How to Add Two Mixed Numbers with Regrouping: Step-by-Step Guide

Understanding Mixed Numbers

• 💡 A mixed number like 2 and 3/5 can be expanded into its whole number and fractional parts: 2 + 3/5.
• 🎯 Similarly, 4 and 2/3 can be represented as 4 + 2/3.

Combining Whole Numbers and Fractions

• ➕ Combine the whole number components: 2 + 4 = 6.
• ➕ The expression becomes 6 + 3/5 + 2/3.

Adding Fractions with Common Denominators

• 🧮 To add the fractions 3/5 and 2/3, find a common denominator.
• ✖️ Multiply the first fraction by 3/3 and the second by 5/5 to get 9/15 and 10/15.
• ➕ Add the numerators: 9 + 10 = 19.
• 📈 The sum of the fractions is 19/15.

Handling Improper Fractions and Regrouping

• ⚖️ The total sum is 6 + 19/15.
• 🧩 Since 19/15 is an improper fraction, break it down: 19/15 = 15/15 + 4/15.
• 🌟 Recognize that 15/15 equals 1.
• ➡️ The expression is now 6 + 1 + 4/15.

Final Mixed Number Result

• 💯 Add the whole numbers: 6 + 1 = 7.
• ✅ The final answer is 7 and 4/15.