proportion by which

USAGE SUMMARY

The phrase "proportion by which" is correct and usable in written English.
It can be used when discussing ratios, comparisons, or relationships between quantities or values. Example: "The proportion by which the population has increased over the last decade is significant."

✓ Grammatically correct

Science

News & Media

Formal & Business

Human-verified examples from authoritative sources

Exact Expressions

18 human-written examples

The first method searches for the best proportion by which to factor setup times into unit production times.

Computers & Industrial Engineering

In a widely read treatise titled "Divina Proportione" (1509), the Italian mathematician Luca Pacioli echoed fashionable opinions of the day by declaring that our body measurements express "every ratio and proportion by which God reveals the innermost secrets of nature".

The New York Times - Books

In a widely read treatise titled "Divina Proportione" (1509), the Italian mathematician Luca Pacioli echoed fashionable opinions of the day by declaring that our body measurements express "every ratio and proportion by which God reveals the innermost secrets of nature". Pacioli's close friend Leonardo da Vinci provided illustrations.

The New York Times - Books

This method also depends on the proportion by which a pixel is going to be observed as background.

EURASIP Journal on Advances in Signal Processing

Here the telling figure is "35%." That's the proportion by which the state budget has expanded since Gov. Arnold Schwarzenegger took office in 2003.

Forbes

In model (2.1) (0leqtheta<1) is the proportion by which the pest density is reduced by killing or trapping once the number of pests reaches (V_{L}), while τ is the constant number of natural enemies released at this time t.

Advances in Difference Equations

Human-verified similar examples from authoritative sources

Similar Expressions

42 human-written examples

In fact, those are the rough proportions by which the 1914 populations were smaller than today's.

The Guardian

By undertaking a detailed phylogenetic analysis, we were able to further separate the contribution by various African regions into 7-10 genetically diverse groups/regions and estimate the proportions by which these regions contributed to the admixed African and American populations.

Plosone

A thoroughly studied aspect of translation that demonstrates its adaptation capacities is the different proportions by which synonymous codons are used, a phenomenon known as 'codon usage bias'.

eLife

The results relating to possible shifts in the proportions by which single domains impact on the intention remain ambiguous in the present study.

BMC Medical Informatics and Decision Making

In the present study, we use the estimated abundances in order to estimate the proportions by which different protein classes contribute to mitotic chromosomes and to construct classifier I.

Cell

Expert writing Tips

Best practice

When using "proportion by which", ensure the context clearly defines what is being measured or compared. For example, specify "the proportion by which sales increased" rather than just "the proportion by which".

Common error

Avoid using "proportion by which" when "percentage by which" is more appropriate. "Percentage" is specifically for values out of 100, while "proportion" is more general.

Linguistic Context

The phrase "proportion by which" functions as a prepositional phrase that modifies a noun or verb, specifying the extent or degree of change in relation to a particular quantity or amount. As Ludwig AI highlights, it is usable in written English.

Expression frequency: Uncommon

Frequent in

Science

65%

News & Media

20%

Formal & Business

15%

Less common in

Encyclopedias

0%

Wiki

0%

Reference

0%

Ludwig's WRAP-UP

In summary, "proportion by which" is a grammatically sound and usable phrase that indicates the extent or degree of change relative to a specific quantity. Ludwig AI confirms its validity, and our analysis reveals it's most commonly found in scientific and formal contexts. While related phrases like "ratio by which" or "degree to which" offer similar meanings, it's essential to choose the most appropriate alternative based on the specific context. Pay close attention to avoid confusion with "percentage by which", which is specifically for values out of 100. Using these insights will empower you to use the phrase more effectively in your writing.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

ratio by which

Replaces "proportion" with "ratio", emphasizing a quantitative relationship between two amounts.

fraction by which

Substitutes "proportion" with "fraction", highlighting a part of a whole.

amount by which

Replaces "proportion" to focus the emphasis on an actual quantity.

percentage by which

More specific than "proportion by which", using "percentage" when dealing with hundredths.

degree to which

Shifts from quantity to intensity, using "degree" to indicate the extent of something.

extent to which

Similar to "degree to which", focusing on the range or scope of an effect or change.

level to which

Similar to “degree by which”, but “level” emphasizes a determined value.

scale by which

Introduces a reference to a graded range to evaluate the increase.

rate at which

Expresses the speed or frequency of a process.

index by which

It is used when “index” provides a clear reference or measurement system.

FAQs

How can I use "proportion by which" in a sentence?

Use "proportion by which" to indicate the relative amount or degree of change. For example, "The proportion by which the budget increased was unexpected."

What's a good alternative to "proportion by which"?

Alternatives include "ratio by which", "degree to which", or "amount by which", depending on the context.

Is it correct to say "percentage by which" instead of "proportion by which"?

While similar, "percentage by which" is more specific and should be used when dealing with values expressed as a percentage. "Proportion by which" is more general.

What's the difference between "proportion by which" and "degree to which"?

"Proportion by which" refers to a relative quantity, while "degree to which" refers to the extent or intensity of something. Choose based on whether you're describing amount or intensity.