Course: 1.8 评价带有给定值的变量表达式

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评价带有给定值的变量表达式
Jenny is making cookies for the school bake sale. One dozen cookies will be sold for $3.50 and one dozen muffins will be sold for $4.50. To quickly calculate the amount of money raised, Jenny has written the following variable expression :
::珍妮正在为学校面包销售做饼干。十几个饼干将以3.50美元的价格出售,十几个松饼将以4.50美元的价格出售。为了快速计算募集的资金数额,珍妮写了以下可变表达式:

$\begin{aligned} 3.50 c + 4.50 m \end{aligned}$ where $\begin{aligned} c = \end{aligned}$ the number of dozens of cookies sold and $\begin{aligned} m = \end{aligned}$ the number of dozens of muffins sold.
::3.50c+4.50米,其中c=售出几十个饼干的数量,m=售出几十个松饼的数量。

At the end of day, Jenny knows that 311 dozen cookies and 235 dozen muffins were sold. How can she use the variable expression to determine the total amount of money raised?
::最终,珍妮知道有311打饼干和235打松饼被卖掉。她如何使用变数表达法来决定筹得的钱总额?

In this concept, you will learn to evaluate variable expressions with given values for the variables.
::在此概念中,您将学习用给定的变量值来评价变量表达式。

Variable Expressions
::变量表达式

Before you can evaluate a variable expression with a given value for the variable, you must be able to identify a variable expression.
::在对变量中带有给定值的变量表达式进行评价之前,必须能够识别变量表达式。

A variable expression is a group of numbers and mathematical operations that contains one or more variables. A variable expression does not contain an equal sign.
::变量表达式是指包含一个或多个变量的一组数字和数学操作。变量表达式不包含等号。

A variable is a letter used to represent an unknown quantity.
::变量是指用于表示未知数量的字母。

The variable expression $\begin{aligned} 3 x - 6 + 5 y \end{aligned}$ contains the variables $\begin{aligned} x \end{aligned}$ and $\begin{aligned} y \end{aligned}$ the constant six. A constant is a term in an expression that is simply a number.
::变量表达式 3x-6+5y 包含变量 x 和 y 常数 6。常数是表达式中仅是一个数字的一个术语。

When values for the variable or variables are given and substituted into the expression, the values should be written inside parenthesis. This will allow you to see what operations have to be performed to evaluate the expression.
::当变量或变量的值被给定并替换为表达式时,值应写在括号内。这样可以让您看到需要执行哪些操作来评价表达式。

Let’s look at an example of evaluating a variable expression when you have been given a value for the variable.
::让我们查看一个示例,当您被给定变量值时,用于评价变量表达式。

Evaluate the variable expression:
::评估变量表达式 :

$\begin{aligned} 4.2 g + 1.5 when g = 8 \end{aligned}$
::4.2g+1.5 g=8时

To evaluate this variable expression you may have to review performing mathematical operations with decimals.
::要评价此变量表达式, 您可能需要用小数数来审查数学操作。

First, substitute $\begin{aligned} g = 8 \end{aligned}$ into the variable expression.
::首先,将 g=8 替换为变量表达式。

$\begin{aligned} 4.2 (8) + 1.5 \end{aligned}$

Next, multiply: $\begin{aligned} 4.2 (8) = 33.6 \end{aligned}$ to clear the parenthesis. Write the new expression.
::下一步,乘以:4.2(8)=33.6来清除括号。写新表达式。

$\begin{aligned} 33.6 + 1.5 \end{aligned}$
Then, add:
::33.6+1.5 然后,加上:

$\begin{aligned} 33.6 + 1.5 = 35.1 \end{aligned}$
The answer is 35.1
::33.6+1.5=35.1 答案是35.1

Let’s look at an example of evaluating a variable expression that has more than one variable.
::让我们来看看一个实例,用来评价一个具有多个变量的变量表达式。

Evaluate the variable expression:
::评估变量表达式 :

$\begin{aligned} 5 a b + 2 a - 7 \end{aligned}$ when $\begin{aligned} a = 2 \end{aligned}$ and $\begin{aligned} b = 4 \end{aligned}$
::5ab+2a-7 a=2和b=4

First, substitute the values $\begin{aligned} a = 2 \end{aligned}$ and $\begin{aligned} b = 4 \end{aligned}$ into the variable expression.
::首先,将值a=2和b=4替换为变量表达式。

$\begin{aligned} 5 (2 \times 4) + 2 (2) - 7 \end{aligned}$

Next, multiply: $\begin{aligned} (2 \times 4) = 8 \end{aligned}$ and write the new expression:
::下一个, 乘数 : (2x4) = 8, 并写入新表达式 :

$\begin{aligned} 5 (8) + 2 (2) - 7 \end{aligned}$

Next, multiply: $\begin{aligned} 5 (8) = 40 \end{aligned}$ to clear the parenthesis. Write the new expression.
::下一个, 乘: 5( 8) =40 清除括号。写入新表达式。

$\begin{aligned} 40 + 2 (2) - 7 \end{aligned}$

Next, multiply: $\begin{aligned} 2 (2) = 40 \end{aligned}$ to clear the parenthesis. Write the new expression.
::下一个, 乘: 2(2)=40 清除括号。写入新表达式。

