12.3语句作为单变量表达式

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  语句作为单变量表达式

  

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  Mrs. Hughes knows that students dread final exams, so this semester she is going to allow her cooking class to bake cakes for its final exam. She plans to divide the 24 members of the class into six groups of four, and each group will bake a cake as their final grade. Mrs. Hughes is making a list of all the items she needs to purchase for the cakes. Eggs are at the top of her list because each group will need six eggs. There are 12 eggs in a dozen. How can Mrs. Hughes use this information to determine how many dozens of eggs the class will need?
  ::Hughes夫人知道学生害怕期末考试,所以这个学期她将允许她的烹饪班为期末考试烤蛋糕。她计划把该班的24名成员分成六组,四组,每个组将烤蛋糕作为期末成绩。Hughes夫人正在编制一份她需要购买的蛋糕清单。鸡蛋在她名单上排在首位,因为每个组需要6个鸡蛋。12个鸡蛋在12个中。Hughes夫人如何使用这些信息来确定该班需要多少个鸡蛋?

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  In this concept, you will learn how to write sentences as single- variable  equations.
  ::在这个概念中,你将学会如何将句子写成单变量方程式。

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  Writing Sentences as Single-Variable Equations
  ::作为单一可变等数的书写句

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  Expressions contain some combination of numbers, variables and  operations , but does not have an equals sign. When you have an equals sign, you have an  equation  not an  expression .
  ::表达式包含一些数字、变量和操作的组合,但没有等号。当您有一个等号时,您有一个公式而不是表达式。

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  An equation has an equal sign. One side of the equation equals the other side of the equation.
  ::方程式有一个等效符号。方程式的一面等于方程式的另一面 。

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  The following is an equation.
  ::以下是一个等式。

  $\begin{array}{r}5+9=14\end{array}$  

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  Here five plus nine is equal to fourteen. The quantity on one side of the equal sign is the same as the quantity on the other side of the equal sign.
  ::这里的五加九等于十四。 等号的一面的数量与等号的另一面的数量相同 。

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  You can also have equations with variables in them. When you have a variable in an equation, there is an unknown quantity.
  ::您也可以有含有变量的方程式。当您在方程式中有变量时,数量未知。

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  Take a look at the following equation which contains a variable.
  ::查看包含变量的以下方程式 。

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  Five plus an unknown number is equal to fifteen.
  ::五加一个未知号码等于十五

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  To write an equation for this phrase, start by working through the problem from the left to the right.
  ::要写出这个短语的方程式, 首先从从左到右解决问题。

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  First, write the expression for the initial part of the equation, “Five plus.”
  ::首先,写出方程最初部分的表达式,“五加五”。

  $\begin{array}{r}5+\end{array}$  

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  Next, let the “unknown number” be the variable  $\begin{array}{r}x\end{array}$ .
  ::接下来,让“未知数字”成为变量 x 。

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  $\begin{array}{r}x\end{array}$
  ::x x

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  Then, express “Is equal to fifteen” with an equal sign and number.
  ::然后,以相同的符号和数字表示“等于15”。

  $\begin{array}{r}=15\end{array}$

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  The answer is  $\begin{array}{r}5+x=15\end{array}$
  ::答案是5+x=15

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  Here is another equation.
  ::这是另一个方程式。

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  Six  less than  a number is equal to ten.
  ::少于一个数字的6等于10。

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  First, write the expression for “Six less than.” Since this is “six less than” the  order  is reversed. It becomes some number or quantity minus 6.
  ::首先,写上“少于六点”的字句。 因为这“ 少于六点 ” , 顺序被颠倒。 它会变成数字或数量减6。

  $\begin{array}{r}-6\end{array}$  

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  Next, let the “unknown number” be the variable  $\begin{array}{r}x\end{array}$ .
  ::接下来,让“未知数字”成为变量 x 。

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  $\begin{array}{r}x\end{array}$
  ::x x

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  Then, express “Is equal to ten” with an equal sign and number.
  ::然后,你应当以一个相等的牌号和数字,而说:十等于十。

  $\begin{array}{r}=10\end{array}$

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  The answer is  $\begin{array}{r}x-6=10\end{array}$ .
  ::答案是 x - 6 = 10 。

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  Here is an example that uses  multiplication .
  ::以下是一个使用乘法的例子。

