• Title/Summary/Keyword: natural number division

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Teaching Multiplication & Division of Fractions through Contextualization (맥락화를 통한 분수의 곱셈과 나눗셈 지도)

  • Kim, Myung-Woon;Chang, Kyung-Yoon
    • School Mathematics
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    • v.11 no.4
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    • pp.685-706
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    • 2009
  • This dissertation is aimed to investigate the reason why a contextualization is needed to help the meaningful teaching-learning concerning multiplications and divisions of fractions, the way to make the contextualization possible, and the methods which enable us to use it effectively. For this reason, this study intends to examine the differences of situations multiplying or dividing of fractions comparing to that of natural numbers, to recognize the changes in units by contextualization of multiplication of fractions, the context is set which helps to understand the role of operator that is a multiplier. As for the contextualization of division of fractions, the measurement division would have the left quantity if the quotient is discrete quantity, while the quotient of the measurement division should be presented as fractions if it is continuous quantity. The context of partitive division is connected with partitive division of natural number and 3 effective learning steps of formalization from division of natural number to division of fraction are presented. This research is expected to help teachers and students to acquire meaningful algorithm in the process of teaching and learning.

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Correlations between the Important Physical Properties of Natural Gas (천연가스 주요 물성 간의 상관식)

  • Ha, Youngcheol;Lee, Seongmin;Her, Jaeyoung;Lee, Kangjin;Lee, Seungjun
    • Korean Chemical Engineering Research
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    • v.47 no.5
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    • pp.599-607
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    • 2009
  • This study was conducted to derive the five correlations which could predict specific gravity(or heating value), compression factor, density, etc., if we know heating value or specific gravity only. To make a sufficient number of raw data for regression, SGERG EOS was modified into equation of heating value. Based on these raw data, five correlations were obtained and the uncertainties of the correlations were evaluated. The results showed that the uncertainties were near 0.1% in most conditions of natural gas and so the correlations could be used in natural gas industry and academic fields.

An Analysis on Concepts and Methods of Teaching Fractions (분수 개념 지도 내용과 방법 분석)

  • Kang, Wan
    • Journal of Educational Research in Mathematics
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    • v.24 no.3
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    • pp.467-480
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    • 2014
  • Concepts related to the fraction should be taught with formative thinking activities as well as concrete operational activities. Teaching improper fraction should follow the concept of fraction as a relation of two natural numbers. This concept is also important not to be skipped before teaching the fraction such as "4 is a third of 12". Mixed number should be taught as a sum of a natural number and a proper fraction. Fraction as a quotient of a division is a hard concept to be taught since it requires very high abstractive thinking process. Learning the transformation of division into multiplication of fractions should precede that of fraction as a quotient of a division.

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Pebbling Numbers on Graphs (그래프 위에서의 Pebbling 수)

  • Chun, Kyung-Ah;Kim, Sung-Sook
    • The Journal of Natural Sciences
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    • v.12 no.1
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    • pp.1-9
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    • 2002
  • Let G be a connected graph on n vertices. The pebbling number of graph G, f(G), is the least m such that, however m pebbles are placed on the vertices of G, we can move a pebble to any vertex by a sequence of moves, each move taking two pebbles off one vertex and placing one on an adjacent vertex. In this paper, we compute the pebbling number of the Petersen Graph. We also show that the pebbling number of the categorical Product G.H is (m+n)h where G is the complete bipartite graph $K_{m,n}$ and H is the complete graph with $h(\geq4)$ vertices.

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A Study on the Teaching of 'a Concept of Fraction as Division($b{\div}a=\frac{b}{a}$)' in Elementary Math Education - Based on a Analysis of the Korean Successive Elementary Math Textbooks (초등수학에서 '나눗셈으로서의 분수($b{\div}a=\frac{b}{a}$)' 개념 지도에 관한 연구 - 한국의 역대 초등수학 교과서에 대한 분석을 중심으로)

  • Kang, Heung Kyu
    • Journal of Elementary Mathematics Education in Korea
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    • v.18 no.3
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    • pp.425-439
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    • 2014
  • The concept of a fraction as division is a core idea which serves as a axiom in the process of a extension of the natural number system to rational number system. Also, it has necessary position in elementary mathematics. Nevertheless, the timing and method of the introduction of this concept in Korean elementary math textbooks is not well established. In this thesis, I suggested a solution of a various topics which is related to this problem, that is, transforming improper fraction to mixed number, the usage of quotient as a term, explaining the algorithm of division of fraction, transforming fraction to decimal.

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Selection and Characterization of Forest Soil Metagenome Genes Encoding Lipolytic Enzymes

  • Hong, Kyung-Sik;Lim, He-Kyoung;Chung, Eu-Jin;Park, Eun-Jin;Lee, Myung-Hwan;Kim, Jin-Cheol;Cho, Gyung-Ja;Cho, Kwang-Yun;Lee, Seon-Woo
    • Journal of Microbiology and Biotechnology
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    • v.17 no.10
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    • pp.1655-1660
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    • 2007
  • A metagenome is a unique resource to search for novel microbial enzymes from the unculturable microorganisms in soil. A forest soil metagenomic library using a fosmid and soil microbial DNA from Gwangneung forest, Korea, was constructed in Escherichia coli and screened to select lipolytic genes. A total of seven unique lipolytic clones were selected by screening of the 31,000-member forest soil metagenome library based on tributyrin hydrolysis. The ORFs for lipolytic activity were subcloned in a high copy number plasmid by screening the secondary shortgun libraries from the seven clones. Since the lipolytic enzymes were well secreted in E. coli into the culture broth, the lipolytic activity of the subclones was confirmed by the hydrolysis of p-nitrophenyl butyrate using culture supernatant. Deduced amino acid sequence analysis of the identified ORFs for lipolytic activity revealed that 4 genes encode hormone-sensitive lipase (HSL) in lipase family IV. Phylogenetic analysis indicated that 4 proteins were clustered with HSL in the database and other metagenomic HSLs. The other 2 genes and 1 gene encode non-heme peroxidase-like enzymes of lipase family V and a GDSL family esterase/lipase in family II, respectively. The gene for the GDSL enzyme is the first description of the enzyme from metagenomic screening.

