Get Ready to Learn:
✓ Adding mixed numbers with same denominators
✓ Adding mixed numbers with different denominators
✓ Real-world applications
✓ Problem-solving strategies
Let's build on what you already know! 🚀
Click any topic to jump directly to that section!
A mixed number has two parts:
• A whole number
• A proper fraction (numerator is less than denominator)
2 whole parts and ⅓ of another part
5 whole parts and ¾ of another part
That's 1 whole plus ⅔ more!
Today we're learning to ADD mixed numbers together!
Example:
2⅓ + 1⅔
Both fractions have 3 on the bottom - this is EASIER!
Example:
2½ + 1⅓
The fractions have different bottoms (2 and 3) - requires an extra step!
We'll start with same denominators (easier) and then move to different denominators (our main focus today)!
Step 1: Add the whole numbers
Step 2: Add the fractions (numerators only)
Step 3: Keep the same denominator
Step 4: Simplify if needed (convert improper fractions to mixed numbers)
This is the easier case - let's see examples!
Step 1: Add the whole numbers
2 + 1 = 3
Step 2: Add the fractions
⅖ + ⅗ = (2+3)/5 = ⅘
Step 3: Combine them
3 + ⅘ = 3⅘
Step 1: Add the whole numbers
3 + 2 = 5
Step 2: Add the fractions
¾ + ¾ = (3+3)/4 = 6/4
Step 3: Simplify 6/4
6/4 = 1²⁄₄ = 1½
Step 4: Add to the whole number
5 + 1½ = 6½
When your fraction is improper (like 6/4), you MUST convert it to a mixed number and add it to your whole number!
Step 1: Add whole numbers: 1 + 2 = 3
Step 2: Add fractions: ⅝ + ⅝ = 6/8
Step 3: Simplify: 6/8 = ¾
Step 4: Combine: 3 + ¾ = 3¾
Problem 1: 1⅓ + 2⅓
Step 1: Add whole numbers: 1 + 2 = 3
Step 2: Add fractions: ⅓ + ⅓ = ⅔
Step 3: Combine: 3 + ⅔ = 3⅔
Answer: 3⅔
Problem 2: 4⅕ + 1⅘
Step 1: Add whole numbers: 4 + 1 = 5
Step 2: Add fractions: ⅕ + ⅘ = 5/5 = 1
Step 3: Combine: 5 + 1 = 6
Answer: 6
Problem 3: 2⅞ + 3⅞
Step 1: Add whole numbers: 2 + 3 = 5
Step 2: Add fractions: ⅞ + ⅞ = 14/8
Step 3: Simplify: 14/8 = 1⁶⁄₈ = 1¾
Step 4: Combine: 5 + 1¾ = 6¾
Answer: 6¾
Problem 4: 5⅔ + 2⅓
Step 1: Add whole numbers: 5 + 2 = 7
Step 2: Add fractions: ⅔ + ⅓ = 3/3 = 1
Step 3: Combine: 7 + 1 = 8
Answer: 8
Steps:
1. Add the whole numbers together
2. Add the fractions together (add numerators, keep denominator)
3. If the fraction is improper, convert it to a mixed number
4. Add any extra whole number to your total
5. Simplify your final answer
Example:
2⅗ + 1⅘ = ?
• Whole numbers: 2 + 1 = 3
• Fractions: ⅗ + ⅘ = 7/5 = 1⅖
• Combine: 3 + 1⅖ = 4⅖
This is our PRIMARY FOCUS today!
When denominators are DIFFERENT, you cannot add the fractions directly!
Example:
2½ + 1⅓
The fractions have different denominators (2 and 3)
You CANNOT add ½ + ⅓ directly!
1. Convert mixed numbers to improper fractions
2. Find common denominator
3. Add the fractions
4. Convert back to mixed number
Best for: Complex fractions
1. Add whole numbers
2. Find common denominator for fractions
3. Add the fractions
4. Combine and simplify
Best for: Simple problems
We'll practice BOTH methods so you can choose what works best!
