课程： 1.13单变量表达式

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选择节单变量表达式

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单变量表达式
Ayako just got her first job at her local arcade. In her interview, the manager said she would earn either $8 or $9 an hour. When he called to offer her the job, Ayako was so excited that she forgot to ask what she would be paid. Ayako plans to work 20 hours per week. How can Ayako figure out how much she will get paid each week?
::Ayako刚在本地的游乐场获得第一份工作。在她的面试中,经理说她每小时挣8美元或9美元。当他打电话给她提供工作时,Ayako非常兴奋,以至于她忘了问她会得到什么报酬。Ayako计划每周工作20小时。Ayako如何知道她每周能得到多少钱?

In this concept, you will learn how to evaluate single variable expressions with given values.
::在此概念中,您将学习如何用给定值来评价单个变量表达式。

Variable Expressions
::变量表达式

A variable is a letter that is used to represent an unknown quantity. Often, $\begin{aligned} x \end{aligned}$ or $\begin{aligned} y \end{aligned}$ represents the unknown quantity, but any letter, usually lowercase, can be used as a variable.
::变量是指用于表示未知数量的字母。通常, x 或 Y 表示未知数量,但任何字母,通常是小写字母,都可以作为变量使用。

A variable can be used in any sort of mathematical expression . A variable expression is an expression with one or more operations that has variables but no equals sign.
::变量可以用于任何类型的数学表达式。可变表达式是一个具有一个或多个操作的表达式,该操作带有变量,但无等号。

To understand variable expressions a little better, let’s think about some ways that you can show addition , subtraction , multiplication and division in mathematics.
::要想更好地理解变数表达式, 让我们想想一些方法, 来显示数学的增量、减法、乘法和分法。

Addition can be shown by using a + sign.
::添加可使用 + 符号显示。

Subtraction can be shown using a subtraction or minus sign $\begin{aligned} - \end{aligned}$ .
::减法可以用减法或减法符号-显示。

Multiplication can be shown in different ways:
::乘法可以不同方式显示:

Using the times symbol, e.g. $\begin{aligned} 5 \times 6 = 30. \end{aligned}$
::使用时间符号,例如5×6=30。

Using two sets of " data-term="Parentheses" role="term" tabindex="0"> parentheses , e.g. $\begin{aligned} (5) (6) = 30 \end{aligned}$
::使用两套括号括号,例如(5) (6) = 30

Using a variable next to a number, e.g. $\begin{aligned} 6 x \end{aligned}$ indicates 6 multiplied by the unknown $\begin{aligned} x \end{aligned}$
::使用数字旁边的变量,例如 6 x 表示 6 乘未知 x

Using one number next to parentheses, e.g. 4(3) = 12
::使用括号旁边的一个数字,例如4(3)=12

Division can be shown in different ways:
::各司可以不同方式显示:

Using the division symbol, e.g. $\begin{aligned} 6 \div 2 = 3 \end{aligned}$
::使用分割符号,例如, 6 2 = 3

Using the fraction bar , e.g. $\begin{aligned} \frac{6}{2} = 3 \end{aligned}$
::使用分数条,例如 6 2 = 3

Depending on the situation, you should expect to see operations shown in different ways.
::视情况而定,你应该期望看到以不同方式显示行动。

Often you will be asked to evaluate variable expressions with a given value for the variable.
::通常会要求您用给定值来评价变量表达式。

Evaluate 5 + a when a = 18.
::评价5+a=18时。

First, substitute the given value for the variable. In this case, substitute 18 in for a .
::首先,将给定值替换为变量。在此情况下,将给定值替换为 a 。

$\begin{aligned} 5 + a & Substitute 18 in place of a \\ 5 + 18 \end{aligned}$

Next, add.
::下加。

$\begin{aligned} 5 + 18 & Add 5 + 18 \\ 23 \end{aligned}$

The answer is 23.
::答案是23岁

Let's look at an example.
::让我们举个例子。

Evaluate $\begin{aligned} b - 22 \end{aligned}$ when $\begin{aligned} b \end{aligned}$ is 40.
::评价b - 22,b为40。

First, substitute the given value for the variable. In this case, substitute 40 in for $\begin{aligned} b \end{aligned}$ .
::首先,将给定值替换为变量。在此情况下,将 40 替换为 b 。

$\begin{aligned} b - 22 & Substitute 40 in place of b \\ 40 - 22 \end{aligned}$

Then subtract.
::然后减。

$\begin{aligned} 40 - 22 & Subtract 40 - 22 \\ 18 \end{aligned}$

The answer is 18.
::答案是18岁

Let's look at another example.
::让我们再举一个例子。

Evaluate $\begin{aligned} 7 x \end{aligned}$ when $\begin{aligned} x \end{aligned}$ is 12.
::当x为12时评价 7 x 。

First, substitute the given value for the variable. In this case, substitute 12 in for $\begin{aligned} x \end{aligned}$ . Then multiply.
::首先,将给定值替换为变量。在此情况下, x 的替代值为12。然后乘以。

