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  • 带有变量的书写公式

    Expressing the World Around Us with Math
    ::以数学表达我们周围的世界,

    The ability to use math to represent the structure and performance of any business directly contributes to the success of that business. Math is used for simple calculations like profit, and for more complex formulas like determining the lifetime value of a customer. Every day CEOs use math to make major decisions that may well affect the future success of their business.
    ::利用数学来代表任何企业的结构和业绩的能力直接有助于该企业的成功。 数学用于简单的计算,比如利润,以及更复杂的公式,比如确定客户的终身价值。 首席执行官每天使用数学来做出可能影响其未来业务成功的重大决定。

    Can you think of any examples of how businesses use math?
    ::你能想到企业如何使用数学的例子吗?

      

    Vocabulary
    ::词汇表

    You  will begin by learning about expressions, equations, and their basic components:
    ::首先,你将学习表达式、方程式及其基本组成部分:

    lesson content
    Flow chart of Vocab Words
    • A variable is a letter that stands for a number. The number a variable stands for can change based on the circumstances of the situation.
      ::一个变量是表示数字的字母。一个变量表示的数字可以根据情况变化。
    • A coefficient is a number that is placed in front of a variable to multiply it. A variable with no visible coefficient has a coefficient of 1.
      ::系数是放在变量前面以乘以该变量的数值。 没有可见系数的变量的系数为1。
    • A constant is a number that does not change. A constant is different from a coefficient because a constant cannot be attached to a variable.
      ::常数是一个不改变的数值。常数与系数不同,因为常数不能附加在变量上。
    • An operator is a symbol that defines what action to take with a number. The operators that we will be dealing with are +, -, x and ÷.
      ::操作员是一个符号,用来定义对数字要采取的行动。我们将处理的操作员是 +, -, x 和 + 。
    • A term is a group of numbers or variables separated by a + or - operator. A term can be one letter, one number, or a collection of letters and numbers.
      ::一个术语是指由 + 或 - 运算符分隔的一组数字或变量。一个术语可以是一个字母、一个数字或一系列字母和数字。

     

    Writing Expressions
    ::书写表达式

    An expression is a combination of variables, constants, and operators. An expression can consist of one or more terms .
    ::表达式是变量、常数和运算符的组合。表达式可以由一个或多个术语组成。

    Use the interactive below to identify the parts of an expression.
    ::使用下面的交互效果来标明表达式的各个部分。

     

     

     

     

    Discussion Question
    ::讨论问题

    How can 12 be both a constant and a term?
    ::12年怎么能既是一个常数又是一个术语呢?

     

    Expressions are used to represent relationships between variables, coefficients, and constants. In business, since there are so many factors that can affect the outcomes, expressions are used to represent the relationship, and the variables are filled in later when the numbers are known. Additionally, expressions allow us to plug in different values to see how the outcome will change.
    ::表达式用于代表变量、 系数和常数之间的关系。 在企业中,由于有许多因素可以影响结果,所以表达式被用来代表关系,当数字为人所知时,变量会稍后被填入。此外,表达式允许我们插入不同的值,以观察结果会如何变化。

    Example
    ::示例示例示例示例

    S tart with a simple and common relationship: An amusement park sells tickets for adults at $15 and tickets for children at $8. What is an expression for the revenue (money earned) from selling ' A ' adult tickets on a given day? If you do not immediately see the relationship, draw a table to help figure it out.
    ::以简单而共同的关系为起点:一个游乐园以15美元为成人售票,以8美元为儿童售票。在某一天出售“A”成人票所得收入(金钱)的表达方式是什么?如果你没有立即看到这种关系,请绘制一张表格来帮助解决。

    Adult Tickets Sold 1 2 3 A
    Revenue 15 30 45 ?