$\begin{aligned} 40 + 4 - 7 \end{aligned}$

Next, add: $\begin{aligned} 40 + 4 = 44 \end{aligned}$ and write the new expression.
::下加:40+4=44,并写下新表达式。

$\begin{aligned} 44 - 7 \end{aligned}$
Then, subtract:
::44 - 7 然后减去:

$\begin{aligned} 44 - 7 = 37 \end{aligned}$
The answer is 37.
::44 -7=37 答案是37

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Jenny and her bake sale.
::早些时候,你得到一个问题关于珍妮和她的面包销售。

Jenny wrote a variable expression $\begin{aligned} 3.50 c + 4.50 m \end{aligned}$ where $\begin{aligned} c \end{aligned}$ represents the number of dozens of cookies and $\begin{aligned} m \end{aligned}$ represents the number of dozens of muffins.
::珍妮写了一个3.50c+4.50m的变数表达式, c代表了几十个饼干的数量, 代表了几十个松饼的数量。

There were 311 dozen cookies and 235 dozen muffins sold.
::卖了311打饼干和235打松饼

First, substitute the values $\begin{aligned} c = 311 \end{aligned}$ and $\begin{aligned} m = 235 \end{aligned}$ into the variable expression. $\begin{aligned} 3.50 (311) + 4.50 (2.35) \end{aligned}$
::首先,将c=311和m=235的值改为可变表达式3.50(311)+4.50(2.35)

Next, clear the " data-term="Parentheses" role="term" tabindex="0"> parentheses by multiplying.
::接下来,通过乘法清除括号。

$\begin{aligned} 3.50 (311) = 1088.50 and 4.50 (235) = 1057.50 \end{aligned}$

::3.50(311)=1088.50和4.50(235)=1057.50

Then, add:
$\begin{aligned} $ 1088.50 \\ \underline{+ $ 1057.50} \\ $ 2146.00 \end{aligned}$

::然后加上:1088.50美元+1057.50美元_2146.00美元

The answer is $2146.00
::答案是2146.00美元

Example 2
::例2

Evaluate the following variable expression:
::评估以下变量表达式:

$\begin{aligned} 5 a + 2 b - 17 \end{aligned}$ when $\begin{aligned} a = 3 \end{aligned}$ and $\begin{aligned} b = 4 \end{aligned}$
::5a+2b-17a=3和b=4

First, substitute the values $\begin{aligned} a = 3 \end{aligned}$ and $\begin{aligned} b = 4 \end{aligned}$ into the expression.
::首先,将值a=3和b=4替换为表达式。

$\begin{aligned} 5 (3) + 2 (4) - 17 \end{aligned}$

Next, multiply: $\begin{aligned} 5 (3) = 15 \end{aligned}$ to clear the parenthesis.
::5(3)+2(4)-17 下一个,乘:5(3)=15来清除括号。

$\begin{aligned} 15 + 2 (4) - 17 \end{aligned}$

Next, multiply: $\begin{aligned} 2 (4) = 8 \end{aligned}$ to clear the parenthesis.
::15+2(4)-17 下一个,乘以:2(4)=8来清除括号。

$\begin{aligned} 15 + 8 - 17 \end{aligned}$
Then, add and subtract, in order from left to right:
::15+8-17 然后,按从左到右顺序增减:

$\begin{aligned} 15 + 8 = 23 - 17 = 6 \end{aligned}$
The answer is 6.
::15+8=23 -17=6 答案是6

Example 3
::例3

Evaluate the following variable expression:
::评估以下变量表达式:

$\begin{aligned} 6 x y + 2 x - 7 \end{aligned}$ when $\begin{aligned} x = 4 \end{aligned}$ and $\begin{aligned} y = 5 \end{aligned}$
::x=4 和 y=5 时 6xy+2x-7

First, substitute the values $\begin{aligned} x = 4 \end{aligned}$ and $\begin{aligned} y = 5 \end{aligned}$ into the variable expression.
::首先,将数值 x=4 和 y=5 替换为变量表达式。

$\begin{aligned} 6 (4) (5) + 2 (4) - 7 \end{aligned}$

Next, multiply: $\begin{aligned} 6 (4) = 24 \end{aligned}$ to clear the parenthesis.
::6(4)(5)+2(4)-7 下一个,乘:6(4)=24以清除括号。

$\begin{aligned} 24 (5) + 2 (4) - 7 \end{aligned}$

Next, multiply: $\begin{aligned} 24 (5) = 120 \end{aligned}$ to clear the parenthesis.
$\begin{aligned} 120 + 2 (4) - 7 \end{aligned}$
Next, multiply: $\begin{aligned} 2 (4) = 8 \end{aligned}$ to clear the parenthesis.
::24(5)+2(4)-7 下一个,乘:24(5)=120来清除括号。 120+2(4)-7Next,乘:2(4)=8来清除括号。

$\begin{aligned} 120 + 8 - 7 \end{aligned}$
Then, add and subtract, in order from left to right.
::120+8-7 然后,按从左到右顺序增减。

