课程： 1.14包含一个或多个变量的表达式

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选择节包含一个或多个变量的表达式

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包含一个或多个变量的表达式
Dexter is in charge of ticket sales at his town’s water park. He has to report to his boss how many tickets he sells and how much money the water park makes in ticket sales each day - adult tickets ($7), child tickets ($5). Today, Dexter has sold 100 adult and 125 child tickets. Yesterday, he sold 120 adult and 120 child tickets. Can Dexter write an expression to figure out today’s ticket sales, and use this to compare today’s sales to yesterday’s?
::Dexter负责本镇水公园的售票。 Dexter必须向他的上司报告他每天售出多少票和水公园在售票中赚多少钱 — — 成人票(7美元 ) 、儿童票(5美元 ) 。今天,Dexter卖了100张成人票和125张儿童票。昨天,他卖了120张成人票和120张儿童票。 Dexter能写出一个表来了解今天的售票销售情况,并利用这个表来比较今天的销售与昨天的销售情况吗?

In this concept, you will learn how to evaluate expressions that have multiple variables and/or multiple operations .
::在此概念中,您将学习如何评价具有多个变量和/或多个操作的表达式。

Expressions with Multiple Variables
::带有多个变量的表达式

When evaluating expressions with multiple variables and multiple operations, it is important to remember the .
::在用多个变量和多个操作来评价表达式时,必须记住。

Order of Operations
::行动命令令

P - " data-term="Parentheses" role="term" tabindex="0"> parentheses
::P - 括号括号

E- exponents
::电子前台

MD - multiplication and division , in order from left to right
::MD - 乘数和除法,按从左到右顺序排列

AS - addition and subtraction , in order from left to right
::AAS - 增减,按从左到右顺序排列

Whenever you are evaluating an expression with more than one operation in it, always refer back to the order of operations.
::当您在评价一个表达式时,如果该表达式中有一个以上的操作,则总是要参照操作的顺序。

Let's look at an example of an expression with multiple variables and operations.
::让我们看看一个带有多个变量和操作的表达式的例子。

Evaluate $\begin{aligned} 6 a + b \end{aligned}$ when $\begin{aligned} a \end{aligned}$ is 4 and $\begin{aligned} b \end{aligned}$ is 5.
::如果a为4,b为5,则评价6 a+b。

First, you can see that there are two variables in this expression, $\begin{aligned} a \end{aligned}$ and $\begin{aligned} b \end{aligned}$ . There are also two operations here: multiplication, seen in "6 times the value of $\begin{aligned} a \end{aligned}$ " and addition, seen in " $\begin{aligned} + b \end{aligned}$ ". You are given values for $\begin{aligned} a and b \end{aligned}$ .
::首先,你可以看到,这个表达式有两个变量,a和b。这里还有两个操作:乘法,在 " +b " 中看到乘法,乘法是 " a的6倍 " ,加法是 " +b " 。给一个和b的值是给定的。

First, substitute the given values for each variable into the expression.
::首先,将表达式中每个变量的给定值替换为给定值。

$\begin{aligned} 6 a + b \\ 6 (4) + 5 \end{aligned}$

Then, evaluate the expression according to order of operations.
::然后,按照行动顺序来评估表达方式。

$\begin{aligned} 6 (4) + 5 \\ 24 + 5 \\ 29 \end{aligned}$

The answer is 29.
::答案是29。

Let’s look at another example with multiple variables and expressions.
::让我们看看另一个多变量和表达式的例子。

Evaluate $\begin{aligned} 7 b - d \end{aligned}$ when $\begin{aligned} b \end{aligned}$ is 7 and $\begin{aligned} d \end{aligned}$ is 11.
::评价7b-d,b为7,d为11。

First, substitute the given values in for the variables.
::首先,将给定值替换为变量。

$\begin{aligned} 7 (7) - 11 \end{aligned}$

Then, evaluate the expression according to order of operations.
::然后,按照行动顺序来评估表达方式。

$\begin{aligned} 49 - 11 \\ 38 \end{aligned}$

The answer is 38.
::答案是38岁

Sometimes you may have an expression that is all variables. Evaluate this in the same way.
::有时您可能有所有变量的表达式。以同样的方式评估它。

Evaluate $\begin{aligned} a b + c d \end{aligned}$ when $\begin{aligned} a \end{aligned}$ is 4, $\begin{aligned} b \end{aligned}$ is 3, $\begin{aligned} c \end{aligned}$ is 10 and $\begin{aligned} d \end{aligned}$ is 6.
::如果a为4,b为3,c为10,d为6,则评价a b + c d为4,b为3,c为10,d为6。

