Class Note: How to Add Mixed Numbers

Objective

Understand the step-by-step process of adding mixed numbers.

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Example 1:

Problem

Add: 4 and 2/3 + 5 and 1/4

Steps

1. Write as sums:

   • 4 and 2/3 = 4 + 2/3
   • 5 and 1/4 = 5 + 1/4

2. Add the whole numbers:

   • 4 + 5 = 9

3. Add the fractions:

   • 2/3 + 1/4
   • Find common denominator (3 and 4): LCD is 12
   • Convert:
     • (2/3) × (4/4) = 8/12
     • (1/4) × (3/3) = 3/12
   • Add numerators: 8 + 3 = 11
   • So, 8/12 + 3/12 = 11/12

4. Final Answer:

   • 9 + 11/12
   • 9 and 11/12

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Example 2:

Problem

Add: 3 and 2/5 + 4 and 6/7

Steps

1. Write as sums:

   • 3 and 2/5 = 3 + 2/5
   • 4 and 6/7 = 4 + 6/7

2. Add the whole numbers:

   • 3 + 4 = 7

3. Add the fractions:

   • 2/5 + 6/7
   • Find common denominator (5 and 7): LCD is 35
   • Convert:
     • (2/5) × (7/7) = 14/35
     • (6/7) × (5/5) = 30/35
   • Add numerators: 14 + 30 = 44
   • So, 14/35 + 30/35 = 44/35 (improper fraction)

4. Convert improper fraction to mixed number:

   • 44/35 = 1 and 9/35
   • Add 1 to whole number part: 7 + 1 = 8
   • Fractional part: 9/35

5. Final Answer:

   • 8 and 9/35

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Summary of Steps for Adding Mixed Numbers

1. Separate whole numbers and fractions.
2. Add whole numbers.
3. Find common denominators for the fractions.
4. Add the fractions.
5. If necessary, convert improper fractions to mixed numbers and add to whole number.
6. Write the final mixed number answer.

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Key Tip: Always check if the fractional part is an improper fraction and convert it as needed.