Expanding Fractions
Expanding Fractions - Related Videos
10:09
Fractional Distillation
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2023
Source: Laboratory of Dr. Nicholas Leadbeater — University of Connecticut Distillation is perhaps the most common laboratory technique employed by chemists for the purification of organic liquids. Compounds in a mixture with different boiling points separate into individual components when the mixture is carefully distilled. The two main types of distillation are "simple distillation" and "fractional distillation", and both are widely used in organic chemistry laboratories. Simple distillation...
06:36
Preparation of Expanded Chitin Foams and their Use in the Removal of Aqueous Copper
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Cited by 1 •
2021
This study describes a method to expand chitin into a foam by chemical techniques that require no specialized equipment.
09:01
An Optimized Method for Isolating and Expanding Invariant Natural Killer T Cells from Mouse Spleen
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Cited by 17 •
2015
Here we present an adapted protocol that can be used to generate a large number of murine invariant natural killer T cells from mouse spleen. The protocol outlines an approach by which splenic iNKT cells can be enriched for, isolated and expanded in vitro using a limited number of animals and reagents.
09:27
New Tools to Expand Regulatory T Cells from HIV-1-infected Individuals
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Cited by 4 •
2013
CD4+ Regulatory T cells are potent immune-modulators and serve important functions in immune homeostasis. The paucity of these cells in peripheral blood makes functional studies challenging, specifically in the context of HIV-1-infection. We here describe a method to isolate and expand functional CD4+ Tregs from peripheral blood from HIV-1-infected individuals.
11:35
Fabrication of an Expandable Brain Matrix Customizable Across Developmental Stages
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2026
An innovative method to build expandable brain matrices to cut either coronal or sagittal slices is described for application to neonatal piglets. This budget-friendly approach utilizes acrylic plates carved using templates from agarose gel brain molding, applies to multiple species, and allows for expansion to accommodate brain growth.
FAQs
Using the same nonzero multiplier preserves the relationship between the numerator and denominator, so the fraction represents the same rational number. Applying different multipliers changes that relationship and produces a different value. Excluding zero also matters because multiplying both parts by zero would not create a meaningful equivalent fraction for comparison or calculation.
The multiplier determines how detailed the new numerator and denominator become. For example, multiplying 2/3 by 4 produces 8/12, while another nonzero whole-number multiplier produces a different equivalent form. In practice, the useful choice depends on the mathematical task, especially when a particular denominator is needed to work with other fractions.
Expanding and simplifying move in opposite directions while preserving value. Expansion creates a form with larger parts, whereas simplification rewrites a fraction using smaller common factors when possible. Seeing both as value-preserving transformations helps students recognize that a fraction can have multiple equivalent representations and supports later work with ratios and algebraic expressions.
First, choose a nonzero whole-number multiplier that suits the task. Next, multiply the numerator by that number and multiply the denominator by the same number. Finally, check that the new fraction represents the original value. For instance, applying 4 to both parts of 2/3 gives 8/12, an equivalent expanded form.
Expanding can place fractions into forms that make their denominators easier to compare. Once fractions share a suitable denominator, their numerators provide a direct way to examine their relative sizes. This use connects the procedure with proportional reasoning, because each rewritten fraction preserves the same relationship between its numerator and denominator.
Addition and subtraction become easier when fractions are rewritten with a common denominator. Expanding supplies equivalent forms that can share that denominator without changing the values of the original fractions. After the numerators are combined or compared, the resulting expression can be interpreted or simplified as appropriate, supporting accurate work with rational numbers.