Concept Of Fraction Research Articles

ANALYSIS OF STUDENTS' UNDERSTANDING OF MATHEMATICAL CONCEPTS ON FRACTIONS IN GRADE VIII AT SMP NEGERI 2 MAZINO

This study aims to describe and identify the factors contributing to the low understanding of mathematical concepts related to fractions among students. This research is qualitative in nature with a descriptive approach. The informants in this study are 18 eighth-grade students from SMP Negeri 2 Mazino. Data were analyzed through the steps of data reduction, data presentation, and conclusion drawing. The data collection techniques used are tests and interviews. The results show that, overall, students exhibit low understanding of concepts when distinguishing between two fractions, with 18% categorized as very poor. In classifying fractions by type, the percentage is 19% in the very poor category. For ordering fractions from smallest to largest, the percentage is 37%, categorized as poor. In simplifying addition and subtraction operations involving fractions, 22% fall into the poor category. Additionally, in relating everyday life to fraction concepts, the percentage is 60%, categorized as sufficient, while 20% fall into the very poor category. Factors influencing this include a lack of understanding of the statements in the tests, not comprehending the questions posed, being less meticulous in understanding simple fractions, and difficulty in interpreting word problems related to fraction operations. In conclusion, eighth-grade students at SMP Negeri 2 Mazino demonstrate low understanding in completing tests on fractions. It is recommended that teachers create a question-and-answer space in their lesson plans to enhance students' conceptual understanding when working with fractions.

Support Tool for Fractions Concepts in Basic Education

Support Tool for Fractions Concepts in Basic Education

Development of Three-Tier Diagnostic Test to Measure Misconceptions of Grade 5 Students about Fractions

This research developed a measuring instrument in the form of a three-tier diagnostic test to measure students' misconceptions in fraction material in grade V. This research aims to determine (1) the validity, reliability, and item characteristics of the three-tier diagnostic test and (2) the level of misconceptions of grade V elementary school students in Pontianak. This research used quantitative approach and test development model by Mardapi, that has nine steps. The subjects were fifth-grade students in Pontianak City, and the developed test instruments focused on addition-subtraction of fractions, each with two sets of questions A and B. The instrument were analyzed for content and construct validity, reliability, and item characteristics based on IRT using Partial Credit Model (PCM). The results show that the developed test instrument demonstrated strong content and construct validity. Reliability analysis shows high reliability, with Cronbach's Alpha values >0,7. Item fit analysis reveal that 91% and 73% were fit, therefore the unfit items were fixed or eliminated. The analysis of misconceptions shows that 39.52% of students do not understand the concept of fractions’ addition and subtraction, and 29.09% experienced misconceptions. Additionally, 12.61% have false positives, and 8.97% have false negatives. Only 6.30% understood the concept correctly, and 3.52% guessed correctly or understood but had doubts. Generally, the final test instrument demonstrated good validity, reliability and item qualities.

Analisis Kesulitan Belajar Matematika Dalam Menyelesaikan Soal Materi Operasi Hitung Pecahan Pada Siswa Kelas V SD Negeri Morkepek

The purpose of this study was to determine the difficulty of learning mathematics and the factors that cause mathematics learning difficulties in solving problems of fraction counting operation material in fifth grade students of SD Negeri Morkepek. This research uses a method with a descriptive qualitative approach. This research uses data collection techniques with interview techniques and documentation. The results of this study are 1). Math learning difficulties in using facts, namely students have difficulty in translating fraction story problems into a form of solution according to symbols or fraction numbers correctly. 2). Math learning difficulties in using concepts, namely students are unable to master the prerequisite concepts of fraction calculation operation material regarding determining the KPK. 3). Difficulty in using principles, namely students have difficulty in connecting the concept of fractions into the right calculation relation. 4). Difficulty in using skills, namely students are unable to complete the problem solving according to the fraction calculation procedure.