Method 1: Convert to Improper Fractions
1. Convert each mixed number to an improper fraction
2. Find the Least Common Denominator (LCD)
3. Convert both fractions to equivalent fractions with the LCD
4. Add the numerators, keep the LCD
5. Convert back to a mixed number
6. Simplify if possible
Method 2: Add Whole and Fractions Separately
1. Add the whole numbers together
2. Find the LCD for the fractions
3. Convert fractions to have the LCD
4. Add the fractions
5. If improper, convert and add to whole number
6. Simplify final answer
Step 1: Convert to improper fractions
2½ = (2×2+1)/2 = 5/2
1⅓ = (1×3+1)/3 = 4/3
Step 2: Find LCD of 2 and 3
LCD = 6
Step 3: Convert to equivalent fractions
5/2 = 15/6 (multiply by 3/3)
4/3 = 8/6 (multiply by 2/2)
Step 4: Add the fractions
15/6 + 8/6 = 23/6
Step 5: Convert to mixed number
23 ÷ 6 = 3 R5
Step 1: Add whole numbers
2 + 1 = 3
Step 2: Find LCD of fractions (2 and 3)
LCD = 6
Step 3: Convert fractions to LCD
½ = 3/6
⅓ = 2/6
Step 4: Add the fractions
3/6 + 2/6 = 5/6
Step 5: Combine
3 + 5/6 = 3⅚
Both methods give the same answer! Use whichever you prefer.
Step 1: Convert to improper fractions
3¼ = 13/4
2⅔ = 8/3
Step 2: Find LCD of 4 and 3 = 12
Step 3: Convert to LCD
13/4 = 39/12
8/3 = 32/12
Step 4: Add
39/12 + 32/12 = 71/12
Step 5: Convert to mixed number
71 ÷ 12 = 5 R11
Step 1: Add whole numbers
1 + 2 = 3
Step 2: Find LCD of 5 and 4 = 20
Step 3: Convert fractions
⅖ = 8/20
¾ = 15/20
Step 4: Add fractions
8/20 + 15/20 = 23/20
Step 5: Convert 23/20 to mixed number
23/20 = 1³⁄₂₀
Step 6: Add to whole number
3 + 1³⁄₂₀ = 4³⁄₂₀
Using Method 1:
Convert: 14/3 + 7/2
LCD = 6
28/6 + 21/6 = 49/6
49 ÷ 6 = 8 R1
When working with different denominators, always find the LCD first before adding!
Why we need a common denominator:
You can only add fractions when they have the same denominator!
How to find the LCD (Least Common Denominator):
Method 1: List multiples of each denominator until you find a match
Method 2: Multiply the denominators (works but might not be the LCD)
Example: LCD of 3 and 4
Multiples of 3: 3, 6, 9, 12, 15...
Multiples of 4: 4, 8, 12, 16...
LCD = 12
Always convert BOTH fractions to the LCD before adding!
Problem 1: 2⅓ + 1½
Method 1:
Convert: 7/3 + 3/2
LCD = 6
14/6 + 9/6 = 23/6 = 3⅚
Answer: 3⅚
Problem 2: 1¼ + 2⅔
Method 2:
Whole numbers: 1 + 2 = 3
LCD of 4 and 3 = 12
¼ = 3/12, ⅔ = 8/12
3/12 + 8/12 = 11/12
3 + 11/12 = 3¹¹⁄₁₂
Answer: 3¹¹⁄₁₂
Problem 3: 3⅖ + 1¾
Convert: 17/5 + 7/4
LCD = 20
68/20 + 35/20 = 103/20
103 ÷ 20 = 5 R3
Answer: 5³⁄₂₀
Problem 4: 2½ + 3⅔
Whole numbers: 2 + 3 = 5
LCD of 2 and 3 = 6
½ = 3/6, ⅔ = 4/6
3/6 + 4/6 = 7/6 = 1⅙
5 + 1⅙ = 6⅙
Answer: 6⅙
Problem 5: 4⅚ + 2¼
Convert: 29/6 + 9/4
LCD = 12
58/12 + 27/12 = 85/12
85 ÷ 12 = 7 R1
Answer: 7¹⁄₁₂
Problem 6: 1⅗ + 2⅞
Whole numbers: 1 + 2 = 3
LCD of 5 and 8 = 40
⅗ = 24/40, ⅞ = 35/40
24/40 + 35/40 = 59/40 = 1¹⁹⁄₄₀
3 + 1¹⁹⁄₄₀ = 4¹⁹⁄₄₀
Answer: 4¹⁹⁄₄₀
Problem 7: 5⅓ + 1⅘
Convert: 16/3 + 9/5
LCD = 15
80/15 + 27/15 = 107/15
107 ÷ 15 = 7 R2
