Why do we use division when we use per something?

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Discussion Overview

The discussion revolves around the use of division and fractions in the expression "per something," exploring the underlying reasons for this mathematical representation. The scope includes conceptual clarification and technical explanation.

Discussion Character

  • Conceptual clarification, Technical explanation, Debate/contested

Main Points Raised

  • Some participants note that "three per hundred" can be expressed as a ratio (3:100) or a fraction (3/100), indicating a relationship between two quantities.
  • One participant asserts that "three per hundred" should be understood as "3 out of 100," while another later corrects this to affirm it as "3 out of a hundred, or 3/100."
  • Another participant questions the reasoning behind using division in this context, seeking a deeper understanding of the terminology.
  • It is proposed that expressions like "6 per cent" literally mean "6 per 100," which reflects a ratio, and similar reasoning applies to units like miles per hour (mph), indicating a division of miles by time in hours.
  • One participant emphasizes that "per" distinctly indicates both division and fraction.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of "per" and its mathematical implications, indicating that the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Some statements rely on specific interpretations of terms and may depend on the context in which "per" is used, leading to potential ambiguities in understanding.

Cash Fulton
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Why do we use division/fractions to represent per something?
 
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Three per hundred, for example, means 3 out of 100, so we can write it as a ratio, 3:100, or a fraction, 3/100
 
3 per hundred is 3:97.
 
pasmith said:
3 per hundred is 3:97.
Ah yes, good catch. I should have said "three out of a hundred, or 3/100"
 
phinds said:
Three per hundred, for example, means 3 out of 100, so we can write it as a ratio, 3:100, or a fraction, 3/100
Doesn't really answer my question. I am asking why that is.
 
Cash Fulton said:
Doesn't really answer my question. I am asking why that is.
Why it is, is because of what the words mean. When we say, for example, 6 per cent (literally 6 per 100) we are expressing a ratio: ##\frac 6 {100}##. It's similar for units such as mph (miles per hour). We are talking about a ratio of miles driven per (divided by) the time in hours.
 
"per" distinctly indicates both DIVISION and FRACTION.
 

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