$\begin{aligned} 120 + 8 = 128 - 7 = 121 \end{aligned}$
The answer is 121.
::120+8=128-7=121 答案是121

Example 4
::例4

Evaluate the following variable expression:
::评估以下变量表达式:

$\begin{aligned} 9 x + 18 y + 5 \end{aligned}$ when $\begin{aligned} x = - 6 \end{aligned}$ and $\begin{aligned} y = 2 \end{aligned}$
::9x+18y+5 时x @%6 和 y=2

First, substitute the values $\begin{aligned} x = - 6 \end{aligned}$ and $\begin{aligned} y = 2 \end{aligned}$ into the variable expression.
::首先,将值 x6 和 y=2 替换为变量表达式。

$\begin{aligned} 9 (- 6) + 18 (2) + 5 \end{aligned}$

Next, multiply: $\begin{aligned} 9 (- 6) = - 54 \end{aligned}$ to clear the parenthesis.
::9(-6)+18(2)+5 下一个,乘:9(-6)54来清除括号。

$\begin{aligned} - 54 + 18 (2) + 5 \end{aligned}$

Next, multiply: $\begin{aligned} 18 (2) = 36 \end{aligned}$ to clear the parenthesis.
::-54+18(2)+5 下一个,乘:18(2)=36来清除括号。

$\begin{aligned} - 54 + 36 + 5 \end{aligned}$

Then, add and subtract, in order from left to right.
::-54+36+5 然后,按从左到右顺序增减。

$\begin{aligned} - 54 + 36 = - 18 + 5 = - 13 \end{aligned}$

The answer is -13.
::答案是 -13

Review
::回顾

Evaluate each variable expression using the given values for each variable.
::使用每个变量的给定值来评价每个变量表达式。

$\begin{aligned} 6 a + 7 \end{aligned}$ when $\begin{aligned} a \end{aligned}$ is 8
::8岁时6a+7

$\begin{aligned} 9 x - y \end{aligned}$ when $\begin{aligned} x \end{aligned}$ is 2 and $\begin{aligned} y \end{aligned}$ is 4
::9 - y x 2 和 y 4 时为 9 - y

$\begin{aligned} 5 a + b^{2} \end{aligned}$ when $\begin{aligned} a \end{aligned}$ is 12 and $\begin{aligned} b \end{aligned}$ is 4
::5a+b2,a为12,b为4

$\begin{aligned} (\frac{8}{x}) + 2 \end{aligned}$ when $\begin{aligned} x \end{aligned}$ is 4
:8x)+2 x为 4

$\begin{aligned} 6 x + 2.5 \end{aligned}$ when $\begin{aligned} x \end{aligned}$ is 2
::6x+2.5 x 是 2 时

$\begin{aligned} y^{2} + 4 \end{aligned}$ when $\begin{aligned} y \end{aligned}$ is 9
::9岁时为y2+4

$\begin{aligned} 7 x + 2 y \end{aligned}$ when $\begin{aligned} x \end{aligned}$ is 3 and y is 5
::7x+2yx为 3, y为 5

$\begin{aligned} 9 x y + x^{2} \end{aligned}$ when $\begin{aligned} x \end{aligned}$ is 4 and $\begin{aligned} y \end{aligned}$ is 2
::9xy+x2 时, x为 4, y为 2

$\begin{aligned} 3 a b + b^{3} \end{aligned}$ when $\begin{aligned} a \end{aligned}$ is 9 and $\begin{aligned} b \end{aligned}$ is 2
::3ab+b3 时为 9, b为 2

$\begin{aligned} 16 x y^{2} + 14 \end{aligned}$ when $\begin{aligned} x \end{aligned}$ is 3 and $\begin{aligned} y \end{aligned}$ is 4
::16xy2+14 x 3 和 y 4 时

$\begin{aligned} 6 x y + 4 x \end{aligned}$ when $\begin{aligned} x \end{aligned}$ is 2 and $\begin{aligned} y \end{aligned}$ is 7
::6xy+4x x 2 和 Y 7 时为 6xy+4x

$\begin{aligned} 16 y + 8 x y \end{aligned}$ when $\begin{aligned} x \end{aligned}$ is 3 and $\begin{aligned} y \end{aligned}$ is 4
::16y+8xy x 3 和 Y 4 时为 16y+8xy

$\begin{aligned} 3 x^{2} + 24 y \end{aligned}$ when $\begin{aligned} x \end{aligned}$ is 3 and $\begin{aligned} y \end{aligned}$ is 4
::3x2+24y x 3 和 y 4 时

$\begin{aligned} - x y + 8 x y \end{aligned}$ when $\begin{aligned} x \end{aligned}$ is 3 and $\begin{aligned} y \end{aligned}$ is 4
::- x为 3, y为 4时xy+8xy

$\begin{aligned} 22 x + 4 y - 3 x y \end{aligned}$ when $\begin{aligned} x \end{aligned}$ is 3 and $\begin{aligned} y \end{aligned}$ is 4
::22x+4y-3xy x 3 和 y 4 时

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。

Section outline

General

评价带有给定值的变量表达式

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)

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)