Course: 12.2作为表达式的乘法和除法短语

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作为表达式的乘法和除法短语
The Cashway Sluggers have just won the city’s Little League Baseball championship game, and Mr. Amos has volunteered to take his son’s team to dinner. Mr. Amos tells the 16 team members that he is going to split $125 evenly between the team members. How can he use the information he has to figure out how much each member of the baseball team will be allotted for lunch?
::阿莫斯先生告诉16个团队成员,他将在团队成员之间平均分配125美元。他如何使用他掌握的信息来决定棒球团队每位成员将分配多少午餐?

In this concept, you will learn to write multiplication and division phrases as single variable expressions.
::在此概念中,您将学习将乘数和除法短语写成单个变量表达式。

Writing Multiplication and Division Phrases as Expressions
::乘法和除法词组作为表达式

Here are some key words that mean multiplication and division.
::下面是一些关键词,它意味着乘法和除法。

Multiplication:
::乘法 :

product
::产品产品

times
::时间时间

groups
::组群

Division:
::分区 :

split up
::分开拆开

quotient
::商数

divided
::已除和除

These key words will indicate what operation is involved in the expression .
::这些关键词将表明该表达式涉及何种操作。

When deciphering phrases, identify any numbers first. Next, identify the operation involved. Then, identify the variable.
::当破译词组时, 请先识别任何数字。接下来, 识别所涉及的操作。然后识别变量。

Once you have identified all the elements, you can write the expression.
::一旦您确定了所有元素,您就可以写入表达式。

Here is an example.
::举一个例子。

The product of eight and a number
::8和数的产物

To write this as an expression, first, identify any numbers.
::将此写成表达式, 首先, 标明任何数字。

The number in this phrase is eight.
::这个短语中的号码是8。

8

Next, identify the operation.
::下一位,确认行动

The word “product” means multiply.
::“产品”一词是指乘数。

$\begin{aligned} \times \end{aligned}$

Then, identify the variable.
::然后,识别变量。

“A number” means use a variable. Let $\begin{aligned} y \end{aligned}$ represent the variable.
::“数字”是指变量。让y代表变量。

$\begin{aligned} y \end{aligned}$
::y y , y

The answer is $\begin{aligned} 8 y \end{aligned}$ .
::答案是 8 y 。

Remember that a number next to a variable means multiply. You could have also used " data-term="Parentheses" role="term" tabindex="0"> parentheses to show multiplication.
::记住变量旁边的一个数字意味着乘法。您也可以使用括号来显示乘法。

"> $\begin{aligned} 8 (y) \end{aligned}$
::8项

Now let’s look at writing an expression for phrase with division.
::现在让我们看看用除法来写一个短语表达式。

Twenty-four divided by a number
::二十四除以一个数字

First, identify any numbers.
::首先,找出任何数字。

24

Next, identify the operation.
::下一位,确认行动

Divided by means division $\begin{aligned} (\div) \end{aligned}$
::按收入划分(_________________________________________________________________________________________________________________________________

Then, identify the variable. “A number” means use a variable.
::然后,标明变量。 " 数字 " 是指使用变量。

$\begin{aligned} y \end{aligned}$
::y y , y

The answer is $\begin{aligned} 24 \div y \end{aligned}$ .
::答案是24 y。

You can also use a fraction bar to show division.
::您也可以使用分数栏来显示分割区。

24

___ (this means divided by)
:这是指除以)

$\begin{aligned} y \end{aligned}$
::y y , y

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about the championship dinner.
::早些时候,有人给了你一个关于冠军晚宴的问题

Before the Cashway Sluggers divide the $125 Mr. Amos is giving the team for dinner, they must decide whether to eat at a local burger restaurant or a sub shop. Hamburger combo lunches are $6 at the burger restaurant, and sub sandwich combos are $8 each. Mr. Amos is going to split $125 between the 16 team members.
::阿莫斯先生在给团队提供晚餐之前,必须决定是在当地的汉堡店还是子店吃饭。汉堡组合午餐在汉堡餐厅6美元,三明治组合每个8美元。阿莫斯先生将在16名团队成员之间分配125美元。

What variable expression can the team use to decide which restaurant to eat at?
::团队用什么变式表达方式来决定哪家餐厅可以吃?

First, identify the numbers involved.
::首先,确定所涉及的数字。

16 – Number of team members
::16 - 小组成员人数

125 – Amount the team has to be split
::125 - 团队必须拆分的数额

Next, identify the operation involved. “Split” mean division.
::其次,确定所涉行动。 " 分割 " 是指分割。

$\begin{aligned} \div \end{aligned}$

Then, identify the unknown number which will be the variable $\begin{aligned} y \end{aligned}$ . How much each team member will have to spend is the unknown number or variable.
::然后,确定未知的变量 y 的编号。每个团队成员需要花费多少是未知的数字或变量。

$\begin{aligned} y \end{aligned}$
::y y , y

Finally, write the expression and solve.
::最后,写出表达和解答。

$\begin{aligned} \begin{array}{rcl} y & = & 125 \div 16 \\ y & = & 7.81 \end{array} \end{aligned}$

