Math Antics: Understanding Percents

Introduction to Percents

• A percent is a fraction with 100 as the denominator.
• Common misconception: percents apply only when there are 100 items.

Using Percents in Various Situations

• Example 1: Test Scores
  • Scoring 90% on a 50-question test.
  • Converting 90%: It's equivalent to 90/100.
  • Find actual score: 100 to 50 questions = divide by 2.
    • 90/100 = 45/50 after dividing both numerator and denominator by 2.
• Example 2: Candy Bar
  • 50% means 50/100; equivalent to 1/2 of the candy bar.
• Example 3: Large Numbers
  • 65% of Americans liking football.
  • Example fraction: 205,636,600/316,364,000 simplifies to 65/100.

Understanding Equivalent Fractions

• Equivalent fractions represent the same value with different numerators and denominators.
• Creating Equivalent Fractions:
  • Multiplying: Multiply numerator and denominator by the same number (e.g., 2/3 = 8/12 by multiplying by 4).
  • Dividing: Divide numerator and denominator by the same number (e.g., 6/20 = 3/10 by dividing by 2).

Why Convert to Percents?

• Comparison Ease
  • Percents offer a consistent scale (0 to 100) for comparison.
  • Example: Comparing test scores of different question totals.
    • Scores: 40/80, 18/30, 12/16, 96/120, 19/20.
    • Convert to percent form: 50%, 60%, 75%, 80%, 95%.

Common Percent-Fraction Equivalents

• 1/2 = 50%
• 1/4 = 25%
• 3/4 = 75%
• 1/3 ≈ 33.33% (repeating, rounded to 33%)
• 2/3 ≈ 66.66% (repeating, rounded to 67%)

Conclusion

• Percents are equivalent fractions with 100 as the denominator.
• Practicing with equivalent fractions helps solve many math problems involving percentages.
• Further learning available at Math Antics.