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  The product of three and a number is thirty.
  ::3和30的产物。

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  First, note that product means multiplication. 
  ::首先,注意产品意味着乘法。

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  $\begin{array}{r}x\end{array}$
  ::x x

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  Next, identify the numbers involved on the left side of the equal sign.
  ::下一步,确定在等号左侧涉及的数字。

  $\begin{array}{r}3\end{array}$

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  Then, let the “unknown number” be the variable  $\begin{array}{r}y\end{array}$ .
  ::以“未知数字”为变量y。

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  $\begin{array}{r}y\end{array}$
  ::y y , y

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  Finally, express “Is 30” with an equal sign and number.
  ::最后,表示“是30”,标志和数字相等。

  $\begin{array}{r}=30\end{array}$

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  The answer is  $\begin{array}{r}3y=30\end{array}$ .
  ::答案是 3 y = 30 。

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were given a problem about Mrs. Hughes and her delicious final exams.
  ::之前,你得到一个问题 关于休斯太太 和她美味的期末考试。

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  Before Mrs. Hughes goes to the grocery store, she has to determine how many dozens of eggs to purchase for her cooking class, which will be baking cakes as final exams. The class has been divided into six groups of four students. Mrs. Hughes is writing a list of items she needs to purchase for the cakes. One of the items is eggs. Each group needs six eggs for its cake, which is 36 eggs together. How can Mrs. Hughes use a single  variable equation  to decide how many dozens of eggs she needs to purchase?
  ::在Hughes夫人去杂货店之前,她必须确定为她的烹饪班购买多少个鸡蛋,这些鸡蛋将作为最后考试的烘烤蛋糕。该班分为六组四名学生。Hughes夫人正在准备一份她需要购买的蛋糕物品清单。其中一个是鸡蛋。每组需要6个鸡蛋来做蛋糕,也就是36个鸡蛋。Hughes夫人如何使用一个变量方程式来决定她需要购买多少个鸡蛋?

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  First, identify the key information.
  ::首先,确定关键信息。

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  • The groups need a combined total of 36 eggs.
    ::这些组共需要36个蛋。
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  • There are 12 eggs in a dozen.
    ::12个鸡蛋在12个中。

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  Next, express the situation in an equation.
  ::接下来,用方程式来表达情况

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  Thirty-six eggs divided by 12 is an unknown number.
  ::36个蛋除以12是未知数字。

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  Then, write the first part of the equation.
  ::然后写出方程的第一部分

  $\begin{array}{r}36÷12\end{array}$

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  Finally, let  $\begin{array}{r}y\end{array}$  represent the unknown dozens of eggs she will need.
  ::最后,让我们代表她需要的 未知的几十个鸡蛋。

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  $\begin{array}{r}y\end{array}$
  ::y y , y

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  Now, write the equation.
  ::现在,写方程式。

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  $\begin{array}{r}36÷12=y\end{array}$
  ::36 = 12 = y

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  The answer is 3.
  ::答案是3

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  Mrs. Hughes needs to purchase three dozen eggs for the class to bake cakes.
  ::休斯太太需要买三打鸡蛋 班上要烤蛋糕

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  Example 2
  ::例2

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  Write a single-variable equation for “six times a number divided by two is equal to four.”
  ::写一个单变量方程式,用于“数字除以2的六倍等于4” 。

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  Work through the problem from the left to the right.
  ::从左到右,通过问题工作。

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  First, note that “Six times” is multiplication.
  ::第一,注意“六倍”是乘法。

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  $\begin{array}{r}6x\end{array}$
  ::6x 6 x

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  Next, let  $\begin{array}{r}y\end{array}$  represent the unknown number.
  ::接下来,让y 代表未知的数字。

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  $\begin{array}{r}y\end{array}$
  ::y y , y

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  Then, express “is divided by 2.”
  ::然后说:你们除以2。

  $$\begin{array}{r}\frac{6y}{2}\end{array}$$

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  Finally, express “is four” with an equal sign and number.
  ::最后,表示“是四”,标志和数字相等。

  $\begin{array}{r}=4\end{array}$

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  The answer is  $\begin{array}{r}\frac{6y}{2}=4\end{array}$ .
  ::答案是 6 y 2 = 4 。