Cold plasma/alkaline pretreatment facilitates corn stalk fractionation and valorization towards zero-waste approach

The present study employed alkaline hydrogen peroxide pretreatment coupled with cold plasma for corn stalk’s complex biopolymers fractionation and valorization through enzymatic hydrolysis. This hurdle approach enables the prolonged generation of reactive oxidative species, initiating chemical reactions otherwise hardly possible under ambient conditions. A delignification rate between 76±1 and 86±2 % was obtained under different process parameters in a significantly shorter time compared to conventional alkaline pretreatment. Up to 94±4 % of cellulose in treated biomass was converted to glucose after enzymatic hydrolysis, achieving around 3.5 times higher glucose yield than the raw biomass. Different spectroscopic analyses confirmed specific alterations in the structure of the lignin-rich fraction caused by cold plasma. Micro- and nanoscale lignin particles obtained were rich in total phenolic content, reaching up to 140±20 and 107±12 µg gallic acid equivalents (GAE) per mg of lignin, respectively. The proposed concept of corn stalk fractionation through biorefinery can open new opportunities for valorizing different agricultural waste types.

A Study on Ejection Fraction in Patients with Mitral and Aortic Regurgitation Based on Cardiovascular Models

Background: Whether it is healthy or patients with mitral and aortic regurgitation, clinicians cannot measure the regurgitation of the valve when using two-dimensional echocardiography to measure ejection fraction. Whether the mitral valve and aortic valve are in a healthy state or in a reflux state, there is a reflux volume. The actual stroke output will be less than the stroke output measured by echocardiography, making the calculated ejection fraction higher. Methods: This article proposes for the first time the concept of net ejection fraction (NEF) as the percentage of net stroke output to left ventricular end diastolic volume. The net stroke output is the integral of aortic valve flow during one cardiac cycle at the same time. Using a systemic arterial circulation model, investigate the relationship between ejection fraction and net ejection fraction through numerical simulation methods. Results: The final results showed a strong linear correlation between mitral regurgitation volume (VRmi), aortic regurgitation volume (VRao), and the difference between ejection fraction and net ejection fraction (DEF). The net ejection fraction of the moderate mitral regurgitation group decreased by an average of 26.3% ± 9.95% compared to the ejection fraction measured by echocardiography. The severe mitral regurgitation group showed a decrease of 31.9% ± 9.3%. Moderate descent of aortic valve by 25.8% ± 11.1%. Severe aortic valve descent of 30.9% ± 10.3%. Conclusions: Clinical doctors can evaluate the left ventricular systolic function of patients based on the ejection fraction measured by echocardiography combined with valve regurgitation. The net ejection fraction avoids overestimation of left ventricular systolic function and has high reliability. It can accurately reflect the left ventricular systolic function of patients with mitral and aortic regurgitation, and has certain guiding significance for clinical doctors to grasp the patient's condition.

Development of Papercraft Visual Media On Grade IV Fraction Material In Elementary School

The lack of utilization of learning media makes it difficult for students to learn the concept of fractions, including students having difficulty understanding the teacher's explanation and difficulty performing calculations. Creating beautiful papercraft media to teach math is the driving force behind this research. The purpose of this research is to develop visual papercraft media and to find out whether visual papercraft media is feasible to be used as learning media in the Mathematics content in the classroom. This research uses the Research and Development (R&D) method using the 4-D model which goes through four stages, namely: 1. Define, 2. Design, 3. Development (Development), 4. Dissemination (Disseminate). Descriptive questionnaires were used for data collection. Students of SDN Cilincing 03 Pagi who are in grade IV participated as research subjects. This research was conducted by forming large groups and small groups. There were a total of 27 students from class IV B, with 10 students from class IV A forming the small group. The validation results from media experts and material experts showed that papercraft media is very suitable for teaching fractions. Media expert validation results reached 90% with a very feasible category, material expert results reached 91% with a very feasible category, and responses from 10 students in this study reached 94.9% with a very feasible category. In addition, responses from 27 students were at 94% with a very feasible category. It is concluded that papercraft media is a learning media that is very suitable for teaching fraction material in Mathematics subjects to grade IV elementary school students.