$\begin{aligned} 7 x & Substitute 12 in for x \\ 7 (12) & Multiply 7 \times 12 \\ 84 \end{aligned}$

The answer is 84.
::答案是84

Let's look at one more example.
::让我们再举一个例子。

Evaluate $\begin{aligned} \frac{14}{x} \end{aligned}$ when $\begin{aligned} x \end{aligned}$ is 2.
::在x为2时评价 14 x 。

This expression includes a fraction bar, which tells you that this is a division problem.
::此表达式包含一个分数栏, 它告诉您这是一个分割问题。

First, substitute the given value of 2 in for $\begin{aligned} x \end{aligned}$ .
::首先,将给定值为 2 英寸改为 x 。

$\begin{aligned} \frac{14}{x} & Substitute 2 in place of x \\ \frac{14}{2} & = 7 \end{aligned}$

The answer is 7.
::答案是7个

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Ayako and her new job.
::早些时候,你遇到了一个问题关于阿亚科和她的新工作。

Ayako needs to figure out how much she will get paid for working 20 hours a week if she gets paid $8 or $9 an hour.
::阿亚科需要弄清楚如果她每星期得到8美元或9美元的工资,她每周工作20小时能得到多少报酬。

First, write an expression.
::首先,写一个表达方式。

$\begin{aligned} 20 x = \end{aligned}$ ?
::20x=? 20x=?

The given values for the unknown variable, $\begin{aligned} x \end{aligned}$ , are 8 and 9.
::未知变量 x 的给定值为 8 和 9。

Next, substitute 8 in for the variable.
::下一位, 替换变量 8 。

20(8)=160

The answer is 160.
::答案是160个。

Then, substitute 9 in for the variable.
::然后换成变数 9 。

20(9)=180

The answer is 180.
::答案是180

The answer is 160 or 180.
::答案是160或180

Ayako will get paid $160 or $180 per week at her new arcade job.
::Ayako在她新的街机工作时,每周将获得160美元或180美元的工资。

Example 2
::例2

Evaluate $\begin{aligned} 17 + y \end{aligned}$ when $\begin{aligned} y \end{aligned}$ is 12 .
::y 12岁时评价17+y。

$\begin{aligned} 17 + y & Substitute 12 in place of y \\ 17 + 12 & Add 17 + 12 = 29 \\ 29 \end{aligned}$

The answer is 29.
::答案是29。

Example 3
::例3

Evaluate $\begin{aligned} 5 c \end{aligned}$ when $\begin{aligned} c \end{aligned}$ is 9.
::c 9岁时评价5c。

$\begin{aligned} 5 c & Substitute 9 in place of c \\ 5 (9) & Multiply 5 \times 9 \\ 45 \end{aligned}$

The answer is 45.
::答案是45岁

Example 4
::例4

Evaluate $\begin{aligned} 8 \div x \end{aligned}$ when $\begin{aligned} x \end{aligned}$ is 4.
::当 x 是 4 时评价 8 x 。

$\begin{aligned} 8 \div x & Substitute 4 in place of x \\ 8 \div 4 & Divide 8 by 4 \\ 2 \end{aligned}$

The answer is 2.
::答案是2。

Review
::回顾

Evaluate each of the variable expressions when $\begin{aligned} a = 4, b = 5, and c = 6 \end{aligned}$
::当 a = 4, b = 5, c = 6 时, 评估每个变量表达式

$\begin{aligned} 5 + a \end{aligned}$
::5+a 5+a

$\begin{aligned} 6 + b \end{aligned}$
::6+b 6+b 6+b

$\begin{aligned} 7 + c \end{aligned}$
::7+c 7+c

$\begin{aligned} 8 - a \end{aligned}$
::8 - a

$\begin{aligned} 9 c \end{aligned}$
::9 c) 9 c

$\begin{aligned} 10 a \end{aligned}$
::10 a)

$\begin{aligned} 7 c \end{aligned}$
::7c 7c

$\begin{aligned} 9 a \end{aligned}$
::9a 9a

$\begin{aligned} 4 b \end{aligned}$
::4 b 4 b

$\begin{aligned} \frac{16}{a} \end{aligned}$
::16 a) 16 a

$\begin{aligned} \frac{42}{c} \end{aligned}$
::42 c 42 c

$\begin{aligned} \frac{c}{2} \end{aligned}$
::c 2个

$\begin{aligned} 15 a \end{aligned}$
::15 a 15 a

$\begin{aligned} 9 b \end{aligned}$
::9 b 9 b

$\begin{aligned} \frac{15}{b} \end{aligned}$
::15 b 15 b

Review (Answers)
::回顾(答复)

Click to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键。

Resources
::资源

章节大纲

常规

单变量表达式

Variable Expressions ::变量表达式

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

Review ::回顾

Review (Answers) ::回顾(答复)

Resources ::资源

Variable Expressions
::变量表达式

Examples
::实例

Example 1
::例1

Example 2
::例2

Example 3
::例3

Example 4
::例4

Review
::回顾

Review (Answers)
::回顾(答复)

Resources
::资源