节: 增加和减法等等式 | 3.3植物对环境变化的适应

章节大纲

Sal leads an informal cycling team of six people. He wants to register them for a race, but doesn’t know if there is enough space. The maximum number of allowed racers on the course is 138 cyclists. What is the maximum number of cyclists that can already be registered if the whole team can join the race? How can Sal write a single variable equation to represent this problem?
::萨尔领导了一个由六人组成的非正式自行车赛队。他想为他们参加一场赛事注册,但他不知道是否有足够的空间。最多允许参加赛程的赛车手是138名赛车手。如果整个赛车队都能参加比赛,最多可以登记的赛车手人数是多少? 赛车手怎么能够写出一个代表这个问题的变量方程式呢?

In this concept, you will learn how to write addition and subtraction phrases as single variable equations.
::在此概念中,您将学习如何将添加和减法短语作为单一变量方程式进行写入。

Writing Addition and Subtraction Phrases as Equations
::添加和减法词组作为等式

An expression connects numbers and/or variables with operations , such as addition, subtraction, multiplication , and division . Notice that an expression does not have an equal sign. The value of the variable in each expression can change, and you can evaluate an expression using any value for the variable.
::表达式将数字和/或变量与操作连接,例如添加、减法、乘法和除法。注意表达式没有等号。每个表达式中的变量值可以改变,您可以用变量的任何值来评价表达式。

\begin{aligned} 50 - 2 & 4 - a & 12 z & \frac{4 x}{3} \end{aligned}

::50-24-a12z4x3

In the expressions above, $\begin{aligned} a, z, \end{aligned}$ and $\begin{aligned} x \end{aligned}$ are variables.
::在上述表达式中,a、z和x为变量。

An expression that includes one or more variables is called an algebraic expression . You can use algebraic expressions to represent words or phrases. To help you solve word problems, you need to translate words or phrases into operations, variables, or expressions. Let’s start with addition and subtraction phrases. Take a look at this chart.
::包含一个或多个变量的表达式被称为代数表达式。您可以使用代数表达式来表示文字或短语。为了帮助您解决单词问题,您需要将单词或短语转换为操作、变量或表达式。让我们从添加和减号开始。看看这个图表。

Addition Phrases		Subtraction Phrases
$\begin{aligned} 1 \end{aligned}$ plus $\begin{aligned} a \end{aligned}$	$\begin{aligned} 1 + a \end{aligned}$	$\begin{aligned} 4 \end{aligned}$ less $\begin{aligned} d \end{aligned}$	$\begin{aligned} 4 - d \end{aligned}$
$\begin{aligned} 2 \end{aligned}$ and $\begin{aligned} b \end{aligned}$	$\begin{aligned} 2 + b \end{aligned}$	$\begin{aligned} 6 \end{aligned}$ less than $\begin{aligned} g \end{aligned}$	$\begin{aligned} g - 6 \end{aligned}$
$\begin{aligned} 4 \end{aligned}$ more than $\begin{aligned} c \end{aligned}$	$\begin{aligned} c + 3 \end{aligned}$	$\begin{aligned} h \end{aligned}$ fewer than $\begin{aligned} 7 \end{aligned}$	$\begin{aligned} 7 - h \end{aligned}$

The bolded words in the phrases above tell you if you should use addition or subtraction, and the order of the terms . Read the word problem carefully to figure out which operation makes the most sense.
::以上语句中的粗体字表示您是否应该使用增、减、用词顺序。仔细阅读单词问题, 以找出哪个操作最有意义。

Let’s look at an example.
::让我们举个例子。

Abdul has $5 more than Xavier has. Write an algebraic expression to show the number of dollars Abdul has.
::Abdul比Xavier多出5美元。写一个代数表达式来显示 Abdul 的美元数。

The phrase is “$5 more than Xavier.” Use a number, an operation sign, or a variable to represent each part of that phrase.
::使用数字、操作符号或变量代表该短语的每一部分。

Let $\begin{aligned} x \end{aligned}$ stand for the number of dollars Xavier has. “More than” means you are adding.
::x 表示 Xavier 的美元数。 “ 多于” 表示您正在添加。

\begin{aligned} x + 5 \end{aligned}

::x+5 x+5

So, the expression $\begin{aligned} x + 5 \end{aligned}$ represents the number of dollars Abdul has.
::所以,表达式 x+5 代表 Abdul 拥有的美元数。

Let’s look at another example.
::让我们再看看另一个例子。

Change “6 less than a number” into an algebraic expression.
::将“少于数字6”改为代数表达式。

Let “a number” be the variable $\begin{aligned} x \end{aligned}$ . “Less than” means you are subtracting. Be careful about the order, 6 will follow the variable.
::将“ 数字” 改为变量 x。 “ 慢于” 表示您正在减去。注意顺序, 6 将跟随变量。

\begin{aligned} x - 6 \end{aligned}

::x-6 个

The answer is $\begin{aligned} x - 6 \end{aligned}$ .
::答案是 x-6 。

Here is one more example.
::这里还有一个例子。

Lian is $\begin{aligned} x \end{aligned}$ inches shorter than Hannah. Hannah is 65 inches tall. Write an algebraic expression to show Lian’s height in inches.
::Lian 比Hannah短x英寸。 Hannah 高65英寸。写一个代数表达法来显示Lian的身高。

