Basic Concepts in Math and Science - Fractions

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Coursera课程《数学与科学基础概念 - 分数》在线课程总结 这门课程旨在为学员提供对分数概念的全面深入理解。课程强调分数是数学学习中至关重要的基础,许多成年人在处理分数时仍感困难。 课程涵盖了以下关键主题: * **分数的基本定义**: 什么是“分数”。 * **分数类型**: 真分数、假分数、正分数和负分数。 * **分数运算**: 分数的约分、加法、减法、比较、乘法和除法。 * **交叉相乘技巧**: 作为加减和比较分数的快捷方法。 * **假分数与带分数**: 假分数与带分数之间的转换。 此外,课程还重点讲解了分数的五个关键概念: 1. **倒数关系**: "如果 N1 大于 N2,那么 1/N1 就小于 1/N2"。 2. **整体(单位)概念**: "整体"、"1" 或 "unity" 的含义。 3. **真分数的特性**: 真分数总是代表小于 1 的值。 4. **分数的补数**: 分数的补数概念。 5. **等值分数的生成**: 分数分子和分母的等比例变化(仅限乘除法)。 本课程适合所有希望扎实掌握分数基础知识的学习者。

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Fractions is one of those critical math topics in which every child needs to have a very thorough grounding. No child can escape his or her math destiny with Fractions. It is a fact of life that many adults have difficulty even with the most basic concepts involving fractions, never mind the various nuances associated with fractions.This course will provide any student with a very thorough understanding of Fractions. Covered topics include discussions of: what exactly is a "fraction"; proper fractions and improper fractions; positive fractions and negative fractions; reducing fractions; adding fractions; subtracting fractions; comparing fractions; multiplying fractions; dividing fractions; using the cross-multiplication technique as a short-cut to adding, subtracting and comparing fractions; the connection between improper fractions and mixed numbers.The course also covers 5 crucial concepts in the area of "Fractions", those being:(1) the concept that if N1 greater than N2, then 1/N1 is less than 1/N2; (b) the concept of "the whole" or "unity" or "1"; (c) the concept that proper fractions always represent a value less than 1; (d) the concept of the complement of a fraction; (5) the concept of changing a fraction such that any change to the numerator of the fraction must also be reflected in the denominator of the fraction, and that this change is limited to multiplication and division only.

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