• Title/Summary/Keyword: School division

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A Study on Operations with Fractions Through Analogy (유추를 통한 분수 연산에 관한 연구)

  • Kim Yong Tae;Shin Bong Sook;Choi Dae Uk;Lee Soon Hee
    • Communications of Mathematical Education
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    • v.19 no.4 s.24
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    • pp.715-731
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    • 2005
  • There are five contexts of division algorithm of fractions such as measurement division, determination of a unit rate, reduction of the quantities in the same measure, division as the inverse of multiplication and analogy with multiplication algorithm of fractions. The division algorithm, however, should be taught by 'dividing by using reciprocals' via 'measurement division' because dividing a fraction by a fraction results in 'multiplying the dividend by the reciprocal of the divisor'. If a fraction is divided by a large fraction, then we can teach the division algorithm of fractions by analogy with 'dividing by using reciprocals'. To achieve the teaching-learning methods above in elementary school, it is essential for children to use the maniplatives. As Piaget has suggested, Cuisenaire color rods is the most efficient maniplative for teaching fractions. The instruction, therefore, of division algorithm of fractions should be focused on 'dividing by using reciprocals' via 'measurement division' using Cuisenaire color rods through analogy if necessary.

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Justifying the Fraction Division Algorithm in Mathematics of the Elementary School (초등학교 수학에서 분수 나눗셈의 알고리즘 정당화하기)

  • Park, Jungkyu;Lee, Kwangho;Sung, Chang-geun
    • Education of Primary School Mathematics
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    • v.22 no.2
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    • pp.113-127
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    • 2019
  • The purpose of this study is to justify the fraction division algorithm in elementary mathematics by applying the definition of natural number division to fraction division. First, we studied the contents which need to be taken into consideration in teaching fraction division in elementary mathematics and suggested the criteria. Based on this research, we examined whether the previous methods which are used to derive the standard algorithm are appropriate for the course of introducing the fraction division. Next, we defined division in fraction and suggested the unit-circle partition model and the square partition model which can visualize the definition. Finally, we confirmed that the standard algorithm of fraction division in both partition and measurement is naturally derived through these models.

Synthesis of 2,5-Disubstituted Pyrrolidines from N-Alkenyl and Alkynyl N-Benzoyloxysulfonamides Catalyzed by (CuOTf)2・C6H6

  • Liu, Wei-Min;Liu, Zhen-Hong;Cheong, Wei-Wen;Priscilla, Lu-Yi Teo;Li, Yongxin;Narasaka, Koichi
    • Bulletin of the Korean Chemical Society
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    • v.31 no.3
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    • pp.563-569
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    • 2010
  • A new synthetic method of 2,5-disubstituted pyrrolidines is developed by the cyclization of unsaturated N-benzoyloxysulfonamides by $(CuOTf)_2{\cdot}C_6H_6$ in refluxing dichloroethane. Various N-4- and N-5-alkenyl and alkynyl N-benzoyloxysulfonamides are cyclized to give pyrrolidines. The cyclization proceeds via addition of sulfonamidoyl radicals to intramolecular unsaturated bonds or allylic hydrogen abstraction with the radical intermediates.

Innovative Electromagnetic Induction Eddy Current-based Far Infrared Rays Radiant Heater using Soft Switching PWM Inverter with Duty Cycle Control Scheme

  • Tanaka H.;Sadakata H.;Muraoka H.;Okuno A.;Hiraki E.;Nakaoka M.
    • Proceedings of the KIPE Conference
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    • 2001.10a
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    • pp.64-68
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    • 2001
  • This paper presents an innovative prototype of a new conceptual electromagnetic induction heated type far infrared rays radiant heating appliance using the voltage-fed edge-resonant ZVS-PWM high frequency inverter using IGBTs for food cooking and processing which operates under a constant frequency variable power regulation scheme. This power electronic appliance with soft switching high frequency inverter using IGBTs has attracted special interest from some advantageous viewpoints of safety, cleanliness, compactness and rapid temperature response, which is more suitable for consumer power electronics applications.

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Site-Directed Saturation Mutagenesis of Yeast Gcn4p at Codon 242

  • Lee, Jae-Yung;Bae, Yu-Byung;Kim, Jung-Ae;Song, Jae-Mahn;Choe, Mu-Hyeon;Kim, Ick-Young;Kim, Joon
    • Journal of Microbiology and Biotechnology
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    • v.9 no.1
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    • pp.122-125
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    • 1999
  • Gcn4p, a transcriptional activator protein of the yeast, Sacchromyces cerevisiae, binds to the specific sequence in the promoters of many amino acid biosynthetic genes for general control. The serine residue (Ser 242) of Gcn4p directly contacts the DNA. Here, for inspecting the DNA binding properties and the level of transcriptional activation of Gcn4p, we introduced a polymerase chain reaction (PCR) site-directed saturation mutation library into the Ser 242 site using 2 outside primers and 2 oligonucleotides with its codons fully degenerated. The sequencing analysis of 146 samples revealed the even nucleotide distribution within the experimental error showing 23, 26, 25, and 26% frequency of U, C, A, and G bases, respectively. This method turned out to be a simple, fast, and economical method for constructing a library of all 20 amino acids at specific codon.

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Mixed Exocrine and Endocrine Carcinoma in the Stomach: A Case Report

  • Lee, Han-Hong;Jung, Chan-Kwon;Jung, Eun-Sun;Song, Kyo-Young;Jeon, Hae-Myung;Park, Cho-Hyun
    • Journal of Gastric Cancer
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    • v.11 no.2
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    • pp.122-125
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    • 2011
  • We report a rare case of the coexistence of a gastric small cell neuroendocrine carcinoma with a gastric adenocarcinoma. A 62-year-old man presented with epigastric soreness for 1 month. Esophagogastroduodenoscopy revealed a Borrmann type I tumor at the lesser curvature of the lower body of the stomach. The patient underwent a distal gastrectomy with D2 lymph node dissection and the resected specimen exhibited a $3.5{\times}3.5$ cm sized, fungating lesion. Two separated, not intermingling, lesions with non-adenocarcinoma components encircled by well differentiated adenocarcinoma components were identified microscopically. The non-adenocarcinoma component showed neuroendocrine features, such as a solid and trabecular pattern, and the tumor cells showed a high nuclear grade with minimal cytoplasm, indistinct nucleoli, and positive response for synaptophysin, CD56. The final pathological diagnosis was a gastric mixed exocrine-endocrine carcinoma (MEEC) composed of an adenocarcinoma and small cell neuroendocrine carcinoma of the collision type.