The phrase is “ $\begin{aligned} x \end{aligned}$ inches shorter than Hannah.” You also know that Hannah’s height is 65 inches. “Shorter than” means you are subtracting. Be careful about the order, $\begin{aligned} x \end{aligned}$ will follow 65.
::这句话是“比汉娜更短的x英寸 ” 。你也知道汉娜的身高是65英寸。 “短于”意味着你正在减。当心顺序,x将跟随65英寸。

\begin{aligned} 65 - x \end{aligned}

::65 - 时

The answer is $\begin{aligned} 65 - x \end{aligned}$ .
::答案是65 -x。

In a word problem, the word “is” means equals. When you see the word “is” you can set the expression equal to something. This is an equation .
::在单词问题中,“是”一词的意思是等的。当看到“是”一词时,你可以将表达方式设置为等于某物。这是一个等式。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Sal’s biking team.
::先前,Sal的骑车队给您带来了问题。

Sal needs to register his team of six people, but the maximum number of allowed racers on the course is 138 cyclists. Sal needs to write a single variable equation to figure out the maximum number of cyclists that can already be registered so that his team of six can join.
::萨尔需要注册他的六人团队,但最多允许的赛车手人数是138名骑自行车者。萨尔需要写出一个单一的变量方程式,以找出已经注册的骑自行车者人数的最大数量,以便他的六人团队能够加入。

First, let $\begin{aligned} x \end{aligned}$ be the maximum number of cyclists that can be registered. Six more than that will give you the maximum of 138 cyclists. When you can use the phrase “more than” you can use addition.
::首先, 让 x 成为可以注册的自行车骑手的最大数量。超过 6 个, 最多能给您138 个自行车骑手。当您可以使用“ 超过 ” 一语时, 您可以添加。

The answer is $\begin{aligned} x + 6 = 138 \end{aligned}$ .
::答案是 x+6=138。

Example 2
::例2

Write an equation to represent the following phrase.
::写一个方程以表示以下短语。

Four less than an unknown number is eighteen.
::4比未知数字少4是18。

To figure this out, first let “an unknown number” be the variable $\begin{aligned} x \end{aligned}$ . Next, you know the operation is subtraction because of the key phrase “less than”.
::要弄清楚这一点,首先,让“未知数字”成为变量x。接下来,你知道操作会由于关键词“低于”而减去。

So you can write $\begin{aligned} x - 4 \end{aligned}$ since the four is being taken away from the unknown number.
::因此您可以写入 x-4, 因为这4 个是从未知号码中取走的。

The word “is” means equals, and “eighteen” is 18.
::“是”一词的意思是等的,“十八”是18。

\begin{aligned} x - 4 = 18 \end{aligned}

::x-4=18x- 4=18

The answer is $\begin{aligned} x - 4 = 18 \end{aligned}$ .
::答案是 x-4=18。

Example 3
::例3

Write an equation for the following phrase: a number plus five is ten.
::为以下短语写一个方程:数字加5是10。

Let $\begin{aligned} x \end{aligned}$ be “a number”, “plus” means addition, and “is” means equals.
::让 x " a number " , " plus " 是指添加, " is " 是指等同。

The answer is $\begin{aligned} x + 5 = 10 \end{aligned}$ .
::答案是 x+5=10。

Example 4
::例4

Write an equation for the following phrase: six more than a number is eighteen.
::写入以下短语的方程: 数字为 18, 6 个以上。

Let $\begin{aligned} x \end{aligned}$ be “a number”, “more than” means addition, and “is” means equals.
::让 x " a number " 表示 " 多于 " 表示增加, " 是 " 表示等同。

The answer is $\begin{aligned} x + 6 = 18 \end{aligned}$ .
::答案是 x+6=18。

Example 5
::例5

Write an equation for the following phrase: fifteen less than a number is twenty.
::写出以下短语的方程:比数字20少15个。

Let $\begin{aligned} x \end{aligned}$ be “ a number”, “less than” means subtraction (but be careful about order), and “is” means equals.
::让 x " a number " , " 少于 " 表示减法(但要注意顺序), " 是 " 表示等值。

The answer is $\begin{aligned} x - 15 = 20 \end{aligned}$ .
::答案是 x - 15=20 。

Review
::回顾

Write an expression for each phrase.
::每个词组写一个表达式。

5 more than a number
::5个多于一个数字

A number plus six
::A+6 数加6

8 and a number
::8和一个数字

Seven less than a number
::七个小于一个数字

Eight take a way four
::八八走四路,八走四路

Nine more than a number
::9个比一个数字多9个

Write a simple equation for each phrase.
::每个词组写一个简单的方程式。

Five less than a number is ten.
::5比一个数字少10是10。

Eight take away four is a number.
::八号拿掉四号就是一个数字

Five and a number is twelve.
::5个,一个数字是12个。

Sixteen less than an unknown number is eighty.
::不到一个未知数字的16个是80个。

Twenty and a number is fifty five.
::20个数字是55个

A number and fifteen is forty.
::A和15是40。

A number and twelve is sixty.
::A号和12号是60号

Fifteen less than a number is ninety.
::15个不到一个号码是90。

Sixty less than a number is eighty.
::80人比60人少。

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。

章节大纲

Writing Addition and Subtraction Phrases as Equations ::添加和减法词组作为等式

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