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Addition of Mixed Numbers

Mathematics Grade 5 Difficulty 3/5

Beginning of the lesson

Addition of Mixed Numbers

A mixed number combines a whole number with a proper fraction. Adding mixed numbers means combining two or more of these quantities into a single sum.

Example: 23⁄4 + 11⁄2 means adding two quantities that each have whole and fractional parts.

🔑 Key Principle

Mixed Number Structure:

Mixed Number = Whole Part + Fractional Part

23⁄4 = 2 + 3⁄4

To Add Mixed Numbers:
  1. Add the whole parts together
  2. Add the fractional parts together
  3. Combine the results
  4. Regroup if the fractional sum is improper (≥1)
Interactive visualization — available in the full lesson

📘 Method 1: Adding Parts Separately

Same Denominators (Easy Case)

When fractions have the same denominator, adding is straightforward:

Step 1: Add the whole numbers

Step 2: Add the numerators (top numbers)

Step 3: Keep the denominator the same

Step 4: Combine whole and fraction

Step 5: Simplify if needed

Example: 23⁄5 + 11⁄5
= (2 + 1) + (3⁄5 + 1⁄5)
= 3 + 4⁄5
= 34⁄5
Interactive visualization — available in the full lesson
⚠️ Regrouping: When Fractional Sum Exceeds 1

Sometimes when you add the fractions, the sum is an improper fraction (numerator ≥ denominator). You must regroup!

Regrouping Steps
  1. Add the whole parts
  2. Add the fractions
  3. If fraction is improper, convert to mixed number
  4. Add the extra whole to the whole part
Example: 24⁄5 + 13⁄5
= (2 + 1) + (4⁄5 + 3⁄5)
= 3 + 7⁄5 ← improper!
= 3 + 12⁄5
= 42⁄5
More Regrouping Examples
ProblemWorkAnswer
23⁄4 + 13⁄43 + 6⁄4 = 3 + 12⁄441⁄2
35⁄6 + 25⁄65 + 10⁄6 = 5 + 14⁄662⁄3
47⁄8 + 25⁄86 + 12⁄8 = 6 + 14⁄871⁄2
🔄 Different Denominators

When fractions have different denominators, you must first find a common denominator.

Step-by-Step Method
  1. Find the LCD (Least Common Denominator) of the fractions
  2. Convert each fraction to equivalent fraction with LCD
  3. Add the whole parts
  4. Add the converted fractions
  5. Regroup if needed
  6. Simplify the final answer
Finding LCD:

For 1⁄3 and 1⁄4:

Multiples of 3: 3, 6, 9, 12, 15...

Multiples of 4: 4, 8, 12, 16...

LCD = 12

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In the full lesson

  • The complete explanation
  • Worked examples
  • Common mistakes and how to avoid them
  • Test questions: 62
  • AI tutor that answers questions about the topic
  • Progress tracking for students, parents and teachers