coefficient; factor; quotient

简明释义

系数

英英释义

例句

1.In physics, the coefficient 系数 of friction determines how easily one surface can slide over another.

在物理学中，摩擦系数 系数决定了一个表面滑过另一个表面的难易程度。

2.When you divide 20 by 4, the result is 5, which is the quotient 商.

当你将20除以4时，结果是5，这就是商 商。

3.In the equation y = 3x + 5, the number 3 is the coefficient 系数 of x.

在方程y = 3x + 5中，数字3是x的系数 系数。

4.To solve this equation, we need to find the factor 因子 of 12 that adds up to 7.

要解这个方程，我们需要找出12的因子 因子，使其和为7。

5.The factor 因子 of a number is any whole number that can divide it evenly.

一个数字的因子 因子是可以整除它的任何整数。

作文

In mathematics, understanding the concepts of coefficient（系数）, factor（因子）, and quotient（商） is essential for solving equations and performing calculations effectively. Each of these terms plays a significant role in various mathematical operations, and grasping their meanings can enhance one's ability to tackle complex problems.A coefficient is a numerical or constant quantity placed before a variable in an algebraic expression. For instance, in the expression 5x + 3, the number 5 is the coefficient of the variable x. This means that x is being multiplied by 5. Coefficients are crucial in determining the value of variables when solving equations. They help in identifying how many times a variable contributes to the overall value of an expression. Understanding coefficients is fundamental, especially when working with polynomials, as they define the degree and behavior of the polynomial function.On the other hand, a factor is a number or algebraic expression that divides another number or expression evenly, without leaving a remainder. For example, in the expression 12 = 3 × 4, both 3 and 4 are factors of 12. Recognizing factors is important for simplifying expressions, finding common denominators, and solving equations that involve multiplication. The concept of factors extends beyond simple arithmetic; it also applies to algebraic expressions, where factoring can lead to solutions of quadratic equations and other polynomial expressions.The quotient, however, refers to the result obtained when one number is divided by another. In the division equation 20 ÷ 4 = 5, the number 5 is called the quotient. Understanding quotients is vital in various mathematical applications, including fractions, ratios, and proportions. It helps in interpreting the relationship between quantities and is often used in real-world scenarios, such as calculating rates or averages. The concept of quotients is also essential when dealing with algebraic expressions, where division plays a critical role in simplifying and solving equations.In conclusion, the terms coefficient, factor, and quotient are fundamental building blocks in the field of mathematics. A solid understanding of these concepts not only aids in academic pursuits but also enhances problem-solving skills in everyday life. Whether one is tackling simple arithmetic or complex algebra, recognizing the significance of coefficients, factors, and quotients can lead to greater mathematical proficiency and confidence. As students progress through their mathematical education, mastering these terms will undoubtedly serve as a cornerstone for future learning and application in various fields, including science, engineering, and economics.

在数学中，理解系数、因子和商的概念对于有效解决方程和进行计算至关重要。这些术语在各种数学运算中起着重要作用，掌握它们的含义可以增强人们处理复杂问题的能力。系数是一个数字或常量，放置在代数表达式中的变量之前。例如，在表达式5x + 3中，数字5是变量x的系数。这意味着x被乘以5。系数在确定变量的值时至关重要，尤其是在解决方程时。它们帮助识别一个变量对表达式整体值的贡献次数。理解系数是基础，尤其是在处理多项式时，因为它们定义了多项式函数的度和行为。另一方面，因子是一个数字或代数表达式，可以均匀地将另一个数字或表达式分割，而不留下余数。例如，在表达式12 = 3 × 4中，3和4都是12的因子。识别因子对于简化表达式、寻找公分母和解决涉及乘法的方程非常重要。因子的概念超越简单的算术，它还适用于代数表达式，其中因式分解可以导致二次方程和其他多项式表达式的解。而商则是指一个数字被另一个数字除后的结果。在除法方程20 ÷ 4 = 5中，数字5被称为商。理解商在各种数学应用中至关重要，包括分数、比率和比例。它有助于解释数量之间的关系，并且通常用于现实生活场景，例如计算速率或平均值。商的概念在处理代数表达式时也至关重要，因为除法在简化和解决方程中发挥着关键作用。总之，系数、因子和商这三个术语是数学领域的基本构建块。扎实理解这些概念不仅有助于学术追求，还增强了日常生活中的问题解决能力。无论是处理简单的算术还是复杂的代数，认识到系数、因子和商的重要性都能带来更大的数学能力和信心。随着学生在数学教育中的进步，掌握这些术语无疑将成为未来学习和应用的基石，包括科学、工程和经济学等各个领域。