    To determine the revenue, you are multiplying the number of tickets sold by the price per adult ticket ($15). To determine the revenue from selling ' A ' adult tickets, multiply the number of tickets sold ( A ) by the price per adult ticket ($15) to get the expression 15 A .
    ::为了确定收入,您正在将售出的票数乘以每张成人票的价格(15美元)。为了确定售出“A”成人票的收入,您将售出的(A)票数乘以每张成人票的价格(15美元),以获得15A表达式。

    Answer:  15 A
    ::答复:15A

    Notice that our expression is a constant multiplied by a variable.
    ::注意我们的表达式是常数乘以变量。

    Example
    ::示例示例示例示例

    Using the same information from the previous example, what is an expression that can be used to determine the total revenue (money earned) from selling ' A ' adult tickets and ' C ' child tickets on a given day? D rawing a table will help you figure it out. Since any combination of adult and child tickets sold is possible, choose three random values of adult and child tickets sold.
    ::使用上一个例子的相同信息, 可以用什么表达方式来确定在某一天出售“ A” 成人票和“ C” 儿童票的总收入( 挣得的钱 ) ? 绘制一张表格可以帮助你找到答案。 由于可以将成人票和售出的儿童票结合起来, 选择三种随机的成人票和售出的儿童票。

    Adult Tickets Sold 1 2 3 A
    Child Tickets Sold 1 2 3 C
    Revenue 23 46 69 ?

    T o determine the revenue, you are multiplying the number of tickets sold by the price per adult ticket ($15) and adding it to the number of tickets sold by the price per child's ticket ($8). To determine the revenue from selling  A  adult tickets, you will multiply the number of adult tickets sold ( A ) by the price per adult ticket ($15) and add it to the number of child tickets sold ( C ) by the price per  child ticket ($8) to get the expression  15 A + 8 C .
    ::为了确定收入,您正在将售出的票数乘以每张成人票的价格(15美元),并将其与按每张儿童票的价格(8美元)售出的票数相加。为了确定售出A张成人票的收入,您将将售出的(A)成人票数乘以每张成人票的价格(15美元),并将售出的(C)儿童票数乘以每张儿童票数(8美元),以获得15A+8C的表示值。

    Answer:  15 A + 8 C
    ::答复:15A+8C

    Discussion Questions
    ::讨论问题 讨论问题

    1. Would the answer 8 C + 15 A  be incorrect?
      ::答案8C+15A是否不正确?
    2. Does this represent all the revenue from an amusement park on a given day? How else might they earn money?
      ::这是否代表了某一天游乐园的全部收入?他们还能如何赚钱呢?
    3. How would these additional sources of revenue change our total revenue expressions?
      ::这些额外的收入来源将如何改变我们的总收入表达方式?
    4. What type of situation would involve a constant?
      ::哪种情况涉及一个常数?

     

    Writing Equations
    ::书写等量

    An equation is a statement that two expressions are equal.
    ::等式是两个表达式相等的语句 。

    Use the interactive below to identify the parts of an equation.
    ::使用下面的交互式来识别方程的各个部分。

     

     

     

     

    Discussion Questions
    ::讨论问题 讨论问题

    1. How can you tell the difference between an equation and an expression?
      ::您如何辨别方程式和表达式的区别 ?
    2. How can 5 be a constant, term, and expression at the same time?
      ::5 怎么能同时是一个常数、任期和表达方式?

      

    Equations are commonly used in business to state the relationship between an expression and its equal numerical value. For example, the total cost of a business can be determined by adding the fixed cost and the variable cost. Fixed costs are costs which are constant from one period to the next, like rent. Variable costs are costs that change from one period to the next like materials. The materials you buy to make your product will depend on how many products you plan to sell. An ice cream shop, for example, will buy/make more ice cream in the summer because they will have more customers in the summer. The equation for the total cost is as follows:
    ::例如,企业总成本可以通过增加固定成本和可变成本来确定。固定成本是从一个时期到下一个时期的不变成本,如租金。可变成本是从一个时期到下一个时期的成本,与材料一样。您为生产产品而购买的材料将取决于您打算出售多少产品。例如,一个冰淇淋店将在夏季购买/生产更多的冰淇淋,因为他们夏季会有更多的客户。总成本的方程式如下:

