Percentages

Percentages & Fractions

Understand fractions, percentage changes, decimal conversions, and inverse percent problems.

Lessons included in this chapter:

• Fraction Basics: Denominator = total equal parts. Numerator = parts you have.
• Multiplying Fractions: p/q of N = N ÷ q × p. Divide by the bottom, multiply by the top.
• Simplifying Fractions: Divide numerator and denominator by their HCF until no common factor remains.
• Percentage Basics: 10% = ÷10. Build everything else from there: 5% = half of 10%, 25% = ÷4, 50% = ÷2.
• Fraction ↔ Percentage Conversion: Fraction → %: divide top by bottom, multiply by 100. % → Fraction: write /100, simplify.
• Percentage Tricks: (Part ÷ Whole) × 100. Divide the part by the whole, then multiply by 100.
• Percentage Increase & Decrease: % change = (New − Original) ÷ Original × 100. Always divide by the original.
• Reverse Percentages: Original = Final ÷ multiplier. The multiplier is (1 ± rate/100).
• Compound Percentages: Multiply the multipliers — never add the rates. × 1.2 × 0.8 = × 0.96.