• Title/Summary/Keyword: multiplication of fractions

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The Effect of the Estimation Strategy on Placing Decimal Point in Multiplication and Division of Decimals (어림하기를 통한 소수점 찍기가 소수의 곱셈과 나눗셈에 미치는 효과)

  • Lee, Youn-Mee;Park, Sung-Sun
    • Journal of Elementary Mathematics Education in Korea
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    • v.15 no.1
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    • pp.1-18
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    • 2011
  • The purpose of this study was to investigate the effects of estimation strategy on placing decimal point in multiplication and division of decimals. To examine the effects of improving calculation ability and reducing decimal point errors with this estimation strategy, the experimental research on operation with decimal was conducted. The operation group conducted the decimal point estimation strategy for operating decimal fractions, whereas the control group used the traditional method with the same test paper. The results obtained in this research are as follows; First, the estimation strategy with understanding a basic meaning of decimals was much more effective in calculation improvement than the algorithm study with repeated calculations. Second, the mathematical problem solving ability - including the whole procedure for solving the mathematical question - had no effects since the decimal point estimation strategy is normally performed after finishing problem solving strategy. Third, the estimation strategy showed positive effects on the calculation ability. Th Memorizing algorithm doesn't last long to the students, but the estimation strategy based on the concept and the position of decimal fraction affects continually to the students. Finally, the estimation strategy assisted the students in understanding the connection of the position of decimal points in the product with that in the multiplicand or the multiplier. Moreover, this strategy suggested to the students that there was relation between the placing decimal point of the quotient and that of the dividend.

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The Type of Fractional Quotient and Consequential Development of Children's Quotient Subconcept of Rational Numbers (분수 몫의 형태에 따른 아동들의 분수꼴 몫 개념의 발달)

  • Kim, Ah-Young
    • Journal of Educational Research in Mathematics
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    • v.22 no.1
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    • pp.53-68
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    • 2012
  • This paper investigated the conceptual schemes four children constructed as they related division number sentences to various types of fraction: Proper fractions, improper fractions, and mixed numbers in both contextual and abstract symbolic forms. Methods followed those of the constructivist teaching experiment. Four fifth-grade students from an inner city school in the southwest United States were interviewed eight times: Pre-test clinical interview, six teaching / semi-structured interviews, and a final post-test clinical interview. Results showed that for equal sharing situations, children conceptualized division in two ways: For mixed numbers, division generated a whole number portion of quotient and a fractional portion of quotient. This provided the conceptual basis to see improper fractions as quotients. For proper fractions, they tended to see the quotient as an instance of the multiplicative structure: $a{\times}b=c$ ; $a{\div}c=\frac{1}{b}$ ; $b{\div}c=\frac{1}{a}$. Results suggest that first, facility in recall of multiplication and division fact families and understanding the multiplicative structure must be emphasized before learning fraction division. Second, to facilitate understanding of the multiplicative structure children must be fluent in representing division in the form of number sentences for equal sharing word problems. If not, their reliance on long division hampers their use of syntax and their understanding of divisor and dividend and their relation to the concepts of numerator and denominator.

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Investigation of the hydrogen production of the PACER fusion blanket integrated with Fe-Cl thermochemical water splitting cycle

  • Medine Ozkaya;Adem Acir;Senay Yalcin
    • Nuclear Engineering and Technology
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    • v.55 no.11
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    • pp.4287-4294
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    • 2023
  • In order to meet the energy demand, energy production must be done continuously. Hydrogen seems to be the best alternative for this energy production, because it is both an environmentally friendly and renewable energy source. In this study, the hydrogen fuel production of the peaceful nuclear explosives (PACER) fusion blanket as the energy source integrated with Fe-Cl thermochemical water splitting cycle have been investigated. Firstly, neutronic analyzes of the PACER fusion blanket were performed. Necessary neutronic studies were performed in the Monte Carlo calculation method. Molten salt fuel has been considered mole-fractions of heavy metal salt (ThF4, UF4 and ThF4+UF4) by 2, 6 and 12 mol. % with Flibe as the main constituent. Secondly, potential of the hydrogen fuel production as a result of the neutronic evaluations of the PACER fusion blanket integrated with Fe-Cl thermochemical cycle have been performed. In these calculations, tritium breeding (TBR), energy multiplication factor (M), thermal power ratio (1 - 𝜓), total thermal power (Phpf) and mass flow rate of hydrogen (ṁH2) have been computed. As a results, the amount of the hydrogen production (ṁH2) have been obtained in the range of 232.24x106 kg/year and 345.79 x106 kg/year for the all mole-fractions of heavy metal salts using in the blanket.