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  Example 3
  ::例3

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  Write a single-variable equation for "fifteen divided by an unknown number is three."
  ::写入一个单变量方程式“15除以未知数字是3” 。

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  To write an equation for this phrase, start by working your way through the problem from the left to the right.
  ::要写出这个词组的方程式, 首先从从左到右, 从您的工作方式从问题从左到右, 开始 。

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  First, identify the first part of the phrase – “Fifteen divided by”
  ::首先,指出“十五除以”一语的第一部分。

  $$\begin{array}{r}\frac{15}{◻}\end{array}$$

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  Next, let  $\begin{array}{r}y\end{array}$  represent the unknown number.
  ::接下来,让y 代表未知的数字。

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  $\begin{array}{r}y\end{array}$
  ::y y , y

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  Then, express “is three” with an equal sign and number.
  ::然后,你应当用一个相同的符号和数字来表示“是三个”。

  $\begin{array}{r}=3\end{array}$

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  The answer is  $\begin{array}{r}\frac{15}{y}=3\end{array}$ .
  ::答案是15y=3

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  Example 4
  ::例4

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  Write a single-variable equation for "six times an unknown number is thirty-six."
  ::写一个单变量方程式 表示"六倍未知数字是36"

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  First, note that “Six times” is multiplication.
  ::第一,注意“六倍”是乘法。

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  $\begin{array}{r}6x\end{array}$
  ::6x 6 x

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  Next, let  $\begin{array}{r}y\end{array}$  represent the unknown number.
  ::接下来,让y 代表未知的数字。

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  $\begin{array}{r}y\end{array}$
  ::y y , y

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  Then, express “is thirty-six” with an equal sign and number.
  ::然后,你应当以一个相等的标志和数字,而说:36。

  $\begin{array}{r}=36\end{array}$

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  The answer is  $\begin{array}{r}6y=36\end{array}$ .
  ::答案是 6 Y = 36 。

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  Example 5
  ::例5

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  Write a single-variable equation for "fifteen and twelve is an unknown number."
  ::写一个单变量方程式“15和12是未知数字”

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

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  15 and 12
  ::15和12

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  Next, identify the  operation  involved.
  ::下一步,确定所涉行动。

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  “and” means  addition
  ::“和”系指添加

  $\begin{array}{r}+\end{array}$

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  Then, let  $\begin{array}{r}y\end{array}$  represent the unknown number.
  ::那么,让我们来代表未知的数字。

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  $\begin{array}{r}y\end{array}$
  ::y y , y

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  Finally, express “is an unknown number” with equal signs and the variable  $\begin{array}{r}y\end{array}$ .
  ::最后,表示“数字未知”,标志和变量y相同。

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  $\begin{array}{r}=y\end{array}$
  ::=y y

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  The answer is  $\begin{array}{r}15+12=y\end{array}$ .
  ::答案是15+12=y。

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  Review
  ::回顾

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  Write each phrase as a single-variable equation. Use the variable x for unknown values.
  ::将每个词组写成单变量方程。 使用变量 x 来表达未知值 。

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  1. Five less than a number is fifteen.
     ::少于一个数字的5比15是15。
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  2. The sum of a number and six is eighteen.
     ::数字和6的总和是18。
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  3. Twenty divided by a number is four.
     ::20除以一个数字是4。
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  4. Sixteen less than a number is four
     ::16个小于一个数字是4个
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  5. Twelve and a number is twenty.
     ::12个,一个数字是20个。
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  6. The product of six and a number is forty-two.
     ::6的产物和数的产物是42个。
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  7. Eight times a number is forty.
     ::数字8乘以40
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  8. Ten less than a number is twenty-one.
     ::十比一个数字少十是21。
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  9. A number divided by two is seven.
     ::数字除以二是七。
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  10. A number times four is forty-eight.
      ::数字乘以四是四十八
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  11. An unknown divided by two is fourteen.
      ::未知的除以二除以14是14。
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  12. Twelve times an unknown number is sixty.
      ::12倍未知数字是60。
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  13. Fourteen divided by an unknown number is seven.
      ::14除以未知数字是7
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  14. Five and a number is equal to fifty - three.
      ::五和一数字等于五比三
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  15. Ten less than a number is seventeen.
      ::十比一个数字少 17是17。