The answer is: $7.81
::答案是:7.81美元

Each member of the team will have $7.81 to spend, so the team should eat at the burger restaurant.
::团队的每个成员都有7.81美元可花所以团队应该在汉堡店吃饭

Example 2
::例2

Write the phrase as an expression: the quantity six times an unknown number divided by 2.
::将短语写成表达式:数量是未知数字除以2的六倍。

There are two operations in this problem. Let’s break it down.
::这个问题有两个操作。

First, the quantity six times an unknown number becomes $\begin{aligned} 6 x \end{aligned}$ .
::首先,一个未知数字的六倍数量成为6x。

$\begin{aligned} 6 x \end{aligned}$
::6x 6 x

Next, identify the second part of the phrase as divided by two. You can use a fraction bar for division.
::下一步,指定该短语的第二部分除以 2。您可以使用分数栏进行分隔。

$\begin{aligned} \bar{2} \end{aligned}$

Then, because it is divided by the quantity, put the $\begin{aligned} 6 x \end{aligned}$ on top of the fraction bar.
::然后,因为它除以数量, 将 6 x 放在分数条的顶端。

$\begin{aligned} \frac{6 x}{2} \end{aligned}$
::6 x 2 6 x 2

The answer is $\begin{aligned} \frac{6 x}{2} \end{aligned}$
::答案是 6 x 2

Again, this could be written as $\begin{aligned} 6 x \div 2 \end{aligned}$ .
::这也可以写为 6 x 2 。

Example 3
::例3

Write the phrase as an expression: six times an unknown number.
::将短语写成表达式:6倍于未知数字。

First, identify any numbers.
::首先,找出任何数字。

6

Next, identify the operation.
::下一位,确认行动

Times means multiplication $\begin{aligned} (x) \end{aligned}$
::乘以 (x) 表示乘以 (x)

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

Then, identify the variable.
::然后,识别变量。

“An unknown number” means use a variable.
::“数目不详”是指使用变量。

$\begin{aligned} y \end{aligned}$
::y y , y

The answer is "> $\begin{aligned} 6 (y) \end{aligned}$ or $\begin{aligned} 6 y \end{aligned}$ .
::答案是 6 或 6 y 。

Example 4
::例4

Write the phrase as an expression: an unknown number divided by two.
::将短语写成表达式:未知数字除以2。

First, identify any numbers.
::首先,找出任何数字。

2

Next, identify the operation.
::下一位,确认行动

Divided by means division.
::按收入划分。

$\begin{aligned} (\div) \end{aligned}$

Then, identify the variable.
::然后,识别变量。

“An unknown number” means use a variable.
::“数目不详”是指使用变量。

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

The answer is $\begin{aligned} x \div 2 \end{aligned}$ .
::答案是 x 2 。

This can also be written as a fraction .
::这也可以作为一个分数写成。

$\begin{aligned} \frac{x}{2} \end{aligned}$
::x 2 x 2

Example 5
::例5

Write the phrase as an expression: the product of seven and a number.
::将短语写成表达式:7和数字的产物。

First, identify any numbers.
::首先,找出任何数字。

7

Next, identify the operation. Product means multiplication.
::接下来,确认操作。产品意味着乘法。

$\begin{aligned} (x) \end{aligned}$
:x )

Then, identify the variable.
::然后,识别变量。

“And a number” means use a variable.
::“数字”系指使用变量。

$\begin{aligned} y \end{aligned}$
::y y , y

The answer is "> $\begin{aligned} 7 (y) \end{aligned}$ or $\begin{aligned} 7 y \end{aligned}$ .
::答案是 7 或 7 y 。

Review
::回顾

Write single-variable expressions from the following multiplication and division phrases. Use the variable x for unknown values.
::从下面的乘数和分隔短语中写出单变量表达式。对未知值使用变量 x 。

The product of six and a number
::6和数的产物

A number divided by two
::数除以除以 2

Fifteen divided by an unknown number
::十五除以未知数字

A number times seven
::数乘以七乘以七

The product of ten and a number
::以十和数计十的产物,

Eighteen divided by a number
::十八除以数除以十八

Twenty times a number
::二十倍一个数字

A number divided by three
::A除以3除以A除以A除以A除以A除以3

An unknown number divided by twelve
::一个未知数字除以12除以12

An unknown number times sixteen
::未知数乘以十六

The product of five and an unknown quantity
::5 和数量未知的 5 的产物

The quantity six times an unknown number divided by three
::数量是未知数字的六倍,除以三除以三

The quantity four times an unknown number divided by seven
::数量是未知数字的四倍,除以七除以七

The quantity six times an unknown number divided by ten
::数量是未知数字的六倍,除以十

The product of three and an unknown times four
::3和未知乘以4的产物

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

Section outline

General

作为表达式的乘法和除法短语

Writing Multiplication and Division Phrases as Expressions ::乘法和除法词组作为表达式

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

Writing Multiplication and Division Phrases as Expressions
::乘法和除法词组作为表达式

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