Math with Mr. J: Adding Fractions with Unlike Denominators

Introduction

• Key topic: How to add fractions with unlike denominators.
• Requirement: A common denominator is needed to add fractions.

Example 1: 4/9 + 1/3

1. Find Common Denominator
   • Denominators: 9 and 3.
   • Find the least common multiple (LCM).
   • Write out multiples:
     • Multiples of 9: 9, 18, 27, 36.
     • Multiples of 3: 3, 6, 9.
   • LCM is 9.
2. Rename Fractions
   • 4/9 already has a denominator of 9.
   • 1/3 -> need to adjust to 9 as denominator by multiplying numerator and denominator by 3.
   • 1/3 becomes 3/9.
3. Add Fractions
   • Add numerators: 4 + 3 = 7.
   • Keep the denominator: 9.
   • Result: 7/9.
   • Simplify: Already in simplest form.

Example 2: 3/10 + 2/6

1. Find Common Denominator
   • Denominators: 10 and 6.
   • Write out multiples:
     • Multiples of 10: 10, 20, 30, 40.
     • Multiples of 6: 6, 12, 18, 24, 30.
   • LCM is 30.
2. Rename Fractions
   • 3/10 -> Adjust to 30 as denominator.
     • 10 x 3 -> 30, multiply numerator by 3.
     • Result: 9/30.
   • 2/6 -> Adjust to 30 as denominator.
     • 6 x 5 -> 30, multiply numerator by 5.
     • Result: 10/30.
3. Add Fractions
   • Add numerators: 9 + 10 = 19.
   • Keep the denominator: 30.
   • Result: 19/30.
   • Simplify: Already in simplest form.

Summary

• Steps to add fractions with unlike denominators:
  1. Find a common denominator through LCM.
  2. Rename fractions with the common denominator.
  3. Add numerators and keep the same denominator.
  4. Simplify the result if possible.

Additional Resources

• Links to further videos on related topics provided in the description:
  • Detailed explanation on why a common denominator is needed.
  • Additional practice problems, including simplification examples.

Note: Part 2 will include additional examples with simplification.