• East Asian mathematical journal
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• v.38 no.4
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• pp.379-396
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• 2022

In this paper, we investigate distribution strategies in the Egyptian fraction, and through this, we examine the distribution strategies of (fraction)÷(fraction) and then provide some educational implications. The (natural number)÷(natural number) of the sharing situation has the meaning of 'share' per unit, which can be seen as a situation where the unit ratio is determined. These concepts can also naturally be extended to the case of (fraction)÷(fraction) by some problem posing situations. That is to say, the case of (fraction)÷(fraction) can be deduced the case (natural number)÷(natural number) by the re-statement of the problem.

• The Mathematical Education
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• v.48 no.3
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• pp.235-263
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• 2009

The purpose of the study was to investigate the influence of children's understanding of fractions in mathematics problem solving. Kieren has claimed that the concept of fractions is not a single construct, but consists of several interrelated subconstructs(i.e., part-whole, ratio, operator, quotient and measure). Later on, in the early 1980s, Behr et al. built on Kieren's conceptualization and suggested a theoretical model linking the five subconstructs of fractions to the operations of fractions, fraction equivalence and problem solving. In the present study we utilized this theoretical model as a reference to investigate children's understanding of fractions. The case study has been conducted with 6 children consisted of 4th to 5th graders to detect how they understand factions, and how their understanding influence problem solving of subconstructs, operations of fractions and equivalence. Children's understanding of fractions was categorized into "part-whole", "ratio", "operator", "quotient", "measure" and "result of operations". Most children solved the problems based on their conceptual structure of fractions. However, we could not find the particular relationships between children's understanding of fractions and fraction operations or fraction equivalence, while children's understanding of fractions significantly influences their solutions to the problems of five subconstructs of fractions. We suggested that the focus of teaching should be on the concept of fractions and the meaning of each operations of fractions rather than computational algorithm of fractions.

• Journal of the Korean Society of Combustion
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• v.17 no.4
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• pp.38-43
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• 2012

Experimental study was conducted to elucidate flame extinction phenomena in counterflow flame. Using a curtain helium flow significantly reduced buoyancy such that the flame can be positioned at the center between the upper and lower nozzles even at the velocity ratio of 1.0. The curves of critical diluent mole fraction versus global strain rate have C-shapes. The flame oscillation was observed prior to low strain rate flame extinction at both flame conditions with and without minimizing buoyancy force. The results show that, at low strain rate flame, the self-excitation frequency with the order of 1.0 Hz in the case of utilizing pure helium gradually decreases in increase of $N_2$ mole fraction in the curtain flow, meaning that buoyancy suppresses the self-excitation of the outer edge flame.

• 한국연소학회:학술대회논문집
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• 2012.11a
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• pp.23-26
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• 2012

Experimental study was conducted to elucidate flame extinction phenomena in counterflow flame. Using a curtain helium flow significantly reduced buoyancy such that the flame can be positioned at the center between the upper and lower nozzles even at the velocity ratio of 1.0. The curves of critical diluent mole fraction versus global strain rate have C-shapes. The flame oscillation was observed prior to low strain rate flame extinction at both flame conditions with and without minimizing buoyancy force. The results show that, at low strain rate flame, the self-excitation frequency with the order of 1.0 Hz in the case of utilizing pure helium gradually decreases in increase of $N_2$ mole fraction in the curtain flow, meaning that buoyancy suppresses the self-excitation of the outer edge flame.

• Geomechanics and Engineering
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• v.17 no.1
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• pp.19-30
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• 2019

Recent research on the behavior of silty sand tends to advocate the use of equivalent skeleton void ratio to characterize the density state of this type of soil. This paper presents an investigation to explore the physical meaning of the equivalent skeleton void ratio by means of DEM simulations for assemblies of coarse and fine particles under biaxial shear. The simulations reveal that the distribution pattern of fine particles in the soil skeleton plays a crucial role in the overall macroscopic response: The contractive response observed at the macro scale is mainly caused by the movement of fine particles out of the force chains whereas the dilative response is mainly associated with the migration of fine particles into the force chains. In an assembly of coarse and fine particles, neither all of the fine particles nor all of the coarse ones participate in the force chains to carry the external loads, and therefore a more reasonable definition for equivalent skeleton void ratio is put forward in which a new parameter d is introduced to take into account the fraction of coarse particles absent from the force chains.

