through multiplication by

USAGE SUMMARY

The phrase "through multiplication by" is correct and usable in written English.
It can be used in mathematical contexts to describe the process of increasing a quantity by multiplying it with another number. Example: "The area of the rectangle can be calculated through multiplication by its length and width."

✓ Grammatically correct

Science

Academia

Human-verified examples from authoritative sources

Exact Expressions

6 human-written examples

The central topic of this unit is converting matrices to nice form (diagonal or nearly-diagonal) through multiplication by other matrices.

Massachusetts Institute of Technology

The decoded message (hat {u}) is solved through multiplication by the inverse scrambling (descrambling) matrix S −1 and the decoded message m, and the expression of descrambling can be written as hat{u}=(m+e cdot S^{-1}=ucdot Scdot S^{-1}+ecdot S^{-1}=u+ecdot S^{-1} Fig. 2 Examples of an information puncturing and scrambling schemes.

EURASIP Journal on Wireless Communications and Networking

The absorption coefficient units of ℓ/mol H·cm2 were converted into ℓ/mol H2O·cm2 through multiplication by 2. The water contents were calculated using the Beer Lambert law and expressed as wt ppm H2O using the molar mass of H2O and the density of either anorthite or zoisite as the reaction product.

Earth, Planets and Space

Down-regulated genes in some instances are made non-negative through multiplication by negative 1 and are considered to be preferred to the region of the denominator in each respective fold change calculation.

G3: Genes, Genomes, Genetics

In brief, the matrix-notation for propagation of the electric fields as presented in the present study allows the influence of tight focusing to be incorporated through multiplication by an additional "local field" matrix.

Analytical Chemistry

The most basic requirement of dynamic similarity is geometric similarity, which states that all linear measurements of one individual can be transformed into those of another through multiplication by a single factor (Alexander and Jayes, 1983).

Biology Open

Human-verified similar examples from authoritative sources

Similar Expressions

53 human-written examples

Then an improved discrete Fourier transform algorithm is proposed to extract harmonic components, which can dramatically reduce the computation load through replacing multiplication by shift operation.

Measurement

After some calculations, we showed that the method is a linear and implicit technique which may be rewritten in vector form through the multiplication by a real square matrix that, under suitable conditions on the parameters of the analytical and computational models, turns out to be an M-matrix.

Advances in Difference Equations

Simulated tumor cases were obtained through multiplication of the mean by the empirical copy number ratio of 204 prostate cancer cases [ 9].

Genome Medicine

Pitch transposition represents the linear translation of a spectrum through multiplication of all its frequency components by a constant.

Princeton University

First, after passing through the AFB and multiplication by (theta ^_{k,n}) and real taking, the received symbols are used to obtain the ML estimates of the CFO, STO and CIR.

EURASIP Journal on Advances in Signal Processing

Expert writing Tips

Best practice

When describing a process involving scaling or converting units, use "through multiplication by" to clearly indicate the mathematical operation performed. For example, "Convert inches to centimeters through multiplication by 2.54".

Common error

Instead of saying "The result was achieved through multiplication by...", prefer active voice constructions like "We achieved the result by multiplying by...". This makes your writing more direct and engaging.

Linguistic Context

The phrase "through multiplication by" functions as a prepositional phrase, indicating the method or process by which a certain result is achieved. It typically introduces the specific factor used in the multiplicative operation. Ludwig AI shows that this phrase is commonly used to describe transformations or calculations.

Expression frequency: Uncommon

Frequent in

Science

66%

Academia

33%

News & Media

1%

Less common in

Encyclopedias

0%

Wiki

0%

Formal & Business

0%

Ludwig's WRAP-UP

In summary, "through multiplication by" is a prepositional phrase used to describe how a result is achieved using a specific multiplicative factor. Ludwig AI confirms that it is grammatically correct and commonly used in scientific and academic writing to explain mathematical operations precisely. While not exceedingly common, its use provides clarity and accuracy in describing quantitative processes. Alternative phrases include "by means of multiplication" or "via multiplication of", but the original phrase offers directness. Ensure that when using this phrase, you maintain an active voice and specify what is being multiplied and by what factor for maximum clarity.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

by means of multiplication

Replaces "through" with "by means of", emphasizing the method used.

via multiplication of

Substitutes "through" with "via" and restructures the phrase to use a noun.

using multiplication by

Focuses on the tool or method employed in the process.

obtained by multiplying by

Highlights the result of the multiplication process.

calculated through multiplying by

Emphasizes the calculation aspect of the multiplication.

determined by multiplication with

Stresses the determination of a value or result.

derived by multiplying by

Highlights the derivation of a result.

achieved through the process of multiplication by

Elaborates on the method, adding formality.

resulting from multiplication by

Focuses on the outcome of the multiplicative operation.

effected by multiplying by

Highlights the impact or change caused by multiplication.

FAQs

How can I rephrase "through multiplication by" to sound more concise?

Alternatives include "by multiplying by", "via multiplication of", or simply "by multiplication". The best choice depends on the context and desired level of formality.

Is it correct to use "through multiplication of" instead of "through multiplication by"?

While both can be understood, "through multiplication "by"" is generally more common and grammatically preferred when specifying a multiplier. "Through multiplication of" usually refers to the act of multiplying itself.

When is it appropriate to use "through multiplication by" in scientific writing?

It's appropriate when you need to clearly describe how a quantity is derived or transformed by scaling it with another number, especially in equations, methods, or results sections.

What is the difference between saying "achieved by multiplication" and "achieved through multiplication by"?

"Achieved by multiplication" is a general statement, whereas "achieved through multiplication "by"" specifies that the result was obtained by multiplying a certain value, clarifying the multiplicative factor involved.