A COMPUTATIONAL AND FRACTIONAL MATHEMATICAL MODEL FOR ASSESSING HEPATITIS B WITH OPTIMAL THERAPY

This paper presents a mathematical study applied to Hepatitis B disease utilizing fractional calculus and numerical methods. We begin by discussing mathematical fundamentals, focusing on fractional calculus concepts and relevant numerical aspects for disease modeling. We then formulate the problem, describing a nonlinear fractional differential system that models hepatitis B virus (HBV) infection and its response to drug therapy. A detailed theoretical analysis explores system properties and biological implications. We provide a qualitative analysis of the model, discussing important dynamic behaviors such as stability and parameter sensitivity. Subsequently, numerical analysis is performed to validate the model and estimate unknown parameters from patient data. Our findings include significant insights into biological parameters and their impact on therapeutic response. We conclude that the proposed fractional-order model is effective, offering optimal therapeutic strategies for hepatitis B.

A Systematic Review of Evidence-Based Instruction for Developing Fraction Concepts of Autistic Students and Those with Intellectual and Developmental Disability

A Systematic Review of Evidence-Based Instruction for Developing Fraction Concepts of Autistic Students and Those with Intellectual and Developmental Disability

Novel FGM-USDFLD approach in Graded Cohesive Zone Modeling (GCZM): Predicting debonding and crack propagation in composite-patched notched plates

This study uses a graded adhesive approach to investigate the efficacy of composite patch reinforcement on a notched aluminum plate. The methodology employs the volumetric fraction concept of Functionally Graded Materials (FGM) to develop a Graded Cohesive Zone Model (GCZM). A variable field, introduced through a Fortran-based USDFLD subroutine, adapts the formulation of this GCZM. Patch debonding is simulated via adhesive damage using the Cohesive Zone Model (CZM). At the same time, crack initiation and propagation within the plate are modeled using the Extended Finite Element Method (XFEM) implemented in ABAQUS finite element software. The adhesive behavior is characterized by a triangular traction-separation law, with the GCZM incorporating gradation in both shear and normal separation modes relative to the notch radius. The GCZM concept is compared against two non-graded cases, Araldite 420 and AV138 adhesives, with one case replicating a previous study. Three gradation concepts are explored: C-1, where the more resistant Araldite 420 is located at the notch; C-2, at the extremity; and C-3, where it is at both the notch and extremity. These configurations aim to homogenize load transfer to the composite reinforcement and elucidate how different GCZM concepts influence debonding between the plate and composite reinforcement. By implementing USDFLD, this work effectively demonstrates the impact of gradation concepts and volumetric fraction indices on the competition between debonding and crack initiation in the plate. The results provide valuable insights into optimizing adhesive properties for enhanced structural integrity in composite-reinforced metallic structures.

A comprehensive review of the recent numerical methods for solving FPDEs

Abstract Fractional partial differential equations (FPDEs) have gained significant attention in various scientific and engineering fields due to their ability to describe complex phenomena with memory and long-range interactions. Solving FPDEs analytically can be challenging, leading to a growing need for efficient numerical methods. This review article presents the recent analytical and numerical methods for solving FPDEs, where the fractional derivatives are assumed in Riemann-Liouville’s sense, Caputo’s sense, Atangana-Baleanu’s sense, and others. The primary objective of this study is to provide an overview of numerical techniques commonly used for FPDEs, focusing on appropriate choices of fractional derivatives and initial conditions. This article also briefly illustrates some FPDEs with exact solutions. It highlights various approaches utilized for solving these equations analytically and numerically, considering different fractional derivative concepts. The presented methods aim to expand the scope of analytical and numerical solutions available for time-FPDEs and improve the accuracy and efficiency of the techniques employed.

A novel image denoising technique with Caputo type space–time fractional operators

A novel image denoising model, namely Full Fractional Total Variation (TVFF), based on the Rudin-Osher-Fatemi (ROF) and the fractional total variation models is presented. The leading advantage of TVFF model is that it uses fractional derivatives with length scale parameters instead of ordinary derivatives with respect to both time and spatial variables in the diffusion equation. The Riesz–Caputo fractional derivative operator is used to disperse nonlocal influence throughout all directions, whereas the Caputo fractional derivative concept is employed for time fractional derivatives. Therefore, the influence of neighboring pixels is given greater weight compared to those situated farther away and this reflects the consideration behind denoising process better. Moreover, the numerical approach is constructed, and its stability and convergence properties are thoroughly examined. To show the superiority of our model, the denoised images are subjected to visual and numerical comparisons using metrics such as the Signal-to-Noise Ratio (SNR), the Structural Similarity Index Measure (SSIM) and the Edge-Retention Ratio (ERR). The performance of the TVFF method is evaluated under various types of noise, including Poisson, Speckle, and Salt & Pepper, and the results are compared with those obtained using Gauss and Median Filters. Furthermore, the proposed method is applied to both blind and synthetic images, thereby showcasing its versatility and applicability across diverse datasets. The outcomes showcase the substantial potential of our enhanced model as a versatile and efficient tool for image denoising.