• Journal for History of Mathematics
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• v.23 no.3
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• pp.121-140
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• 2010

This study presents one universal mean formula of implicate quantity for speed, temperature, consistency, density, unit cost, and the national income per person in order to avoid the inconvenience of applying different formulas for each one of them. This work is done by using the principle of lever and was led to the formula of two implicate quantity, $M=\frac{x_1f_1+x_2f_2}{f_1+f_2}$, and to help the understanding of relationships in this formula. The value of ratio of fraction cannot be added but it shows that it can be calculated depending on the size of the ratio. It is intended to solve multiple additions with one formula which is the expansion of the mean formula of implicate quantity. $M=\frac{x_1f_1+x_2f_2+{\cdots}+x_nf_n}{N}$, where $f_1+f_2+{\cdots}+f_n=N$. For this reason, this mean formula will be able to help in physics as well as many other different fields in solving complication of structures.

• School Mathematics
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• v.5 no.4
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• pp.421-440
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• 2003

It is difficult for the learner to understand completely the ratio concept which forms a basis of proportional reasoning. And proportional reasoning is, on the one hand, the capstone of children's elementary school arithmetic and, the other hand, it is the cornerstone of all that is to follow. But school mathematics has centered on the teachings of algorithm without dealing with its essence and meaning. The purpose of this study is to analyze the essence of ratio concept from multidimensional viewpoint. In addition, this study will show the direction for improvement of ratio concept. For this purpose, I tried to analyze the historical development of ratio concept. Most mathematicians today consider ratio as fraction and, in effect, identify ratios with what mathematicians called the denominations of ratios. But Euclid did not. In line with Euclid's theory, ratio should not have been represented in the same way as fraction, and proportion should not have been represented as equation, but in line with the other's theory they might be. The two theories of ratios were running alongside each other, but the differences between them were not always clearly stated. Ratio can be interpreted as a function of an ordered pair of numbers or magnitude values. A ratio is a numerical expression of how much there is of one quantity in relation to another quantity. So ratio can be interpreted as a binary vector which differentiates between the absolute aspect of a vector -its size- and the comparative aspect-its slope. Analysis on ratio concept shows that its basic structure implies 'proportionality' and it is formalized through transmission from the understanding of the invariance of internal ratio to the understanding of constancy of external ratio. In the study, a fittingness(or comparison) and a covariation were examined as the intuitive origins of proportion and proportional reasoning. These form the basis of the protoquantitative knowledge. The development of sequences of proportional reasoning was examined. The first attempts at quantifying the relationships are usually additive reasoning. Additive reasoning appears as a precursor to proportional reasoning. Preproportions are followed by logical proportions which refer to the understanding of the logical relationships between the four terms of a proportion. Even though developmental psychologists often speak of proportional reasoning as though it were a global ability, other psychologists insist that the evolution of proportional reasoning is characterized by a gradual increase in local competence.

• Journal of Life Science
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• v.11 no.2
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• pp.166-172
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• 2001

Various types of the seeding of bottle gourd widely used as a rootstock of watermelon has been required to satisfy the farmers need. The study was done to determine the effect of light quality of blue, red and far-red lights treated with light emitting diodes on growth and morphology of bottle goured seeding and chlorophyll content of its cotyledons. The lights were treated in the growth chamber for 7 days to the seeding elapsed 8 days after sowing under natural condition, and 64 hole trays with commercial bedsoil. Plant height, length and diameter of hypocotyl, leaf area of cotyledon and first true leaf, its leaf length, number of true leaves, fraction and total dry weight were measured. Red light shortened and slenderized the hypocotyl, which lengthened by far-red light and thickened by blue light. Plant height was declined in order of far-red light treatment, blue and red lights mainly due to difference of hypocotyl length, Area and length of the first true leaf became smaller and shorter under far-red light than under the other lights. However, blue light increased leaf area of cotyledons. Two cultivars cv. Yongjadaemok and cv. Kunghap had different response to the light treatments in total seedling dry weight(dw); far-red and red light treatments showed the greatest and the least dw of hypocotyl, respectively, while blue and red lights did the greatest dw of the other organs. Among the ratio of each organ dw to total dw, those of hypocotyl and true leaves were different between the light treatments; the highest ratio of hypocotyl dw to total dw was observed in far-red light treatment but the lowest was in red light treatment. Those of the true leaves were the lowest in far-red light and similar response in blue or red light treatment. Chlorophyll content of cotyledons was decreased in order of red light treatment, blue and far-red lights, meaning that short period light treatment may influence photosynthesis of seeding and afterward its growth.