ancient Egypt using only unit fractions (with numerator 1).
- ¼, ½, and ¾ are the most used in recipes globally.
- In music, ½ and ¼ notes are based on fractions.
- Every fraction has an equivalent decimal and vice versa!
Conclusion
Fractions aren’t scary they’re super useful! With real-world relevance and practice, they become exciting instead of confusing. Whether it's splitting a bill, scoring in sports, or baking a cake, understanding fractions helps learners think clearly and solve problems confidently.
Explore more number concepts, quizzes, and math games in our learning hub!
Want to try division next? Head over to our Division Playground and continue your learning journey.