Servo Control of a Current-Controlled Attractive-Force-Type Magnetic Levitation System Using Fractional-Order LQR Control

Recent research on fractional-order control laws has introduced the fractional calculus concept into the field of control engineering. As described herein, we apply fractional-order linear quadratic regulator (LQR) control to a current-controlled attractive-force-type magnetic levitation system, which is a strongly nonlinear and unstable system, to investigate its control performance through experimentation. First, to design the controller, a current-controlled attractive-force-type magnetic levitation system expressed as an integer-order system is extended to a fractional-order system expressed using fractional-order derivatives. Then, target value tracking control of a levitated object is achieved by adding states, described by the integrals of the deviation between the output and the target value, to the extended system. Next, a fractional-order LQR controller is designed for the extended system. For state-feedback control, such as fractional-order servo LQR control, which requires the information of all states, a fractional-order state observer is configured to estimate fractional-order states. Simulation results demonstrate that fractional-order servo LQR control can achieve equilibrium point stabilization and enable target value tracking. Finally, to verify the fractional-order servo LQR control effectiveness, experiments using the designed fractional-order servo LQR control law are conducted with comparison to a conventional integer-order servo LQR control.

Exploring the relationship between students' attitudes and fraction sense proficiency across lower secondary grades

Understanding fractions is a critical mathematical skill necessary for more advanced mathematical concepts and applications. However, many students struggle with fraction sense, which is the foundational understanding and flexible use of fractions. This study aims to explore the relationship between students' attitudes toward learning fractions and their proficiency in fraction sense in lower secondary grades. Using a descriptive-correlational design, data were collected from 296 students aged 13 to 15 using the Fraction Sense Test (FST) and the Attitudes Towards Learning Fractions Questionnaire (ATLF). The study found that students consistently struggled with fractional concepts, achieving low scores across all grades. Nevertheless, a significant, though diminishing, relationship was observed between positive attitudes towards fractions and fraction sense proficiency from Secondary One to Secondary Three. These findings suggest the need to integrate meaningful fraction learning approaches to maintain students' positive attitudes, thereby improving their overall mathematical competence.

Preventable Fraction in the Context of Disease Progression.

The relevance of the epidemiologic concept of preventable fraction to the study of the population-level impact of preventive exposures is unequivocal. Here, we discuss how the preventable fraction can be usefully understood for the class of outcomes that relate to disease progression (e.g., clinical severity given diagnosis), and, under the principal stratification framework, derive an expression for this quantity for this type of outcome. In particular, we show that, in the context of disease progression, the preventable fraction is a function of the effect on the postdiagnosis outcome in the principal stratum in the unexposed group who would have disease regardless of exposure status. This work will facilitate an understanding of the contribution of principal effects to the impact of preventive exposures at the population level.

A Hybrid Control Framework for Chemical Processes with Long Time Delay: Theory and Experiments.

This paper proposes a hybrid control framework based on internal model concepts, sliding mode control methodology, and fractional-order calculus theory. As a result, a modified Smith predictor (SP) is proposed for nonlinear systems with significant delays. The particular predictive approach enhances the sliding mode control (SMC) controller's transient responses for dead-time processes, and the SMC gives the predictive structure robustness for model mismatches by combining the previous methods with fractional order concepts; the result is a dynamical sliding mode controller. A numerical example is considered to evaluate the performance of the proposed approach, where a step change, external disturbance, and parametric uncertainty test are performed. A real application in the TCLab Arduino kit is presented; the proposed method presented good performance with a little amount of chattering, and in the disturbance rejection case, the overshoot increased with an aggressive response; in both cases, better tuning parameters can improve the process response and the controller action.