First, substitute the given values in for the variables.
::首先,将给定值替换为变量。

$\begin{aligned} a b + & c d \\ (4) (3) + & (10) (6) \end{aligned}$

Next, evaluate the expression according to order of operations.
::接下来,根据作业顺序评价表达式。

$\begin{aligned} 12 + 60 \\ 72 \end{aligned}$

The answer is 72.
::答案是72。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Dexter and his tickets.
::早些时候,你对Dexter和他的机票有问题

Dexter needs to write an expression to figure out the total money made from the 100 adult and 125 child tickets he sold today, compared to the 120 adult and 120 child tickets he sold yesterday. The adult tickets cost $7 and the child tickets cost $5.
::Dexter需要写出一个表达方式来了解他今天出售的100张成人机票和125张儿童机票的总金额,而他昨天出售的120张成人机票和120张儿童机票。成人机票和儿童机票费用分别为7美元和5美元。

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

$\begin{aligned} 7 x + 5 y \end{aligned}$

Next, substitute in the given values for today’s ticket sales.
::接下来,以给定价值取代今天的票价销售。

$\begin{aligned} 7 (100) + 5 (125) \end{aligned}$

Then, follow order of operations to multiply and then add.
::然后,按照操作顺序乘以,然后添加。

$\begin{aligned} 7 (100) + 5 (125) & Multiply 7 \times 100 \\ 700 + 5 (125) & Multiply 5 \times 125 \\ 700 + 625 & Add 700 + 625 = 1325 \\ 1, 325 \end{aligned}$

The answer is 1,325.
::答案是1 325

Next, substitute in the given values for yesterday’s ticket sales.
::换成昨天的票价销售。

%20%26%20%5Cquad%20%5Ctext%7BSubstitute%20120%20for%20both%20%7Dx%20%5Ctext%7B%20and%20%7Dy%5C%5C%0A7(120)%2B5(120)%20%26%5C%5C">

$\begin{aligned} 7 (x) + 5 (y) & Substitute 120 for both x and y \\ 7 (120) + 5 (120) \end{aligned}$

Then, follow order of operations to multiply and then add.
::然后,按照操作顺序乘以,然后添加。

$\begin{aligned} 7 (120) + 5 (120) & Multiply 7 \times 120 \\ 840 + 5 (120) & Multiply 5 \times 120 \\ 840 + 600 & Add 840 + 600 = 1440 \\ 1, 440 \end{aligned}$

The answer is 1,440.
::答案是1,440

Finally, subtract 1,325 from 1,440 to get the difference .
::最后,从1,440中减去1,325,以获得差额。

$\begin{aligned} 1, 440 - 1, 325 = 115 \end{aligned}$

The answer is 115.
::答案是115

Dexter can report to his boss that today the park sold $1,325 in tickets, which is $115 less than the $1,440 they sold in tickets yesterday.
::Dexter可以向他的上司报告今天公园卖出了1 325美元的机票比昨天卖的1 440美元少115美元

Example 2
::例2

Evaluate $\begin{aligned} a + a b + c d \end{aligned}$ when $\begin{aligned} a \end{aligned}$ is 4, $\begin{aligned} b \end{aligned}$ is 9, $\begin{aligned} c \end{aligned}$ is 6 and $\begin{aligned} d \end{aligned}$ is 4.
::如果a为4,b为9,c为6,d为4,评价a+a b+cd为4,b为9,c为6,d为4,则评价a+b+cd为4。

First, substitute the given values into the expression.
::首先,将给定值替换为表达式。

$\begin{aligned} 4 + 4 (9) + 6 (4) \end{aligned}$

Next, evaluate according to order of operations.
::下一步,按照行动顺序进行评估。

$\begin{aligned} 4 + 36 + 24 \end{aligned}$

$\begin{aligned} 64 \end{aligned}$

The answer is 64.
::答案是64。

Example 3
::例3

Evaluate $\begin{aligned} 12 x - y \end{aligned}$ when $\begin{aligned} x \end{aligned}$ is 4 and $\begin{aligned} y \end{aligned}$ is 9.
::评价 12 x - y 当 x 4 和 y 9 时 y 。

