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Quick Reference SheetGeneral Math

Percentages, Ratios, and Proportion Cheat Sheet

A compact but richer percentage, ratio, and proportion sheet that keeps base values, equivalent forms, and proportional reasoning visible.

Filename: percentages-ratios-and-proportion-cheat-sheet.pdfFile size: 3 KB

Formula highlights

Percentage of value
part = percentage x whole / 100
Percentage change
change % = (new - old) / old x 100

Core ideas

Percentages describe amounts per hundred, ratios compare linked quantities, and proportional reasoning scales relationships without changing their structure.

Formula highlights

  • Percentage of value: (percent / 100) x base
  • Percentage increase: (change / original) x 100
  • Simplify ratios only after normalising units
  • Equivalent ratios describe the same relationship at different scales

Worked examples

15% of 80 = 12.

Increase from 40 to 50 = 25% increase.

18:24 simplifies to 3:4 because the GCD is 6.

Quick reminders

  • The original value matters in percentage change.
  • A 20% fall followed by a 20% rise does not restore the starting value.
  • Use ratios for comparison and percentages for part-of-whole statements.
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