The Golden Ratio in Art and Architecture (예술과 건축속의 황금비)

  • Kim, Sung-Sook
    • The Journal of Natural Sciences
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    • v.13 no.1
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    • pp.7-14
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    • 2003
  • The Golden Ratio has played a significant role in many parts of geometry, architecture, music, art, and philosophy. This number has been the subject of numerous experiments in psychology. It also appears in the newer domains of technology and fractals, In this paper, we investigate and analyze the golden ratio which appears in art, music, and architecture.

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Effect of Covering the Soil with Naturally Degrading Polymer Film on the Benthic Macroinvertebrates Community Structure in Paddy Field (자연분해비닐 논토양 피복이 저서성 대형무척추동물의 군집구조에 미치는 영향)

  • Park, Jin-Young;Kwon, Soon-Jik;Nam, Hong-Sik;Kang, Chung-Kil;Park, Jong-Kyun
    • Korean journal of applied entomology
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    • v.50 no.2
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    • pp.83-96
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    • 2011
  • This study was conducted to investigate the influence of natural degrading polymer film covering in rice paddies on the benthic macroinvertebrate community structure in Dangsu-dong, Suwon, Gyeonggi-do from May 2009 to September 2009. We compared 5 treatments: golden apple snail farming (GF), natural degrading polymer film + organic farming (NOF), natural degrading polymer film + chemical farming (NCF), conventional farming (CF), and no fertilization (NF) as the control. The total number of species was highest in NOF followed by GF, NF, NCF, and CF. The total number of individuals was highest in NOF followed by NCF, CF, NF, and GF. The Dominance index (DI) ranged from 0.43 to 0.95. The highest dominance index was in GF followed by NCF, NF=CF, and NOF. The species diversity index (H') for each experimental plot ranged from 0.49 to 2.93. The average species diversity index was highest in NOF followed by NF, GF, CF, and NCF. After the natural degrading polymer film covered the paddies, the benthic macroinvertebrates tended to recover, but leeches and aquatic beetles increased. Mollusca and Annelida, which are sensitive taxa, decreased in both species and individual numbers after the soil was covered with the natural degrading polymer film. The number of species tended to recover. However, the number of individuals continued to decrease.d, especially individuals. Since then, the number of species tended to recover. However, the number of individuals decreased.

A Current Status of Natural Heritage Using the Bird's Carcasses in South Korea (국내 천연기념물 멸실신고로 본 자연유산 현황)

  • Lee, Sung-Kyung;Shin, Yong-Un
    • Journal of the Korean Institute of Traditional Landscape Architecture
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    • v.39 no.2
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    • pp.50-54
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    • 2021
  • This study was conducted to investigate the status of carcasses of wild birds among natural monuments in Korea. In Korea, from 2016 to 2020, a total of 38 species and 5,036 individual carcasses of natural monuments were found. The year 2020 saw the highest numbers of species death with 34 and in 2019 the highest number was recorded with 1,095 individuals. In autumn, the largest number of species and the smallest number of individuals were confirmed dead. On the contrary, the smallest number of species and the highest number of individuals were confirmed dead in summer. The largest number of species died in November, and the largest number of individuals died in June. Kestrels accounted for about 20% of the total carcasses, making up the largest number, followed by eagle owls, brown hawk-owls, scops owls, goshawk, eagles and sparrow hawks. In spring and summer, domestic breeding species accounted for most of the carcasses and in winter, the proportion of overwintering individuals such as wooper swans and eagles increased. Reports of lost natural monuments are done by human and the status of the carcasses alone cannot inform the population characteristics of natural monuments when they stay in Korea. However, it is expected that the identified domestic population of strigiformes which has not been investigated in detail because they are nocturnal, and data on the status of carcasses of natural monuments in Korea will provide basic data for the protection of natural monuments.

A Study on the Relationship between the Number of Visitors and Degradation of Natural Resources in Bukhansan National Park (북한산국립공원의 탐방객 수와 훼손의 상관관계 연구)

  • Kang, Da-In;Sung, Hyun-Chan
    • Journal of the Korean Society of Environmental Restoration Technology
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    • v.19 no.4
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    • pp.81-89
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    • 2016
  • This study aims to understand the relationship between visitors and the degradation of natural resources in Bukhansan national park. We analyzed the trend of the number of visitors, destruction of natural resources and decrease of biodiversity per year. We further compared three types of trails, heavily-used trails and rarely-used trails and a trail with limited access, regarding the degree of destruction in the National Park through a field survey. Our result showed that increasing number of visitors had direct and indirect impact on the destruction of natural resources in the National Park. The direct impact came from visitors' excessive use of trails. Naturally, increasing number of visitors caused an immoderate use of natural resources. Physical degradation such as exposure of tree root, poor drainage of trails, trail erosion was more severe than other types of trails. Decreasing biodiversity or mild disturbance around trails is the indirect impact such as broken bough, worn-bark in rarely-used trails. Destruction scale greatly increased as the number of visitors increased. Real-named reservation system helped to prevent trails from degradation. Our result calls for the need of controlling the number of visitors to Bukhansan National Park to mitigate the degradation. We recommend dispersing visitors from the heavily-used trails to other trails and implementing real-named reservation system in the rarely-used trails for the effective management of the national park.