First, substitute 4 for $\begin{aligned} x \end{aligned}$ and 9 for $\begin{aligned} y \end{aligned}$ .
::第一,以x取代4,以y取代9。

$\begin{aligned} 12 x - y & Substitute 4 in place of x and 9 for y \\ 12 (4) - (9) \end{aligned}$

Then, evaluate the expression.
::然后,评估表达方式。

$\begin{aligned} 12 (4) - (9) & Multiply 12 \times 4 = 48 \\ 48 - (9) & Subtract 48 - 9 = 39 \\ 39 \end{aligned}$

The answer is 39.
::答案是39岁

Example 4
::例4

Evaluate $\begin{aligned} \frac{12}{a} + 4 \end{aligned}$ when $\begin{aligned} a \end{aligned}$ is 3.
::评价12 a+4,当a为3时。

First, substitute 3 for $\begin{aligned} a \end{aligned}$ .
::第一,换3,换3

$\begin{aligned} 5 x + 3 y \end{aligned}$

Next, evaluate the expression.
::接下来,评价表达式。

$\begin{aligned} \frac{12}{3} + 4 & Divide 12 \div 3 = 4 \\ 4 + 4 & Add 4 + 4 = 8 \\ 8 \end{aligned}$

The answer is 8.
::答案是8岁

Example 5
::例5

Evaluate $\begin{aligned} 5 x + 3 y \end{aligned}$ when $\begin{aligned} x \end{aligned}$ is 4 and $\begin{aligned} y \end{aligned}$ is 8.
::评价 5 x + 3 y, 当 x 4 和 Y 8 时。

First, substitute 4 for $\begin{aligned} x \end{aligned}$ and 8 for $\begin{aligned} y \end{aligned}$ .
::第一,以x取代4,以y取代8。

$\begin{aligned} 5 x + 3 y & Substitute 4 for x and 8 for y \\ 5 (4) + 3 (8) \end{aligned}$

Then, evaluate the expression.
::然后,评估表达方式。

$\begin{aligned} 5 (4) + 3 (8) & Multiply 5 \times 4 = 20 \\ 20 + 3 (8) & Multiply 3 \times 8 = 24 \\ 20 + 24 & Add 20 + 24 = 44 \\ 44 \end{aligned}$

The answer is 44.
::答案是44

Review
::回顾

Evaluate each multi-variable expression when $\begin{aligned} x = 2 \end{aligned}$ and $\begin{aligned} y = 3 \end{aligned}$ .
::当 x = 2 和 y = 3 时,评价每个多变量表达式。

$\begin{aligned} 2 x + y \end{aligned}$
::2 x + y 2 x + y

$\begin{aligned} 9 x - y \end{aligned}$
::9 x - y y

$\begin{aligned} x + y \end{aligned}$
::x + y + y

$\begin{aligned} x y \end{aligned}$
::x y 年

$\begin{aligned} x y + 3 \end{aligned}$
::xy+3xy+3

$\begin{aligned} 9 y - 5 \end{aligned}$
::9y - 5岁

$\begin{aligned} 10 x - 2 y \end{aligned}$
::10 x - 2 yy 10 x - 2 y

$\begin{aligned} 3 x + 6 y \end{aligned}$
::3 x + 6 y 3 x + 6 y

$\begin{aligned} 2 x + 2 y \end{aligned}$
::2 x + 2 y + 2 y

$\begin{aligned} 7 x - 3 y \end{aligned}$
::7 x - 3 y

$\begin{aligned} 3 y - 2 \end{aligned}$
::3 y y - 2

$\begin{aligned} 10 x - 8 \end{aligned}$
::10 x - 8 个

$\begin{aligned} 12 x - 3 y \end{aligned}$
::12 x - 3 y

$\begin{aligned} 9 x + 7 y \end{aligned}$
::9 x + 7 y

$\begin{aligned} 11 x - 7 y \end{aligned}$
::11 x - 7 y 11 x - 7 y

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

包含一个或多个变量的表达式

Expressions with Multiple Variables ::带有多个变量的表达式

Order of Operations ::行动命令令

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

Example 5 ::例5

Review ::回顾

Review (Answers) ::回顾(答复)

Resources ::资源

Expressions with Multiple Variables
::带有多个变量的表达式

Order of Operations
::行动命令令

Examples
::实例

Example 1
::例1

Example 2
::例2

Example 3
::例3

Example 4
::例4

Example 5
::例5

Review
::回顾

Review (Answers)
::回顾(答复)

Resources
::资源