Subtraction Property
Subtraction Property - Related Videos
09:40
Novel Sequence Discovery by Subtractive Genomics
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Cited by 7 •
2019
The purpose of this protocol is to use a combination of computational and bench research to find novel sequences that cannot be easily separated from a co-purifying sequence, which may be only partially known.
09:43
Measuring Reaction Time and Donders' Method of Subtraction
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2023
Source: Laboratory of Jonathan Flombaum—Johns Hopkins University The ambition of experimental psychology is to characterize the mental events that support the human ability to solve problems, perceive the world, and turn thoughts into words and sentences. But people cannot see or feel those mental events; they cannot be weighed, combined in test tubes, or grown in a dish. Wanting to study mental life, nonetheless, Franciscus Donders, a Dutch ophthalmologist in the early 1800s, came up with a...
01:22
Detection of Internal Carotid Artery Narrowing Using Digital Subtraction Angiography
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2025
Position a human patient with internal carotid stenosis, a condition characterized by narrowing of the internal carotid artery, on the imaging table for digital subtraction angiography (DSA). Insert an angiocatheter into the common carotid artery at the fourth cervical vertebra level. Capture a pre-contrast X-ray image to record background structures like bones and soft tissues using X-ray irradiation. Administer an iodine-based contrast medium into the carotid artery. The contrast medium...
08:57
Improving Infrared Spectroscopy Characterization of Soil Organic Matter with Spectral Subtractions
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Cited by 19 •
2019
SOM underlies many soil functions and processes, but its characterization by FTIR spectroscopy is often challenged by mineral interferences. The described method can increase the utility of SOM analysis by FTIR spectroscopy by subtracting mineral interferences in soil spectra using empirically obtained mineral reference spectra.
03:54
Magnetic Resonance Elastography for Assessing Viscoelastic Properties
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2025
Source: Feng, Y., et al. Viscoelastic Characterization of Soft Tissue-Mimicking Gelatin Phantoms using Indentation and Magnetic Resonance Elastography. J. Vis. Exp. (2022) This video demonstrates the method of magnetic resonance elastography (MRE) for assessing tissue viscoelastic properties by analyzing shear wave propagation through a gelatin phantom, mimicking brain tissue. The process involves generating and capturing shear waves with magnetic resonance imaging or MRI and analyzing wave...
FAQs
Equality is preserved because the two sides begin with the same value, so applying one identical subtraction changes them by the same amount. Their numerical difference remains zero, which means the relationship between the sides is unchanged. This balance-based reasoning lets a solver transform an equation without changing the condition that the unknown must satisfy.
The quantity to subtract is selected according to the term that prevents the unknown from standing alone. In a linear equation, this commonly means removing a constant term from the side containing the unknown. Subtracting that term from both sides produces a simpler equivalent equation, preparing it for the additional operations needed to isolate the unknown.
The same quantity must be subtracted from both sides, and the operation should be recorded consistently. Changing only one side alters the equality rather than transforming it. This requirement applies whether the subtraction removes a constant, simplifies an expression, or forms part of a longer sequence of algebraic transformations.
It provides a justified way to move from one equation to another while preserving the original relationship. Each valid subtraction step narrows the work toward an unknown without introducing an arbitrary change. Because the transformation follows a clear rule, the resulting statement can be examined and verified as a logical consequence of the starting equation.
First, identify the constant or other unwanted term that should be removed from the side containing the unknown. Subtract that quantity from both sides, simplify the resulting expressions, and then apply any additional operations needed to isolate the unknown. The final value should be checked in the original equation to confirm the transformation produced a valid solution.
After isolating the unknown, substitute the proposed value back into the original equation and compare both sides. If they produce equal quantities, the sequence of transformations is supported by the original relationship. If they do not, reviewing each subtraction and simplification step can reveal an inconsistent operation or arithmetic error.
The principle supports arithmetic work, algebraic transformations, and mathematical reasoning whenever an equal relationship must be maintained during a change. In elementary problems it helps organize calculations; in more advanced mathematical contexts, it provides a systematic basis for rewriting equations. Its broader value lies in preserving equality while making expressions easier to analyze.