Adding and Subtracting Fractions
Master fraction addition and subtraction with step-by-step methods. Learn to find common denominators, work with mixed numbers, and solve real-world problems.
Fractions Series Navigation
What You'll Learn
Adding Fractions with Like Denominators
When fractions have the same denominator, we simply add the numerators and keep the denominator the same.
📐 Rule: Adding Like Denominators
a/c + b/c = (a + b)/c
The denominator stays the same; only add the numerators.
Example 1: Basic Addition
Add: 3/8 + 2/8
3/8 + 2/8 = (3 + 2)/8 = 5/8
The answer is already in simplest form.
Example 2: With Simplification
Add: 5/12 + 7/12
5/12 + 7/12 = (5 + 7)/12 = 12/12 = 1
When numerator equals denominator, the fraction equals 1.
Subtracting Fractions with Like Denominators
Similar to addition, when subtracting fractions with the same denominator, subtract the numerators and keep the denominator.
📐 Rule: Subtracting Like Denominators
a/c - b/c = (a - b)/c
Example: Basic Subtraction
Subtract: 7/9 - 4/9
7/9 - 4/9 = (7 - 4)/9 = 3/9 = 1/3
Always simplify your answer when possible!
Finding Common Denominators
To add or subtract fractions with different denominators, we must first find a common denominator.
Using the Product
Multiply the denominators together. Always works but may not give smallest LCD.
For 1/3 and 1/4:
3 × 4 = 12
Finding the LCM
List multiples until you find the smallest one they share.
For 1/6 and 1/8:
6: 6, 12, 18, 24...
8: 8, 16, 24...
Prime Factorization
Break down each denominator into prime factors.
12 = 2² × 3
18 = 2 × 3²
LCM = 2² × 3² = 36
Adding Fractions with Unlike Denominators
📋 Steps to Add Unlike Denominators
- 1 Find the common denominator
- 2 Convert each fraction to equivalent fraction with common denominator
- 3 Add the numerators
- 4 Simplify if possible
Example: Add 2/3 + 1/4
Step 1: Common denominator: 3 × 4 = 12
Step 2: Convert fractions:
2/3 = 8/12 (multiply by 4/4)
1/4 = 3/12 (multiply by 3/3)
Step 3: Add: 8/12 + 3/12 = 11/12
Step 4: Check if simplifiable: 11/12 is already simplified
Answer: 11/12
Working with Mixed Numbers
Mixed numbers combine whole numbers and fractions. There are two methods for adding and subtracting them.
Method 1: Convert to Improper Fractions
Convert mixed numbers to improper fractions, perform the operation, then convert back if needed.
Method 2: Work with Parts Separately
Add or subtract whole numbers and fractions separately, then combine.
Example: Add 2 3/4 + 1 2/3
Using Improper Fractions Method:
2 3/4 = 11/4
1 2/3 = 5/3
Common denominator: 12
11/4 = 33/12
5/3 = 20/12
33/12 + 20/12 = 53/12
Answer: 4 5/12
Practice Problems
➕ Addition Practice
- 1 1/5 + 2/5 = ?
- 2 3/4 + 1/6 = ?
- 3 2/3 + 5/9 = ?
- 4 3 1/2 + 2 3/4 = ?
- 5 4 2/5 + 1 3/10 = ?
➖ Subtraction Practice
- 1 7/8 - 3/8 = ?
- 2 5/6 - 1/4 = ?
- 3 3/4 - 2/3 = ?
- 4 5 1/3 - 2 2/3 = ?
- 5 4 1/6 - 1 3/4 = ?
Word Problems
🍕 Problem 1: Recipe Combination
A recipe calls for 2/3 cup of flour for the crust and 1 1/4 cups of flour for the topping. How much flour is needed in total?
Solution: 2/3 + 1 1/4 = 2/3 + 5/4 = 8/12 + 15/12 = 23/12 = 1 11/12 cups
🧵 Problem 2: Fabric Cutting
A tailor has 5 3/4 yards of fabric. She uses 2 1/3 yards for a dress. How much fabric remains?
Solution: 5 3/4 - 2 1/3 = 23/4 - 7/3 = 69/12 - 28/12 = 41/12 = 3 5/12 yards
🎨 Problem 3: Paint Mixing
An artist mixes 3/8 gallon of blue paint with 1/2 gallon of yellow paint. How much paint does she have in total?
Solution: 3/8 + 1/2 = 3/8 + 4/8 = 7/8 gallon
Teaching Tips for Fraction Operations
👩🏫 Helping Students Understand
Use Visual Models
Fraction bars, circles, or rectangles help students see why we need common denominators
Real-World Examples
Use pizza slices, chocolate bars, or measuring cups to make fractions concrete
Emphasize Equivalence
Show that 1/2 = 2/4 = 3/6 using manipulatives
Check with Estimation
Teach students to estimate (Is the answer more or less than 1?)
Practice Skip Counting
This helps students find common multiples quickly
Common Mistakes to Avoid
❌ Adding Denominators
Remember, denominators don't add! Only numerators add when denominators are the same.
❌ Forgetting to Simplify
Always reduce fractions to lowest terms in your final answer.
❌ Cross-Multiplication Error
This is for comparing fractions, not adding them.
❌ Mixed Number Confusion
Be careful when borrowing in mixed number subtraction.
❌ LCD Mistakes
Double-check your common denominator is actually divisible by both original denominators.
Key Takeaways
Like denominators: Simply add/subtract numerators, keep denominator
Unlike denominators: Find LCD first, then convert both fractions
Mixed numbers: Convert to improper fractions or work parts separately
Always simplify: Reduce your final answer to lowest terms
Related Topics
Ready for Multiplication and Division?
Now that you've mastered adding and subtracting fractions, continue to learn about multiplying and dividing fractions!