Answer: 7²⁄₁₅
Problem 8: 3⅝ + 2⅓
Whole numbers: 3 + 2 = 5
LCD of 8 and 3 = 24
⅝ = 15/24, ⅓ = 8/24
15/24 + 8/24 = 23/24
5 + 23/24 = 5²³⁄₂₄
Answer: 5²³⁄₂₄
Problem 9: 6¾ + 3⅖
Convert: 27/4 + 17/5
LCD = 20
135/20 + 68/20 = 203/20
203 ÷ 20 = 10 R3
Answer: 10³⁄₂₀
Problem 10: 2⅚ + 4⅜
Whole numbers: 2 + 4 = 6
LCD of 6 and 8 = 24
⅚ = 20/24, ⅜ = 9/24
20/24 + 9/24 = 29/24 = 1⁵⁄₂₄
6 + 1⁵⁄₂₄ = 7⁵⁄₂₄
Answer: 7⁵⁄₂₄
Problem 11: 1⅞ + 3⅖
Convert: 15/8 + 17/5
LCD = 40
75/40 + 136/40 = 211/40
211 ÷ 40 = 5 R11
Answer: 5¹¹⁄₄₀
Problem 12: 4⅓ + 2⅚
Whole numbers: 4 + 2 = 6
LCD of 3 and 6 = 6
⅓ = 2/6, ⅚ = ⅚
2/6 + 5/6 = 7/6 = 1⅙
6 + 1⅙ = 7⅙
Answer: 7⅙
1½ looks like this:
2⅓ looks like this:
Solution:
Whole numbers: 1 + 2 = 3
LCD of 2 and 3 = 6
½ = 3/6
⅓ = 2/6
3/6 + 2/6 = 5/6
3⅚ looks like this:
✓ When the whole numbers are large
✓ When you're comfortable with improper fractions
✓ When the fractions are complex
Example: 8⅞ + 6⅚
✓ When the whole numbers are small
✓ When you want to see the steps clearly
✓ When the fractions are simple
Example: 1⅓ + 2½
Both methods work! Choose what makes sense to YOU!
Always make sure you found the LEAST common denominator, not just any common denominator. This keeps your numbers smaller and easier to work with!
Don't forget to simplify your final answer if possible! For example, 4²⁄₄ should be simplified to 4½.
If your fraction part ends up being improper (like 7/4), you MUST convert it to a mixed number and add it to your whole number!
Write down each step! This helps you:
• Find mistakes more easily
• Remember the process
• Get partial credit on tests
Does your answer make sense? If you added 3⅓ + 2½, your answer should be around 5 or 6, not 1 or 20!
The more you practice finding common denominators, the faster you'll get! Common pairs to memorize:
• 2 and 3 → 6
• 3 and 4 → 12
• 2 and 5 → 10
• 4 and 6 → 12
Challenge 1: 5⅞ + 3⅚ + 1½
(Hint: Add two at a time!)
Step 1: Add 5⅞ + 3⅚ first
Whole numbers: 5 + 3 = 8
LCD of 8 and 6 = 24
⅞ = 21/24, ⅚ = 20/24
21/24 + 20/24 = 41/24 = 1¹⁷⁄₂₄
8 + 1¹⁷⁄₂₄ = 9¹⁷⁄₂₄
Step 2: Add 9¹⁷⁄₂₄ + 1½
Whole numbers: 9 + 1 = 10
½ = 12/24
17/24 + 12/24 = 29/24 = 1⁵⁄₂₄
10 + 1⁵⁄₂₄ = 11⁵⁄₂₄
Answer: 11⁵⁄₂₄
Sarah is making cookies. The recipe calls for 2½ cups of flour for chocolate chips cookies and 1⅔ cups of flour for sugar cookies. She wants to make both types. How much flour does she need in total?
Problem: 2½ + 1⅔
Step 1: Add whole numbers: 2 + 1 = 3
Step 2: Find LCD of 2 and 3 = 6
Step 3: Convert fractions:
½ = 3/6
⅔ = 4/6
Step 4: Add fractions: 3/6 + 4/6 = 7/6 = 1⅙
Step 5: Combine: 3 + 1⅙ = 4⅙
Answer: 4⅙ cups of flour
Marcus is building a garden. He needs 3¾ feet of wood for one side and 2⅖ feet of wood for another side. How much wood does he need altogether?
Problem: 3¾ + 2⅖
Method 1 (Convert First):
Convert: 15/4 + 12/5
LCD = 20
75/20 + 48/20 = 123/20
123 ÷ 20 = 6 R3
Answer: 6³⁄₂₀ feet of wood
Emma ran 2⅚ miles on Monday and 3½ miles on Tuesday. What is the total distance she ran over these two days?
