Math with Mr. J: Comparing Fractions

Introduction

• Focus of the video: How to compare fractions.
• Key strategy: Use common denominators and benchmarks.

Comparison Process

1. Common Denominator

   • First, check if the fractions have a common denominator.
   • If they don't, find a common denominator to make comparison easier.

2. Renaming Fractions

   • When finding a common denominator, rename the fractions without changing their value.
   • This involves multiplying both numerator and denominator by the same number.

Detailed Examples

Example 1: Compare 3/8 and 13/16

• Step 1: Common Denominator is 16.
• Step 2: Rename 3/8 to 6/16 (multiply by 2).
• Step 3: Compare 6/16 and 13/16.
  • 3/8 is less than 13/16.
• Strategy: Use 1/2 as a benchmark.
  • 3/8 is less than 1/2, 13/16 is more than 1/2.

Example 2: Compare 2/12 and 8/9

• Step 1: Common Denominator is 36.
• Step 2: Rename 2/12 to 6/36, 8/9 to 32/36.
• Step 3: Compare 6/36 and 32/36.
  • 2/12 is less than 8/9.
• Strategy: 2/12 is less than 1/2, 8/9 is more than 1/2.

Example 3: Compare 3/4 and 6/8

• Step 1: Common Denominator is 8.
• Step 2: Rename 3/4 to 6/8 (multiply by 2).
• Step 3: Compare 6/8 and 6/8.
  • 3/4 is equal to 6/8.

Example 4: Compare 8/10 and 17/20

• Step 1: Common Denominator is 20.
• Step 2: Rename 8/10 to 16/20 (multiply by 2).
• Step 3: Compare 16/20 and 17/20.
  • 8/10 is less than 17/20.

Use of Benchmarks

• 1/2 as a Benchmark: Helps in assessing where fractions stand relatively.
  • If a fraction is less or more than 1/2, it gives a quick comparison insight.

Conclusion

• Use benchmarks like 1/2 to quickly evaluate fractions.
• Ensure to find a common denominator to accurately compare fractions.

End Note: Renaming fractions and using benchmarks provides a systematic way to compare fractions effectively.

• Thank you for watching!
• Sign off: Until next time, peace.