Adding Fractions with Like Denominators

What Are Like Denominators?

Like denominators means the bottom numbers (denominators) are the same.

Examples of like denominators:

• 1/4 and 3/4 (both have 4 on bottom)
• 2/5 and 4/5 (both have 5 on bottom)
• 3/8 and 5/8 (both have 8 on bottom)

The Simple Rule

When denominators are the same:

1. Add the numerators (top numbers)
2. Keep the denominator the same
3. Simplify if needed

Think of it like: You're counting the same type of pieces!

Visual Model: Pizza Slices

Problem: 1/8 + 3/8

Picture it:

• Pizza cut into 8 slices
• You eat 1 slice: 1/8
• Your friend eats 3 slices: 3/8
• Together you ate: 1/8 + 3/8 = 4/8

All the slices are the same size (eighths), so just count them!

You:    [■] out of 8 slices = 1/8
Friend: [■ ■ ■] out of 8 slices = 3/8
Total:  [■ ■ ■ ■] out of 8 slices = 4/8 = 1/2 ✓

Step-by-Step Examples

Example 1: 2/5 + 1/5

Step 1: Check denominators → Both are 5 ✓ Step 2: Add numerators → 2 + 1 = 3 Step 3: Keep denominator → 5 Step 4: Write answer → 3/5

Answer: 2/5 + 1/5 = 3/5 ✓

Example 2: 3/10 + 4/10

Step 1: Denominators both 10 ✓ Step 2: Add numerators → 3 + 4 = 7 Step 3: Keep denominator → 10 Step 4: Answer → 7/10

Answer: 3/10 + 4/10 = 7/10 ✓

When the Answer Needs Simplifying

Example: 2/6 + 2/6

Step 1: Add numerators → 2 + 2 = 4 Step 2: Keep denominator → 6 Step 3: Write answer → 4/6 Step 4: Simplify! → 4/6 = 2/3

Answer: 2/6 + 2/6 = 4/6 = 2/3 ✓

How to simplify:

• Find a number that divides both top and bottom
• 4 and 6 are both divisible by 2
• 4 ÷ 2 = 2 and 6 ÷ 2 = 3
• So 4/6 = 2/3

When You Get an Improper Fraction

Example: 5/8 + 4/8

Step 1: Add numerators → 5 + 4 = 9 Step 2: Keep denominator → 8 Step 3: Answer → 9/8

9/8 is bigger than 1 whole!

Can also write as: 1 1/8 (one and one-eighth)

• 8/8 = 1 whole
• Plus 1/8 more = 1 1/8

Answer: 5/8 + 4/8 = 9/8 = 1 1/8 ✓

Using Number Lines

Adding 1/4 + 2/4:

0 ―――¼―――2/4―――¾―――1
     ↑    ↑
   Start  +2/4
     └─────→ End at 3/4

• Start at 1/4
• Jump 2 more fourths
• Land on 3/4

Answer: 1/4 + 2/4 = 3/4 ✓

Real-World Examples

Measuring cups:

• Recipe needs 1/3 cup oil and 2/3 cup oil
• Total: 1/3 + 2/3 = 3/3 = 1 cup ✓

Walking distance:

• Walk 2/10 mile to park
• Walk 3/10 mile further
• Total: 2/10 + 3/10 = 5/10 = 1/2 mile ✓

Time:

• Study math for 1/4 hour
• Study reading for 2/4 hour
• Total: 1/4 + 2/4 = 3/4 hour (45 minutes) ✓

Three or More Fractions

Example: 1/8 + 3/8 + 2/8

Just keep adding numerators:

• 1 + 3 + 2 = 6
• Keep denominator: 8
• Answer: 6/8 = 3/4 ✓

The Pattern

Notice the pattern:

• 1/5 + 2/5 = 3/5
• 2/7 + 4/7 = 6/7
• 3/10 + 5/10 = 8/10 = 4/5

Rule: Numerators add, denominators stay the same!

Why It Works

Think of fractions as counting:

• 2/8 means "2 eighths"
• 3/8 means "3 eighths"
• Adding them: "2 eighths + 3 eighths = 5 eighths"
• Just like: 2 apples + 3 apples = 5 apples!

You're counting the same-sized pieces.

Practice Strategy

Before you start:

1. Check: Are the denominators the same?
2. If YES → Add numerators, keep denominator
3. If NO → This is a different lesson (unlike denominators)

After you solve:

1. Can you simplify?
2. Is it an improper fraction?
3. Does your answer make sense?

Common Mistakes

❌ Adding denominators too

• WRONG: 1/4 + 2/4 = 3/8
• RIGHT: 1/4 + 2/4 = 3/4

❌ Forgetting to simplify

• 2/8 + 2/8 = 4/8 → Should simplify to 1/2

❌ Changing the denominator

• Keep it the same!

✅ Only add the numerators ✅ The denominator never changes ✅ Simplify your final answer ✅ Check if it's an improper fraction (can convert to mixed number)

Mental Math Tricks

When adding to make 1 whole:

• 1/4 + ?/4 = 4/4 → Need 3/4 more
• 2/5 + ?/5 = 5/5 → Need 3/5 more
• 3/8 + ?/8 = 8/8 → Need 5/8 more

Remember: The denominator tells you how many pieces make one whole!

Check Your Work

Two ways to check:

1. Use pictures

• Draw the fractions
• Count the total shaded parts
• Compare to your answer

2. Think about size

• Is 1/4 + 2/4 more than 1/2?
• 3/4 is bigger than 1/2 ✓
• Makes sense!

Key Takeaways

✅ Like denominators = same bottom number ✅ Add tops, keep bottom the same ✅ Always simplify if you can ✅ Check if you got more than one whole (improper fraction) ✅ Your answer should make sense!

Remember: Fractions with the same denominator are like counting the same type of thing. Just add them up!