Problem: 2⅚ + 3½
Step 1: Add whole numbers: 2 + 3 = 5
Step 2: Find LCD of 6 and 2 = 6
Step 3: Convert fractions:
⅚ = ⅚
½ = 3/6
Step 4: Add fractions: 5/6 + 3/6 = 8/6 = 1⅓
Step 5: Combine: 5 + 1⅓ = 6⅓
Answer: 6⅓ miles
An art project requires 1⅜ yards of red ribbon and 2¾ yards of blue ribbon. How many total yards of ribbon are needed?
Problem: 1⅜ + 2¾
Step 1: Add whole numbers: 1 + 2 = 3
Step 2: Find LCD of 8 and 4 = 8
Step 3: Convert fractions:
⅜ = ⅜
¾ = 6/8
Step 4: Add fractions: 3/8 + 6/8 = 9/8 = 1⅛
Step 5: Combine: 3 + 1⅛ = 4⅛
Answer: 4⅛ yards of ribbon
WRONG: 2½ + 1⅓ = 3⅚ ❌
(You can't just add ½ + ⅓ to get ⅚!)
RIGHT: First find LCD, then add!
½ = 3/6, ⅓ = 2/6
3/6 + 2/6 = 5/6
So 2½ + 1⅓ = 3⅚ ✓
WRONG:
2¾ + 3¾ = 5 6/4 ❌
RIGHT:
2¾ + 3¾ = 5 6/4
But 6/4 = 1½
So the answer is 5 + 1½ = 6½ ✓
WRONG: LCD of 2 and 3 is 2×3 = 6 ✓ (This works!)
BUT: LCD of 4 and 6 is NOT 4×6 = 24
The LCD is actually 12!
Multiplying denominators gives a common denominator, but not always the least common denominator.
NEVER ADD DENOMINATORS!
WRONG: ⅓ + ⅓ = 2/6 ❌
RIGHT: ⅓ + ⅓ = 2/3 ✓
Remember: Add numerators, KEEP the denominator the same!
WRONG:
3½ + 2⅓ = ⅚ ❌
RIGHT:
Don't forget to add 3 + 2 = 5!
The answer is 5⅚ ✓
✓ Add whole numbers
✓ Add fractions (add numerators, keep denominator)
✓ Convert improper fractions if needed
✓ Simplify
✓ Find the LCD of the denominators
✓ Convert both fractions to have the LCD
✓ Add using one of the two methods we learned
✓ Convert improper fractions if needed
✓ Simplify your final answer
Convert to Improper Fractions
• Convert mixed numbers first
• Find LCD
• Add improper fractions
• Convert back to mixed number
Best for: Larger numbers, complex fractions
Add Separately
• Add whole numbers
• Find LCD for fractions
• Add fractions
• Combine everything
Best for: Smaller numbers, step-by-step clarity
Remember: ALWAYS find a common denominator when adding fractions with different denominators!
Problem 1: 4⅔ + 2⅔ (same denominators)
4 + 2 = 6
⅔ + ⅔ = 4/3 = 1⅓
6 + 1⅓ = 7⅓
Answer: 7⅓
Problem 2: 5¾ + 2⅝ (different denominators)
Whole: 5 + 2 = 7
LCD of 4 and 8 = 8
¾ = 6/8
6/8 + 5/8 = 11/8 = 1⅜
7 + 1⅜ = 8⅜
Answer: 8⅜
• Do a few problems every day
• Review your notes before practicing
• Try both methods to see which you prefer
Knowing these by heart will save you time:
• 2 and 3 → 6
• 2 and 4 → 4
• 3 and 4 → 12
• 2 and 5 → 10
• 4 and 6 → 12
• 3 and 6 → 6
• Does your answer make sense?
• Did you simplify completely?
• Did you convert improper fractions?
Today You Mastered:
✓ Adding mixed numbers with same denominators
✓ Adding mixed numbers with different denominators
✓ Two different methods for solving problems
✓ Finding least common denominators
✓ Converting improper fractions to mixed numbers
✓ Solving real-world word problems
✓ Avoiding common mistakes
Coming Up Next:
Subtracting mixed numbers
More complex fraction operations
Multi-step word problems
You're becoming a fraction expert! Keep up the amazing work! 🌟🎯🚀