Multiplication of Infectious Flacherie and Densonucleosis Viruses in the Silkworm, Bombyx mori (가잠의 전염성 연화병 및 농핵병 바이러스 증식에 관한 연구)

  • 김근영;강석권
    • Journal of Sericultural and Entomological Science
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    • v.25 no.2
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    • pp.1-31
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    • 1984
  • Flacherie, as one of the most prevalent silkworm diseases, causes severe economic damage to sericultural industry and its pathogens have been proved to be flacherie virus (FV) and densonucleosis virus (DNV). Multiplications of the viruses in the larvae of the silkworm, Bombyx mori, were studied by the sucrose density gradient centrifugation and electron microscopy. The quantitative and qualitative changes of nucleic acids and proteins were investigated from the midgut and hemolymph in the silkworm larvae infected separately with FV and DNV. The histopathological changes of epithelial cells of infected midgut also were examined by an electron microscope. 1. Purified fractions of FV or DNV in a sucrose density gradient centrifugation yielded one homogenous and sharp peak without a shoulder, suggesting no heterogenous materials in the preparation. Electron microscopy also revealed that FV and DNV were spherical particles, 27nm and 21nm in diameter, respectively. 2. Silkworm larvae showed a decrease in body weight on the 6th day and in midgut weight on the 3rd day after inoculation with FV or DNV. 3. DNA content was higher in the midgut when infected with FV or DNV, but the hemolymph of the infected larvae showed no difference during first 6 days after inoculation, after which DNA concentration declined rapidly. 4. RNA synthesis of silkworm larvae infected separately with FV and DNV was stimulated in the midgut, but RNA content was reduced in the hemolymph at the early stage of virus multiplication. At the late stage of virus multiplication, however, it was extremely reduced in both midgut and hemolymph. 5. The concentration of protein in the midgut and hemolymph of silkworm larvae infected separately with FV and DNV showed no difference from that of the healthy larvae at the early stage of virus multiplication, but it was significantly reduced at the late stage of virus multiplication. 6. There was no difference in the electrophoretic patterns of RNAs extracted from the midgut of healthy or virus-infected larvae. 7. The electrophoresis of proteins extracted from the midgut infected with FV or DNV, when carried out on the 1st and 5th day after virus inoculation, showed no difference from that of the healthy larvae. But, there was an additional band with medium motility in the proteins on the 8th day after virus inoculation, while a band with low mobility shown in the proteins of healthy larvae disappeared in the infected larvae. However, a band with high mobility in the healthy larvae was separated into two fractions in the infected larvae. 8. The electrophoretic pattern of hemolymph proteins of the silkworm larvae infected separately with FV and DNV was similar to that of the healthy larvae, but the concentration of hemolymph proteins in the infected larvae was lower than that of the healthy larvae at the late stage. 9. Two types of inclusion bodies were shown by the double staining of pyronin-methyl green in the columnar cell of the midgut on the 8th day after FV inoculation. 10. Electron microscopy of the infected midgut revealed that the 'cytoplasmic wall' of the goblet cell thickened on the 5th day after FV inoculation and several types of the cytopathogenic structures, such as virus$.$specific vesicles, virus particles, linear structures, tubular structures, and high electron-dense matrices were observed in the cytoplasm of the goblet cell. The virus particles were also observed in the microvilli and the structures similar to spherical virus particles were observed around the virus-specific vesicles, suggesting the virus assembly in the cytoplasm. 11. Fluorescence micrograph of the infected midgut stained with acridine orange showed that the nucleus, the site of DNV multiplication in the columnar cell, enlarged on the 5th day after virus inoculation. 12. Electron microscopic examination of DNV infected midgut revealed that the nucleolus of the columnar cell was broken into granules and those granules dispersed into apical region of the nucleus on the 5th day after virus inoculation. On the 8th day after inoculation, it was also observed that the nucleus of the columnar cell was full with the high electron-dense virogenic stroma which were similar to virus particles. These facts suggest that the virogenic stroma were the sites of virus assembly in the process of DNV multiplication.

