G2 Mathematics K210 comparison becomes fairer when quantities with different-sized bases are placed on a common base. Raw counts answer “how many”; normalised quantities answer “how many per person, per unit area, per hour, per dollar, or as a share of the whole”.
This one-hundred-and-thirtieth Learner’s Guide develops normalisation to a common base. It extends Vol 0110 Comparison-Measure Choice and Vol 0078 Dimensional Consistency.
The normalisation protocol
Identify the raw quantity, identify the base that differs between cases, divide by that base, and state the resulting unit. Use the same denominator definition for every case. Then decide whether raw scale, normalised rate or both are needed for the question.
1. per person
For per person, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
2. per household
For per household, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
3. per student
For per student, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
4. per class
For per class, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
5. per square kilometre
For per square kilometre, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
6. per square metre
For per square metre, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
7. per hour
For per hour, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
8. per minute
For per minute, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
9. per second
For per second, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
10. per item
For per item, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
11. per kilogram
For per kilogram, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
12. per gram
For per gram, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
13. per litre
For per litre, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
14. per dollar
For per dollar, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
15. per $100
For per $100, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
16. per 100 people
For per 100 people, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
17. per 1000 people
For per 1000 people, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
18. percentage of total
For percentage of total, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
19. fraction of whole
For fraction of whole, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
20. ratio to baseline
For ratio to baseline, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
21. index with base 100
For index with base 100, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
22. relative frequency
For relative frequency, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
23. frequency density
For frequency density, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
24. population density
For population density, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
25. occupancy rate
For occupancy rate, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
26. utilisation rate
For utilisation rate, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
27. success rate
For success rate, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
28. error rate
For error rate, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
29. response rate
For response rate, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
30. growth rate
For growth rate, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
31. decline rate
For decline rate, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
32. unit price
For unit price, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
33. unit cost
For unit cost, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
34. unit mass
For unit mass, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
35. unit volume
For unit volume, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
36. unit length
For unit length, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
37. speed
For speed, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
38. fuel efficiency
For fuel efficiency, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
39. fuel consumption
For fuel consumption, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
40. productivity
For productivity, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
41. work rate
For work rate, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
42. flow rate
For flow rate, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
43. data rate
For data rate, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
44. cash burn rate
For cash burn rate, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
45. runway per burn
For runway per burn, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
46. profit margin
For profit margin, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
47. markup
For markup, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
48. return relative to cost
For return relative to cost, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
49. discount percentage
For discount percentage, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
50. tax rate
For tax rate, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
51. interest rate
For interest rate, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
52. percentage change
For percentage change, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
53. percentage-point change
For percentage-point change, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
54. relative change
For relative change, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
55. absolute change
For absolute change, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
56. same total different population
For same total different population, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
57. same population different total
For same population different total, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
58. same count different exposure
For same count different exposure, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
59. same exposure different count
For same exposure different count, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
60. same area different population
For same area different population, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
61. same population different area
For same population different area, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
62. same revenue different cost base
For same revenue different cost base, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
63. same profit different revenue
For same profit different revenue, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
64. same profit different cost
For same profit different cost, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
65. same successes different attempts
For same successes different attempts, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
66. same errors different attempts
For same errors different attempts, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
67. same distance different time
For same distance different time, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
68. same time different distance
For same time different distance, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
69. same work different workers
For same work different workers, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
70. same workers different work
For same workers different work, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
71. same data different duration
For same data different duration, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
72. same duration different data
For same duration different data, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
73. same amount different mass
For same amount different mass, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
74. same amount different volume
For same amount different volume, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
75. normalise before ranking
For normalise before ranking, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
76. normalise before graphing
For normalise before graphing, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
77. normalise before comparing groups
For normalise before comparing groups, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
78. normalise after unit conversion
For normalise after unit conversion, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
79. choose meaningful denominator
For choose meaningful denominator, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
80. avoid tiny denominator distortion
For avoid tiny denominator distortion, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
81. avoid denominator switching
For avoid denominator switching, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
82. preserve denominator in wording
For preserve denominator in wording, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
83. raw and normalised together
For raw and normalised together, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
84. normalisation hides scale
For normalisation hides scale, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
85. normalisation reveals efficiency
For normalisation reveals efficiency, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
86. normalisation can reverse ranking
For normalisation can reverse ranking, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
87. common-base final rule
For common-base final rule, write the numerator and denominator in words before calculating. Explain what one unit of the normalised result means.
For practice, construct two cases where the raw-count ranking and normalised ranking differ. Explain why neither is automatically wrong: they answer different questions. Then identify which comparison the question actually requests.
Check denominator stability. If one case uses people and another uses households, or one rate uses hours while another uses minutes, convert to a genuinely common base before ranking. A shared percentage sign does not guarantee a shared denominator.
Normalisation can clarify and conceal
A per-unit measure reveals intensity or efficiency, but it can hide absolute scale. A small group can have a high rate but a small total impact. Strong answers keep raw and normalised quantities distinct and choose the one aligned with the task.
Links
Use the Mathematics Hub, Vol 0126 Monotonicity Checks, Vol 0118 Conservation and Balance Checks, the Examination Craft hub and the PSLE Learner’s Guide.
Official-source discipline
For the current 2027 SEC G2 school-candidate framework, use the official SEAB G2 syllabus directory and linked K210 Mathematics syllabus. Common-base normalisation is an eduKateSengkang quantitative-reasoning framework, not an additional SEAB syllabus topic.
Final rule
Compare like with like. When bases differ, normalise deliberately, name the denominator, preserve the unit and remember that a fair rate comparison may answer a different question from the raw total.