    Total Cost = Fixed Cost + Variable Cost


    ::费用总额=固定成本+可变成本

    One benefit of equations is that they help us determine unknown information. By knowing the fixed cost and variable cost, you can determine the total cost. Additionally, if you know the total cost and fixed cost, you can determine the variable cost.  This  property of equations can be used to determine what variable values will give us the desired result.
    ::等式的一个好处是它们能帮助我们确定未知信息。通过了解固定成本和可变成本,您可以确定总成本。此外,如果您知道总成本和固定成本,您可以确定可变成本。这种等式的属性可以用来确定什么变量值能给我们预期的结果。

     

    Spreadsheets
    ::电子表格

    S preadsheets are one of the most common ways in which expressions and equations are used in business. It can be helpful to list all the sources of revenue and cost in one place. However, this spreadsheet can be pages long. What if you make a mistake or something in the spreadsheet changes? To avoid having to retype a spreadsheet you can use expressions, also commonly referred to as formulas or functions.
    ::电子表格是商业中使用表达式和方程式的最常见方式之一。 将所有收入和成本来源都列在一个地方会很有帮助。 但是, 这个电子表格可以是长页的。 如果您在电子表格中做出错误或某些更改, 如何? 为了避免重新输入您可以使用的表达式, 也通常被称为公式或函数 。

    For reference, each rectangle in a spreadsheet is called a cell, and each cell is named by their column (a letter) and row (a number). So the cell in column B and row 23 would be called cell B23. In the place of variables, we type the name of a cell. To insert an expression into a cell,  we  type in an expression  that will determine the value of that cell. For example, if you want a cell to stand for the product of a constant (3) and a variable (the value in the cell A2) you can write =3*A2. If you want a cell to stand for the product of two different cells (A1 and A2), you can write =A1*A2. The = symbol identifies that you are inputting an expression rather than a value. Once you fill in all of the variables, the cell will display the value.
    ::对于引用,电子表格中的每个矩形都称为单元格,每个单元格都用其列(字母)和行(数字)命名。因此,列B和行23中的单元格将称为单元格B23。在变量的位置,我们键入单元格的名称。要将表达式插入单元格,我们键入一个表达式,该表达式将确定单元格的值。例如,如果您想要一个单元格站在常数(3)和变量(单元格 A2 中的值)的产物上,您可以写入=3*A2。如果您想要一个单元格站在两个不同单元格(A1和A2)的产物上,您可以写入=A1*A2。该符号表示您输入表达式而不是值。一旦您在所有变量中填满,单元格将显示值。

    In the interactive below, fill out five products for a company in cells in column A and their respective prices in column B. Enter 5 as the quantity in cells C2 through C6. Write an expression in column D to find the value of each cell by multiplying the corresponding B and C cells. For example, the cell D2 should use the formula =B2*C2. The cell D7 should be determined by writing an expression to add cells D2 through D6.
    ::在下文互动部分,填写一个公司在A栏中的五个产品,并在B栏中填写其各自的价格。输入5,作为C2至C6单元格的数量。在D栏中填写一个表达式,通过乘以相应的B和C单元格来查找每个单元格的值。例如,单元格D2应该使用公式=B2*C2. 单元格D7应该通过写出一个表达式来确定,以添加D2至D6单元格。

     

     

     

     

       Summary
    ::摘要

    • An expression is a combination of variables, terms, and operators.
      ::表达式是变量、术语和运算符的组合。
    • An  equation is a statement that two expressions are equal.
      ::等式是两个表达式相等的语句 。
    • Equations and expressions  can be used to  describe real-world situations.  
      ::公式和表达方式可以用来描述现实世界的情况。