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The In Vitro and In Vivo Efficacy of Hen IgY Against Vibrio parahaemolyticus and Vibrio vulnificus

  • Kassim, Neema;Mtenga, Adelard B.;Shim, Won-Bo;Chung, Duck-Hwa
    • Journal of Microbiology and Biotechnology
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    • v.22 no.10
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    • pp.1423-1431
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    • 2012
  • The inhibitory effect of IgY against Vibrio parahaemolyticus and Vibrio vulnificus responsible for seafood-borne diseases was investigated in this study. Water-soluble fractions (WSF) of protein containing IgYs were isolated from the egg yolk of hens initially immunized with formalin-inactivated V. parahaemolyticus or V. vulnificus. Protein, total and specific IgY contents of the WSF were determined. The inhibitory and protective effects of IgYs on the growth of V. parahaemolyticus and V. vulnificus were assayed in liquid medium and in mice. IgYs showed high affinity to their corresponding antigens with high titer from day 28 onwards. Protein contents and total IgY concentrations remained stable throughout the immunization period, whereas specific IgY concentrations increased steadily and reached a plateau at day 49. Specific IgY powder (150 mg/ml) significantly inhibited further multiplication of both V. parahaemolyticus and V. vulnificus in liquid medium as compared with the control IgY. The bacteria count in mice feces was lower in mice pretreated with specific IgYs than in those pretreated with PBS or control IgY. Higher survival of mice was observed in the experimental groups pretreated with either anti-V. parahaemolyticus (75% survival) or anti-V. vulnificus (87% survival) IgYs, compared with those in the control groups pretreated with PBS or nonspecific IgY. All mice in the control groups died within three days after bacteria inoculation; hence, the protective effect of specific IgYs against infection caused by V. parahaemolyticus and V. vulnificus was demonstrated.

Studies on the Antioxidation and Antimicrobial Effect of Smilacis Glabrae Rhizoma (토복령의 항산화작용 및 항균 효과에 대한 연구)

  • 양기호
    • The Journal of Korean Medicine
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    • v.25 no.2
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    • pp.1-8
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    • 2004
  • Objectives : This study was performed to investigate the effects of Smilacis GlabraeRhizoma on antioxidation and antimicrobial activity. Methods : In this study, we investigated the effects of peroxide radicals on hydrogen donating activity and linoleic acid, and the MDA contents on the hepatic lipids of rats, via methanol extractions and subfractions of Smilacis Glabrae Rhizoma. Results : 1. Hydrogen donating activity was very great for the radical scavenging effects, depending on the additional concentration at the fraction level of chloroform and ethyl acetate. 2. The peroxide radicals in linoleic acid were lower depending on the additional concentration, at the fraction level of ethyl acetate, than the controls. We concluded that both had significant anti-oxidation effects. 3. MDA contents of the hepatic lipid had also inhibition effects on lipid radicals, in proportion to the concentration of n-hexane, chloroform, and ethyl acetate fraction level. 4. After extracting Smilads Glabrae Rhizoma with 80% methanol, we experimented with the extracts the antibiosis each concentration, for 5 bacilli, Bacilus subtilis, staphylococcus aureus, Escherichia coli, Salmonela typhimurium, and Alcaligenes faecalis. While the effects showed differentiations by concentration, they had usually the significant inhibition effect for the multiplication at 37.5~75ug/ml. To identify the effective constituents, we identified the antibiosis of the fractions assaying cyclically hexane, chloroform, ethyl acetate, and butanol. The result showed that antimicrobial activation of both Gram-positive and Gram-negative bacillus except for E. coli was measured highest at the fraction level of BuOH and water. Conclusions : This result suggest that the extractions of Smilacis Glabrae Rhizoma, at ethyl acetate fraction, had significant anti-oxidation effects and at BuOH and water fraction had relatively strong antimicrobial activity against Bacilus subtilis, staphylococcus aureus, Salmonela typhimurium, and Alcaligenes faecalis.

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An Analysis of the Elementary Mathematics Textbooks in Singapore: Focused on the Model Method (싱가포르의 초등학교 수학 교과서 분석: 모델 메소드(model method)를 중심으로)

  • Pang, JeongSuk;Kim, EunKyung
    • Education of Primary School Mathematics
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    • v.20 no.3
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    • pp.205-224
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    • 2017
  • A model method has been known as the main characteristic of Singaporean elementary mathematics textbooks. However, little research has been conducted on how the model method is employed in the textbooks. In this study, we extracted contents related to the model method in the Singaporean elementary mathematics curriculum and then analyzed the characteristics of the model method applied to the textbooks. Specifically, this study investigated the units and lessons where the model method was employed, and explored how it was addressed for what purpose according to the numbers and operations. The results of this study showed that the model method was applied to the units and lessons related to operations and word problems, starting from whole numbers through fractions to decimals. The model method was systematically applied to addition, subtraction, multiplication, and division tailored by the grade levels. It was also explicitly applied to all stages of the problem solving process. Based on these results, this study described the implications of using a main model in the textbooks to demonstrate the structure of the given problem consistently and systematically.