A Qualitative Analysis of Leukemia Fractional Order SICW Model

Using a series of fundamental differential equations, including the Caputo derivative, which makes it easier to specify the initial conditions of the differential equations, we present a fractional order concept of leukemia in this study. The universality, positivity, and boundedness of solutions are first established. The local stability properties of the equilibrium are studied using the fractional Routh-Hurwitz stability criteria. The differential equation system has been solved using unconventional finite difference techniques. The Leukemia Fractional Order SICW model introduces several innovative elements compared to traditional epidemiological and disease models. This stands out due to its integration of fractional-order differential equations, inclusion of leukemic cells and immune cells compartments, simulation of treatment strategies, consideration of waning immunity, and its application to leukemia-specific scenarios. These elements collectively make it a valuable tool for studying leukemia dynamics, exploring treatment options, and improving our understanding of how the immune system interacts with cancer cells in leukemia patients. Numerical simulations of the model are shown at the conclusion to interpret our theoretical outcomes in support of various fractional orders of derivative options. From there, we can observe how the evolution of the system components is impacted by the fractional derivative .

Teachers' Multiple Representations on Teaching Fractions at Elementary School: A Commognitive Framework

This research explores how teachers utilize verbal, symbolic, pictorial, and real-life representations using a commognitive framework to support student learning. This research uses a qualitative approach with an exploratory descriptive design. The selection of research subjects was carried out through purposive sampling which was modified to achieve the research objectives. The research focuses on elementary school teachers who have education diplomas and more than 15 years of teaching experience. In this research, our data is in the form of learning video recording data. The collected data was analyzed using the cognition framework and the Lesh Model of multiple representations. The results of this research show two representations that teachers always apply to each commognitive component, namely symbolic representation and real-life representation. Symbolic representations are often used by teachers to solve mathematical problems, especially word problems. Likewise, real life representations are often used because they apply events or occurrences in everyday life. The use of diverse representations has the potential to increase students' understanding and ability to apply fraction concepts in real life.

Variable order fractional diabetes models: numerical treatment

ABSTRACT In this paper, we present two numerical approximation solutions for the updated nonlinear variable order fractional differential equations of diabetes disease. The variable order fractional differential operator is based on the Caputo fractional derivative concept. The first used method is developed using the nonstandard finite difference process, such that a new quick approximation is applied to tackle the nonlinear terms. By applying some reasonable assumptions to the given data, we can prove that this scheme maintains the positivity and boundedness of the discretized solutions. The second method is based on approximation with shifted Jacobi polynomials. The properties of Jacobi polynomials, together with the shifted Jacobi-Gauss-Lobatto nodes were utilized to reduce the proposed system into a set of algebraic nonlinear equations. Furthermore, some numerical experiments are conducted to compare the performance of the introduced schemes. Our numerical simulations show that the nonstandard finite difference approach requires less computational time compared to the Jacobi-Gauss-Lobatto spectral collocation. While the last one is more accurate when used for solving the variable order fractional diabetes model.

The Database Generation for Planar 2-DOF Fractionated Multiple-Joint Kinematic Chains

Abstract According to the fractionation concept and whether containing a multiple-joint, planar kinematic chains (KCs) are primarily categorized as non-fractionated simple-joint kinematic chains (NFS-KCs), fractionated simple-joint kinematic chains (FS-KCs), non-fractionated multiple-joint kinematic chains (NFM-KCs), and fractionated multiple-joint kinematic chains (FM-KCs). Currently, there is a noticeable research gap on the enumeration of FM-KCs, whereas comprehensive investigations have been conducted on the enumeration of the other three types of KCs. Aiming at addressing this research gap, the present study develops a heuristic approach for enumerating all planar 2-DOF FM-KCs. To this end, the composition of 2-DOF FM-KCs is initially analyzed to acquire their two basic classifications. Then, utilizing the characteristic graph generation methods for NFM-KCs and NFS-KCs, the combined characteristic graph and its corresponding combined characteristic number string of a 2-DOF FM-KC are created for solving the isomorphic problem in enumeration procedure. Finally, all non-isomorphic 2-DOF FM-KCs with 9, 11, 13, 15, and 17 links are enumerated, and the corresponding database is established.