Understanding Fractions
Fractions are everywhere — from cooking to construction. Learn to work with them confidently.
What Is a Fraction?
A fraction represents part of a whole. Written as a/b, where:
- Numerator (top number): How many parts you have
- Denominator (bottom number): How many equal parts the whole is divided into
Example: 3/4 means you have 3 out of 4 equal parts — like eating 3 slices of a pizza cut into 4.
Types of Fractions
- Proper fraction: Numerator < denominator (3/4, 2/5). Always less than 1.
- Improper fraction: Numerator ≥ denominator (7/4, 5/3). Equal to or greater than 1.
- Mixed number: A whole number plus a fraction (1 3/4, 2 1/3).
Equivalent Fractions
Fractions that look different but represent the same amount:
1/2 = 2/4 = 3/6 = 4/8 = 50/100
Rule: Multiply (or divide) both numerator and denominator by the same number.
Example 1: Show that 2/3 = 8/12
2/3 × 4/4 = 8/12 ✓ (we multiplied top and bottom by 4)
Simplifying Fractions
Divide both numerator and denominator by their Greatest Common Factor (GCF).
Example 2: Simplify 18/24
GCF of 18 and 24 is 6.
18 ÷ 6 = 3, 24 ÷ 6 = 4
Answer: 3/4
Comparing Fractions
Method 1: Find a common denominator. 3/4 vs 5/6 → 9/12 vs 10/12 → 5/6 is larger.
Method 2: Cross multiply. 3 × 6 = 18 vs 4 × 5 = 20. Since 18 < 20, 3/4 < 5/6.
Adding and Subtracting Fractions
You MUST have a common denominator first.
Example 3: 1/3 + 1/4
Step 1: Find LCD (Least Common Denominator): LCD of 3 and 4 = 12
Step 2: Convert: 1/3 = 4/12, 1/4 = 3/12
Step 3: Add numerators: 4/12 + 3/12 = 7/12
Example 4: 5/6 - 1/4
LCD of 6 and 4 = 12
5/6 = 10/12, 1/4 = 3/12
10/12 - 3/12 = 7/12
Multiplying Fractions
Simply multiply straight across — numerator × numerator, denominator × denominator.
Example 5: 2/3 × 4/5
= (2 × 4) / (3 × 5) = 8/15
Answer: 8/15
Tip: Cross-cancel before multiplying to keep numbers small. In 3/4 × 2/9, the 3 and 9 share factor 3: simplify to 1/4 × 2/3 = 2/12 = 1/6.
Dividing Fractions
Keep, Change, Flip: Keep the first fraction, change ÷ to ×, flip the second fraction.
Example 6: 3/4 ÷ 2/5
= 3/4 × 5/2 = 15/8 = 1 7/8
Converting Between Mixed Numbers and Improper Fractions
Mixed → Improper
Multiply whole number by denominator, add numerator. Keep the denominator.
2 3/5 = (2 × 5 + 3) / 5 = 13/5
Improper → Mixed
Divide numerator by denominator. Quotient = whole number, remainder = new numerator.
17/4: 17 ÷ 4 = 4 remainder 1 → 4 1/4
🎯 Try It Yourself
Test your understanding with these practice problems.
1. Simplify 12/18
💡 Hint: Find the GCF of 12 and 18 (it's 6)
2. What is 2/3 + 1/4?
💡 Hint: Find common denominator: 12. Convert: 8/12 + 3/12
3. What is 3/5 × 2/7?
💡 Hint: Multiply numerators and denominators straight across
4. What is 7/8 ÷ 1/4?
💡 Hint: Flip the second fraction and multiply: 7/8 × 4/1
5. Convert 2 3/4 to an improper fraction
💡 Hint: 2 × 4 + 3 = 11, keep denominator 4
⚠️ Common Mistakes
- ✗Adding numerators AND denominators: 1/3 + 1/4 ≠ 2/7. You need a common denominator first!
- ✗Forgetting to find a common denominator before adding or subtracting fractions.
- ✗When dividing fractions, forgetting to flip the SECOND fraction (not the first).
- ✗Not simplifying the final answer. Always reduce to lowest terms.
- ✗Confusing 'of' with multiplication. '1/3 of 12' means 1/3 × 12 = 4.
🌍 Real Life Example
Doubling a Recipe
A cookie recipe calls for 2/3 cup of sugar. You want to make a double batch, so you need 2/3 × 2 = 4/3 = 1 1/3 cups of sugar. It also calls for 3/4 cup of butter. Double: 3/4 × 2 = 6/4 = 1 1/2 cups of butter. Fractions are essential in cooking, baking, and measuring anything that isn't a whole number.
💡 Key Takeaway
A fraction represents a part of a whole. The numerator (top) tells you how many parts you have; the denominator (bottom) tells you how many equal parts the whole is divided into. To add/subtract, get common denominators. To multiply, go straight across. To divide, flip and multiply.