Simplifying Mixed Numbers

Overview

• Simplifying a mixed number involves simplifying only the fractional part while leaving the whole number unchanged.
• If you know how to simplify a fraction, you can simplify a mixed number.

Example 1: Simplifying 4 and 10/15

• Initial mixed number: 4 and 10/15
• Identify common factors of 10 and 15: 5
• Simplification process:
  • Divide both by 5:
    • 10 ÷ 5 = 2
    • 15 ÷ 5 = 3
• Resulting mixed number: 4 and 2/3
• Check for further simplification:
  • Common factor between 2 and 3 is 1, so this is in simplest form.

Example 2: Simplifying 7 and 12/20

• Initial mixed number: 7 and 12/20
• Identify common factors of 12 and 20: 4
• Simplification process:
  • Divide both by 4:
    • 12 ÷ 4 = 3
    • 20 ÷ 4 = 5
• Resulting mixed number: 7 and 3/5
• Check for further simplification (using different factors):
  • Divide by 2 first:
    • 12 ÷ 2 = 6
    • 20 ÷ 2 = 10
  • New mixed number: 7 and 6/10
  • Simplifying again:
    • 6 ÷ 2 = 3
    • 10 ÷ 2 = 5
• Final result: 7 and 3/5
• Both methods lead to the same final answer, but the first was a quicker single step.

Key Takeaways

• To simplify a mixed number, focus only on the fractional part.
• You can use either the greatest common factor or other common factors to simplify.
• Both methods of simplification are valid as long as you reach the simplest form.

Additional Resources

• Links to videos on simplifying fractions will be available in the description for further practice.